Kaluza–Klein theory

1707:. The full Kaluza field equations are generally attributed to Thiry, who obtained vacuum field equations, although Kaluza originally provided a stress–energy tensor for his theory, and Thiry included a stress–energy tensor in his thesis. But as described by Gonner, several independent groups worked on the field equations in the 1940s and earlier. Thiry is perhaps best known only because an English translation was provided by Applequist, Chodos, & Freund in their review book. Applequist et al. also provided an English translation of Kaluza's article. Translations of the three (1946, 1947, 1948) Jordan articles can be found on the 13635: 3259: 6775: 719:, and an equation for the scalar field. Kaluza also introduced the "cylinder condition" hypothesis, that no component of the five-dimensional metric depends on the fifth dimension. Without this restriction, terms are introduced that involve derivatives of the fields with respect to the fifth coordinate, and this extra degree of freedom makes the mathematics of the fully variable 5D relativity enormously complex. Standard 4D physics seems to manifest this "cylinder condition" and, along with it, simpler mathematics. 2916: 6740: 13890: 12291: 36: 144: 3254:{\displaystyle {\begin{aligned}{\widetilde {R}}_{\mu \nu }-{\frac {1}{2}}{\widetilde {g}}_{\mu \nu }{\widetilde {R}}&=0\Rightarrow \\R_{\mu \nu }-{\frac {1}{2}}g_{\mu \nu }R&={\frac {1}{2}}\phi ^{2}\left(g^{\alpha \beta }F_{\mu \alpha }F_{\nu \beta }-{\frac {1}{4}}g_{\mu \nu }F_{\alpha \beta }F^{\alpha \beta }\right)+{\frac {1}{\phi }}(\nabla _{\mu }\nabla _{\nu }\phi -g_{\mu \nu }\Box \phi ),\end{aligned}}} 4628: 13902: 2223: 4883: 1258: 3568:. In the Kaluza theory, the gravitational constant can be understood as an electromagnetic coupling constant in the metric. There is also a stress–energy tensor for the scalar field. The scalar field behaves like a variable gravitational constant, in terms of modulating the coupling of electromagnetic stress–energy to spacetime curvature. The sign of 4372: 2419: 4056: 1995: 2728:. Note that the scalar field cannot be set to a constant without constraining the electromagnetic field. The earlier treatments by Kaluza and Klein did not have an adequate description of the scalar field and did not realize the implied constraint on the electromagnetic field by assuming the scalar field to be constant. 1445: 750:; Brans and Dicke were apparently unaware of Thiry or Scherrer. The full Kaluza equations under the cylinder condition are quite complex, and most English-language reviews, as well as the English translations of Thiry, contain some errors. The curvature tensors for the complete Kaluza equations were evaluated using 1051: 4670: 5689: 5200:

is particle electric charge. Thus electric charge is understood as motion along the fifth dimension. The fact that the Lorentz force law could be understood as a geodesic in five dimensions was to Kaluza a primary motivation for considering the five-dimensional hypothesis, even in the presence of the

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Without this assumption, the field equations become much more complex, providing many more degrees of freedom that can be identified with various new fields. Paul Wesson and colleagues have pursued relaxation of the cylinder condition to gain extra terms that can be identified with the matter fields,

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article of the same year, gave a more detailed treatment that explicitly invoked the techniques of Schrödinger and de Broglie. It recapitulated much of the classical theory of Kaluza described above, and then departed into Klein's quantum interpretation. Klein solved a Schrödinger-like wave equation

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This is another expression of the "Kaluza miracle". The same hypothesis for the 5D metric that provides electromagnetic stress–energy in the Einstein equations, also provides the Lorentz force law in the equation of motions along with the 4D geodesic equation. Yet correspondence with the Lorentz

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In the 1940s, the classical theory was completed, and the full field equations including the scalar field were obtained by three independent research groups: Thiry, working in France on his dissertation under Lichnerowicz; Jordan, Ludwig, and Müller in Germany, with critical input from Pauli and

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This equation can be recast in several ways, and it has been studied in various forms by authors including Kaluza, Pauli, Gross & Perry, Gegenberg & Kunstatter, and Wesson & Ponce de Leon, but it is instructive to convert it back to the usual 4-dimensional length element

9301:. However, the article does demonstrate that electromagnetism and gravity share the same number of dimensions, and this fact lends support to Kaluza–Klein theory; whether the number of dimensions is really 3 + 1 or in fact 4 + 1 is the subject of further debate. 6645: 6917:

of this bundle metric, one finds that it is constant on each fiber: this is the "Kaluza miracle". One did not have to explicitly impose a cylinder condition, or to compactify: by assumption, the gauge group is already compact. Next, one takes this scalar curvature as the

4623:{\displaystyle {\frac {dU^{\nu }}{d\tau }}+{\widetilde {\Gamma }}_{\alpha \beta }^{\mu }U^{\alpha }U^{\beta }+2{\widetilde {\Gamma }}_{5\alpha }^{\mu }U^{\alpha }U^{5}+{\widetilde {\Gamma }}_{55}^{\mu }(U^{5})^{2}+U^{\mu }{\frac {d}{d\tau }}\ln {\frac {c\,d\tau }{ds}}=0.} 8813: 6376: 2234: 3874: 2551: 3714: 3508: 2872: 2218:{\displaystyle {\widetilde {R}}_{ab}\equiv \partial _{c}{\widetilde {\Gamma }}_{ab}^{c}-\partial _{b}{\widetilde {\Gamma }}_{ca}^{c}+{\widetilde {\Gamma }}_{cd}^{c}{\widetilde {\Gamma }}_{ab}^{d}-{\widetilde {\Gamma }}_{bd}^{c}{\widetilde {\Gamma }}_{ac}^{d}} 6860:. If a distinction is drawn, then it is that Yang–Mills theories occur on a flat spacetime, whereas Kaluza–Klein treats the more general case of curved spacetime. The base space of Kaluza–Klein theory need not be four-dimensional spacetime; it can be any ( 5325: 6381:

Just as the five-dimensional metric comprises the four-dimensional metric framed by the electromagnetic vector potential, the five-dimensional stress–energy tensor comprises the four-dimensional stress–energy tensor framed by the vector 4-current.

1289: 6229: 2633: 8408: 734:. Klein introduced the hypothesis that the fifth dimension was curled up and microscopic, to explain the cylinder condition. Klein suggested that the geometry of the extra fifth dimension could take the form of a circle, with the radius of 4878:{\displaystyle {\widetilde {\Gamma }}_{\alpha \beta }^{\mu }=\Gamma _{\alpha \beta }^{\mu }+{\frac {1}{2}}g^{\mu \nu }k^{2}\phi ^{2}(A_{\alpha }F_{\beta \nu }+A_{\beta }F_{\alpha \nu }-A_{\alpha }A_{\beta }\partial _{\nu }\ln \phi ^{2}).} 891: 6390:

Kaluza's original hypothesis was purely classical and extended discoveries of general relativity. By the time of Klein's contribution, the discoveries of Heisenberg, Schrödinger, and de Broglie were receiving a lot of attention. Klein's

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militates strongly for a fifth dimension irrespective of the cylinder condition. Most authors have therefore employed the cylinder condition in deriving the field equations. Furthermore, vacuum equations are typically assumed for which

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No experimental or observational signs of extra dimensions have been officially reported. Many theoretical search techniques for detecting Kaluza–Klein resonances have been proposed using the mass couplings of such resonances with the

5541: 1458:, and the equations of motion from the five-dimensional geodesic hypothesis. The resulting field equations provide both the equations of general relativity and of electrodynamics; the equations of motion provide the four-dimensional 6851:

U(1). In Kaluza–Klein theory this group suggests that gauge symmetry is the symmetry of circular compact dimensions. Once this geometrical interpretation is understood, it is relatively straightforward to replace U(1) by a general

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on the five-dimensional space. In other words, the cylinder condition of the previous development is dropped, and the stress–energy now comes from the derivatives of the 5D metric with respect to the fifth coordinate. Because the

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had an earlier, similar idea. But in that case, a fifth component was added to the electromagnetic vector potential, representing the Newtonian gravitational potential, and writing the Maxwell equations in five dimensions.

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In his 1921 article, Kaluza established all the elements of the classical five-dimensional theory: the metric, the field equations, the equations of motion, the stress–energy tensor, and the cylinder condition. With no

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It has been an objection to the original Kaluza hypothesis to invoke the fifth dimension only to negate its dynamics. But Thiry argued that the interpretation of the Lorentz force law in terms of a five-dimensional

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is normally understood to be due to concentrations of matter in four-dimensional space, the above result is interpreted as saying that four-dimensional matter is induced from geometry in five-dimensional space.

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moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This extra dimension is a

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should dominate the equation, perhaps in contradiction to experience. This was the main shortfall of the five-dimensional theory as Kaluza saw it, and he gives it some discussion in his original article.

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to 5D, with a metric tensor of 15 components. Ten components are identified with the 4D spacetime metric, four components with the electromagnetic vector potential, and one component with an unidentified

742:. Klein also made a contribution to the classical theory by providing a properly normalized 5D metric. Work continued on the Kaluza field theory during the 1930s by Einstein and colleagues at Princeton. 4366: 3595:

in the metric is fixed by correspondence with 4D theory so that electromagnetic energy densities are positive. It is often assumed that the fifth coordinate is spacelike in its signature in the metric.

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article suggested that the fifth dimension is closed and periodic, and that the identification of electric charge with motion in the fifth dimension can be interpreted as standing waves of wavelength

8099: 8203: 2414:{\displaystyle {\widetilde {\Gamma }}_{bc}^{a}\equiv {\frac {1}{2}}{\widetilde {g}}^{ad}(\partial _{b}{\widetilde {g}}_{dc}+\partial _{c}{\widetilde {g}}_{db}-\partial _{d}{\widetilde {g}}_{bc}).} 8684: 3866: 6240: 2921: 7555: 5429: 4051:{\displaystyle {\widetilde {U}}^{b}{\widetilde {\nabla }}_{b}{\widetilde {U}}^{a}={\frac {d{\widetilde {U}}^{a}}{ds}}+{\widetilde {\Gamma }}_{bc}^{a}{\widetilde {U}}^{b}{\widetilde {U}}^{c}=0.} 7238: 7633: 2453: 1760: 3605: 3390: 2764: 6715: 5956: 6426:

of the atom. The quantization of electric charge could then be nicely understood in terms of integer multiples of fifth-dimensional momentum. Combining the previous Kaluza result for

1984: 7312: 7176: 5237: 3795: 3756: 3379: 1841: 1799: 804: 6958:, to a single quantity: the scalar curvature on the bundle (as a whole), one obtains simultaneously all of the needed field equations, for both the spacetime and the gauge field. 6503: 5728: 1440:{\displaystyle {\widetilde {g}}^{ab}\equiv {\begin{bmatrix}g^{\mu \nu }&-A^{\mu }\\-A^{\nu }&g_{\alpha \beta }A^{\alpha }A^{\beta }+{\frac {1}{\phi ^{2}}}\end{bmatrix}}.} 5475: 885:. Then decompose the 5D metric so that the 4D metric is framed by the electromagnetic vector potential, with the scalar field at the fifth diagonal. This can be visualized as 682:. In their setup, the vacuum has the usual 3 dimensions of space and one dimension of time but with another microscopic extra spatial dimension in the shape of a tiny circle. 3599:

In the presence of matter, the 5D vacuum condition cannot be assumed. Indeed, Kaluza did not assume it. The full field equations require evaluation of the 5D Einstein tensor

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as seen in the recovery of the electromagnetic stress–energy tensor above. The 5D curvature tensors are complex, and most English-language reviews contain errors in either

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in both radiation-dominated (early universe) and matter-dominated (later universe) forms. The general equations can be shown to be sufficiently consistent with classical

6420: 3797:, as does the English translation of Thiry. See Williams for a complete set of 5D curvature tensors under the cylinder condition, evaluated using tensor-algebra software. 2908: 8596: 7708: 6985:. However, an attempt to convert this interesting geometrical construction into a bona-fide model of reality flounders on a number of issues, including the fact that the 6127: 2559: 3593: 1046:{\displaystyle {\widetilde {g}}_{ab}\equiv {\begin{bmatrix}g_{\mu \nu }+\phi ^{2}A_{\mu }A_{\nu }&\phi ^{2}A_{\mu }\\\phi ^{2}A_{\nu }&\phi ^{2}\end{bmatrix}}.} 10357: 9191: 9159: 9112: 8560: 8314: 7945: 7000:

Even in the absence of a completely satisfying theoretical physics framework, the idea of exploring extra, compactified, dimensions is of considerable interest in the

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acts as a coupling constant between the gravitational field and the electromagnetic field. If the base manifold is four-dimensional, the Kaluza–Klein manifold

8856: 8836: 8616: 8273: 8253: 8119: 8014: 7994: 7799: 7735: 6950:) of the gauge connection. On the flip side, the action is stationary against variations of the gauge connection precisely when the gauge connection solves the 6668: 5198: 5178: 3531: 3336: 3282: 1281: 9270:-like boson at the LHC establishes a new empirical test which can be applied to the search for Kaluza–Klein resonances and supersymmetric particles. The loop 5964: 754:

in 2015, verifying results of Ferrari and Coquereaux & Esposito-Farese. The 5D covariant form of the energy–momentum source terms is treated by Williams.

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except in very specific cases: the dimension of the total space must be 2 mod 8, and the G-index of the Dirac operator of the compact space must be nonzero.

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to vary from fiber to fiber. In this case, the coupling between gravity and the electromagnetic field is not constant, but has its own dynamical field, the

5896:{\displaystyle {\widetilde {U}}_{5}={\widetilde {g}}_{5a}{\widetilde {U}}^{a}=\phi ^{2}{\frac {c\,d\tau }{ds}}(kA_{\nu }U^{\nu }+U^{5})={\text{constant}}.} 4176: 13520: 633: 570: 6934:

with respect to variations of either the metric on the base manifold, or of the gauge connection. Variations with respect to the base metric gives the

5059:{\displaystyle {\widetilde {\Gamma }}_{5\alpha }^{\mu }={\frac {1}{2}}g^{\mu \nu }k\phi ^{2}(F_{\alpha \nu }-A_{\alpha }\partial _{\nu }\ln \phi ^{2}).} 1283:

indicates the fifth coordinate by convention, even though the first four coordinates are indexed with 0, 1, 2, and 3. The associated inverse metric is

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is particularly simple under the cylinder condition. Start with the alternate form of the geodesic equation, written for the covariant 5-velocity:

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emerges from the 5D vacuum equations as a source in the 4D equations: field from the vacuum. This relation allows the definitive identification of

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that exist in the Higgs interactions allow any particle with electric charge and mass to run in such a loop. Standard Model particles besides the

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in theoretical physics and is often embedded in more sophisticated theories. It is studied in its own right as an object of geometric interest in

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The Kaluza–Klein theory has a particularly elegant presentation in terms of geometry. In a certain sense, it looks just like ordinary gravity in

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As an approach to the unification of the forces, it is straightforward to apply the Kaluza–Klein theory in an attempt to unify gravity with the

4065: 1684:{\displaystyle ds^{2}\equiv {\widetilde {g}}_{ab}\,dx^{a}\,dx^{b}=g_{\mu \nu }\,dx^{\mu }\,dx^{\nu }+\phi ^{2}(A_{\nu }\,dx^{\nu }+dx^{5})^{2}.} 13664: 12325: 11101: 7084:

However, Klein's approach to a quantum theory is flawed and, for example, leads to a calculated electron mass in the order of magnitude of the

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Lichnerowicz, A.; Thiry, M. Y. (1947). "Problèmes de calcul des variations liés à la dynamique classique et à la théorie unitaire du champ".

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An article from July 2018 gives some hope for this theory; in the article they dispute that gravity is leaking into higher dimensions as in

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decay, but if there are new particles beyond the Standard Model, they could potentially change the ratio of the predicted Standard Model

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Khachatryan, V.; et al. (CMS Collaboration) (2011). "Search for microscopic black hole signatures at the Large Hadron Collider".

6640:{\displaystyle mU^{5}={\frac {cq}{G^{1/2}}}={\frac {h}{\lambda ^{5}}}\quad \Rightarrow \quad \lambda ^{5}\sim {\frac {hG^{1/2}}{cq}},} 13906: 12065: 11811: 10051:

Ferrari, J. A. (1989). "On an approximate solution for a charged object and the experimental evidence for the Kaluza-Klein theory".

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Wesson, P. S.; Ponce de Leon, J. (1995). "The equation of motion in Kaluza–Klein cosmology and its implications for astrophysics".

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causes three of the space dimensions to expand to cosmological size while the remaining dimensions of space remained microscopic.

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and other members of the Space–Time–Matter Consortium. In this version of the theory, it is noted that solutions to the equation

4311: 626: 11078: 7403: 11847: 11801: 11384: 11333: 10892: 357: 8055: 13767: 11985: 11410: 10877: 10792: 10717: 10639: 10617: 10333: 10184: 10155: 9361: 8808:{\displaystyle S({\widehat {g}})=\Lambda \int _{M}\left(R(g)-{\frac {1}{\Lambda ^{2}}}|F|^{2}\right)\operatorname {vol} (g).} 8159: 767:, it merely extends general relativity to five dimensions. One starts by hypothesizing a form of the five-dimensional metric 432: 86: 6371:{\displaystyle {\widetilde {T}}_{M}^{5\mu }=\rho {\frac {dx^{\mu }}{ds}}{\frac {dx^{5}}{ds}}=\rho U^{\mu }{\frac {q}{kmc}}.} 1715:

archives. The first correct English-language Kaluza field equations, including the scalar field, were provided by Williams.

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Pardo, Kris; Fishbach, Maya; Holz, Daniel E.; Spergel, David N. (2018). "Limits on the number of spacetime dimensions from

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is simply one that is invariant under rotations of the circle. Suppose that this metric gives the circle a total length

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gave Kaluza's classical five-dimensional theory a quantum interpretation, to accord with the then-recent discoveries of

694:, who sent his results to Einstein in 1919 and published them in 1921. Kaluza presented a purely classical extension of 68: 13506: 12318: 11722: 11390: 10938: 10921: 10862: 738:. More precisely, the radius of the circular dimension is 23 times the Planck length, which in turn is of the order of 619: 7190: 3709:{\displaystyle {\widetilde {G}}_{ab}\equiv {\widetilde {R}}_{ab}-{\frac {1}{2}}{\widetilde {g}}_{ab}{\widetilde {R}},} 3503:{\displaystyle {\frac {k^{2}}{2}}={\frac {8\pi G}{c^{4}}}{\frac {1}{\mu _{0}}}={\frac {2G}{c^{2}}}4\pi \epsilon _{0},} 13674: 12093: 11727: 11043: 10872: 10625:(Includes reprints of the above articles as well as those of other important papers relating to Kaluza–Klein theory.) 9663:

Thiry, M. Y. (1948). "Sur la régularité des champs gravitationnel et électromagnétique dans les théories unitaires".

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That there always exists such a connection, even for fiber bundles of arbitrarily complex topology, is a result from

7570: 2867:{\displaystyle {\widetilde {R}}_{5\alpha }=0={\frac {1}{2}}g^{\beta \mu }\nabla _{\mu }(\phi ^{3}F_{\alpha \beta }).} 1721: 135: 119: 1450:

This decomposition is quite general, and all terms are dimensionless. Kaluza then applies the machinery of standard

13855: 12690: 10785: 8563: 580: 322: 12047: 9786:"Der Zusammenhang zwischen den Variationsprinzipien der projektiven und der vierdimensionalen Relativitätstheorie" 6750: 12920: 12655: 11760: 10844: 4661: 9916:

Scherrer, W. (1941). "Bemerkungen zu meiner Arbeit: "Ein Ansatz für die Wechselwirkung von Elementarteilchen"".

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force law requires that we identify the component of 5-velocity along the fifth dimension with electric charge:

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with the electromagnetic vector potential. Therefore, the field needs to be rescaled with a conversion constant

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cross-section to the experimentally observed cross-section. Hence a measurement of any dramatic change to the

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to be acceptable on physical principles, while still leaving considerable freedom to also provide interesting

5320:{\displaystyle {\widetilde {\Gamma }}_{55}^{\mu }=-{\frac {1}{2}}g^{\mu \alpha }\partial _{\alpha }\phi ^{2}.} 1941: 13706: 13654: 12862: 12368: 12311: 12294: 12036: 11941: 11871: 11343: 10867: 10742: 9954:

Scherrer, W. (1950). "Über den Einfluss des metrischen Feldes auf ein skalares Materiefeld (2. Mitteilung)".

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Brans, C. H.; Dicke, R. H. (November 1, 1961). "Mach's Principle and a Relativistic Theory of Gravitation".

9205:. The technique of introducing compact dimensions to obtain a higher-dimensional manifold is referred to as 6989:

must be introduced in an artificial way (in nonsupersymmetric models). Nonetheless, KK remains an important

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The equations of motion are obtained from the five-dimensional geodesic hypothesis in terms of a 5-velocity

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using an expansion in terms of fifth-dimensional waves resonating in the closed, compact fifth dimension.

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of the five-dimensional theory were never adequately provided by Kaluza or Klein because they ignored the

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In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of a very small

806:, where Latin indices span five dimensions. Let one also introduce the four-dimensional spacetime metric 93: 12887: 10548: 9469: 7008:

communities. A variety of predictions, with real experimental consequences, can be made (in the case of

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This equation shows the remarkable result, called the "Kaluza miracle", that the precise form for the

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on the base manifold, and a gauge invariant metric on the tangent of each fiber, one can construct a

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Gegenberg, J.; Kunstatter, G. (1984). "The motion of charged particles in Kaluza–Klein space–time".

8127: 8023: 7950: 7744: 6224:{\displaystyle {\widetilde {T}}_{M}^{\mu \nu }=\rho {\frac {dx^{\mu }}{ds}}{\frac {dx^{\nu }}{ds}}.} 2696: 2628:{\displaystyle F_{\alpha \beta }\equiv \partial _{\alpha }A_{\beta }-\partial _{\beta }A_{\alpha },} 809: 13825: 13327: 13247: 13062: 12996: 12358: 12241: 11791: 11551: 11462: 11338: 11219: 11048: 8957: 8624: 6935: 5912: 1844: 746:

Fierz; and Scherrer working alone in Switzerland. Jordan's work led to the scalar–tensor theory of

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Coquereaux, R.; Esposito-Farese, G. (1990). "The theory of Kaluza–Klein–Jordan–Thiry revisited".

8569: 8403:{\displaystyle S({\widehat {g}})=\int _{P}R({\widehat {g}})\operatorname {vol} ({\widehat {g}}).} 7681: 46: 12834: 13943: 13612: 13585: 13232: 12973: 12779: 12670: 12642: 12465: 12196: 12059: 11965: 11923: 11597: 11561: 11170: 11054: 9260: 8667: 7182: 6910: 6884: 6793: 3571: 3534: 747: 532: 522: 467: 457: 242: 194: 19:

This article is about gravitation and electromagnetism. For the mathematical generalization of

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Williams, Lance L. (2012). "Physics of the Electromagnetic Control of Spacetime and Gravity".

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Jordan, P. (1946). "Relativistische Gravitationstheorie mit variabler Gravitationskonstante".

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Scherrer, W. (1949). "Über den Einfluss des metrischen Feldes auf ein skalares Materiefeld".

9239: 9088: 8525:{\displaystyle R({\widehat {g}})=\pi ^{*}\left(R(g)-{\frac {\Lambda ^{2}}{2}}|F|^{2}\right),} 8278: 7715: 7496: 7351: 7009: 6990: 6951: 6857: 4305:

Then the 5D geodesic equation can be written for the spacetime components of the 4-velocity:

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The five-dimensional (5D) theory developed in three steps. The original hypothesis came from

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The vacuum field equations obtained in this way by Thiry and Jordan's group are as follows.

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cross-section predicted by the Standard Model is crucial in probing the physics beyond it.

8838:, one regains the Maxwell equations. Applying the variational principle to the base metric 7899: 7383: 7253: 7001: 6877: 6429: 6074: 5511: 5480: 5333: 5207: 2721: 2430: 868: 659: 512: 407: 272: 267: 262: 224: 10540: 9388:"Über die Möglichkeit, das elektromagnetische Feld und das Gravitationsfeld zu vereinigen" 7996:

that are consistent with both the fiber metric, and the metric on the underlying manifold

731: 8: 13777: 13387: 13272: 12925: 12824: 12450: 12181: 12176: 12166: 11998: 11947: 11765: 11750: 11576: 11507: 11455: 9259:. An analysis of results from the LHC in December 2010 severely constrains theories with 9210: 8675: 7885: 7367: 7078: 6865: 6809: 6454: 12171: 10709: 10672: 10592: 10561: 10535: 10501: 10493: 10436: 10267: 10232: 10208:(translated by George Field ed.). New York: Pergamon Press. pp. Supplement 23. 10064: 9988: 9886: 9851: 9801: 9752: 9700: 9588: 9528: 9482: 9448: 6094: 6061:{\displaystyle {\widetilde {T}}_{M}^{ab}=\rho {\frac {dx^{a}}{ds}}{\frac {dx^{b}}{ds}},} 4150: 1472: 683: 13805: 13575: 13432: 13352: 13252: 13212: 13142: 13092: 13057: 12892: 12769: 12665: 12406: 12246: 12146: 12070: 11928: 11909: 11903: 11854: 11796: 11705: 11623: 11541: 11518: 11486: 11431: 10897: 10854: 10768: 10698: 10684: 10658: 10505: 10479: 10448: 10422: 10339: 10173: 10076: 10016: 9898: 9815: 9766: 9712: 9600: 9574: 9542: 9390:[On the possibility of unifying the gravitational and electromagnetic fields]. 9356: 9220: 9219:

The above development generalizes in a more-or-less straightforward fashion to general

8841: 8821: 8601: 8258: 8238: 8104: 7999: 7979: 7784: 7720: 7668: 7375: 7323: 6919: 6653: 5183: 5163: 3516: 3321: 3267: 1466:, and one finds that electric charge is identified with motion in the fifth dimension. 1455: 1451: 1266: 695: 442: 372: 312: 12819: 10751: 10700:

Five-Dimensional Physics: Classical and Quantum Consequences of Kaluza–Klein Cosmology

10680: 13691: 13397: 13302: 13137: 13047: 13017: 12813: 12708: 12660: 12554: 12256: 12088: 12080: 11681: 11638: 11415: 11323: 11067: 10995: 10713: 10688: 10635: 10613: 10600: 10579: 10509: 10452: 10343: 10329: 10275: 10240: 10202: 10180: 10151: 10080: 9902: 9341: 9316: 8154: 7561: 7096: 6717: cm, and thereby an explanation for the cylinder condition in this small value. 4916: 1463: 1459: 727: 712: 517: 297: 179: 12126: 9819: 9770: 9716: 9604: 4295:{\displaystyle ds^{2}=c^{2}\,d\tau ^{2}+\phi ^{2}(kA_{\nu }\,dx^{\nu }+dx^{5})^{2}.} 13870: 13617: 13602: 13543: 13407: 13342: 13312: 13192: 13132: 13097: 13042: 13032: 12945: 12897: 12855: 12760: 12753: 12746: 12739: 12732: 12650: 12440: 12348: 12161: 12151: 12098: 12075: 11653: 11397: 11091: 10985: 10676: 10630:

Duff, M. J. (1994). "Kaluza–Klein Theory in Perspective". In Lindström, Ulf (ed.).

10596: 10565: 10497: 10444: 10440: 10321: 10271: 10236: 10126: 10068: 10031: 9992: 9890: 9855: 9805: 9756: 9704: 9592: 9546: 9532: 9486: 9162: 7672: 7664: 7660: 7484: 7387: 7355: 7347: 7107: 6931: 6914: 6883:

The construction can be outlined, roughly, as follows. One starts by considering a

6832: 1469:

The hypothesis for the metric implies an invariant five-dimensional length element

838:, where Greek indices span the usual four dimensions of space and time; a 4-vector 704: 667: 595: 507: 462: 13012: 12221: 10760: 10219:

Gross, D. J.; Perry, M. J. (1983). "Magnetic monopoles in Kaluza–Klein theories".

7020:

in the extra compactified dimension(s). If a spatial extra dimension is of radius

13792: 13659: 13487: 13442: 13392: 13377: 13367: 13262: 13227: 13052: 12622: 12396: 12236: 12211: 12136: 12131: 12014: 11975: 11937: 11881: 11755: 11691: 11096: 11017: 10977: 10943: 10735: 10364: 9975: 9366: 9326: 9271: 8050: 7923:

that is the fiber of the U(1)-bundle of electromagnetism. In this discussion, an

7058: 6671: 2877:

It has the form of the vacuum Maxwell equations if the scalar field is constant.

751: 480: 397: 302: 13332: 12019: 10546:

Klein, Oskar (1926). "Quantentheorie und fünfdimensionale Relativitätstheorie".

10403:

L. Castellani et al., Supergravity and superstrings, vol. 2, ch. V.11.

9873:

Ludwig, G.; Müller, C. (1948). "Ein Modell des Kosmos und der Sternentstehung".

9737:"Über die Feldgleichungen der Gravitation bei variabler "Gravitationslonstante"" 9467:

Klein, Oskar (1926). "Quantentheorie und fünfdimensionale Relativitätstheorie".

6774: 13830: 13529: 13462: 13457: 13417: 13357: 13187: 13177: 13172: 13167: 13082: 13077: 13072: 13037: 13022: 12950: 12627: 12490: 12261: 11933: 11917: 11913: 11816: 11786: 11643: 11546: 11296: 10767:

Edward Witten (2014). "A Note On Einstein, Bergmann, and the Fifth Dimension",

9279: 9243: 7854:{\displaystyle \mathrm {d} F=0\quad {\text{and}}\quad \mathrm {d} {\star }F=0.} 7801:. In the absence of charges and currents, the free-field Maxwell equations are 7492: 7346:

The equations governing ordinary gravity in free space can be obtained from an

7127: 7066: 6970: 6947: 6943: 1850:

The classic results of Thiry and other authors presume the cylinder condition:

1700: 764: 691: 204: 199: 165: 13347: 13267: 9596: 7896:

To build the Kaluza–Klein theory, one picks an invariant metric on the circle

13922: 13800: 13759: 13452: 13437: 13412: 13402: 13372: 13317: 13292: 13222: 13217: 13182: 13157: 13117: 12907: 12559: 12475: 12353: 12334: 12251: 12231: 12226: 12141: 12009: 11837: 11781: 11613: 11566: 11233: 10902: 9894: 9859: 9565:

Goenner, H. (2012). "Some remarks on the genesis of scalar–tensor theories".

9346: 9198: 8206: 7738: 7676: 7017: 6906: 6869: 6844: 6118: 679: 492: 425: 327: 307: 13237: 9996: 8946:{\displaystyle R_{ij}-{\frac {1}{2}}g_{ij}R={\frac {1}{\Lambda ^{2}}}T_{ij}} 707:" or the "dilaton". Correspondingly, the 5D Einstein equations yield the 4D 13782: 13713: 13622: 13580: 13570: 13482: 13322: 13202: 13152: 13122: 13107: 12915: 12882: 12774: 12700: 12680: 12617: 12480: 12271: 12191: 12156: 11686: 11648: 11191: 11000: 10131: 10114: 9351: 9298: 7648: 7100: 7013: 7005: 6962: 6840: 6836: 6825: 6234:

The mixed component provides a 4-current source for the Maxwell equations:

2725: 1915:{\displaystyle {\frac {\partial {\widetilde {g}}_{ab}}{\partial x^{5}}}=0.} 1802: 1712: 1708: 1704: 700: 502: 487: 452: 412: 219: 10777: 10741:(A simplified presentation of the search made for extra dimensions at the 10036: 9810: 9785: 9761: 9736: 6824:

In modern geometry, the extra fifth dimension can be understood to be the

5906: 4140:{\displaystyle c^{2}\,d\tau ^{2}\equiv g_{\mu \nu }\,dx^{\mu }\,dx^{\nu }} 13696: 13590: 13558: 13553: 13477: 13447: 13427: 13287: 13242: 13197: 13162: 13112: 12877: 12846: 12607: 12564: 12055: 12024: 11571: 11160: 10607: 10145: 9267: 7099:

data for the signature of effects associated with large extra dimensions/

7085: 6966: 6891: 6848: 6814: 865:

identified with the electromagnetic vector potential; and a scalar field

723: 663: 537: 382: 377: 252: 209: 189: 184: 156: 10325: 8618:

on the fiber bundle is related to the electromagnetic field strength as

7181:

may be re-expressed so that in four dimensions, these solutions satisfy

7016:). For example, on the simplest of principles, one might expect to have 6739: 13422: 13362: 13297: 12960: 12940: 12839: 12798: 12612: 12266: 11832: 11676: 11671: 11374: 10569: 10072: 9708: 9644:

Thiry, M. Y. (1948). "Les équations de la théorie unitaire de Kaluza".

9490: 9242:

and is sometimes taken to be synonymous. If the underlying manifold is

7335: 6423: 1454:

to this metric. The field equations are obtained from five-dimensional

347: 10663: 9077:{\displaystyle T^{ij}=F^{ik}F^{jl}g_{kl}-{\frac {1}{4}}g^{ij}|F|^{2},} 13337: 13127: 13067: 12713: 12587: 12508: 12503: 12498: 11663: 11379: 11361: 11165: 11142: 10577:

Witten, Edward (1981). "Search for a realistic Kaluza–Klein theory".

10115:"Field Equations and Lagrangian of the Kaluza Energy-Momentum Tensor" 9537: 9512: 9321: 9275: 9256: 9228: 8101:

needs to agree with metric on the fiber over a point in the manifold

7371: 6853: 2686:{\displaystyle \Box \equiv g^{\mu \nu }\nabla _{\mu }\nabla _{\nu },} 675: 497: 392: 159:

produced by colliding protons decaying into hadron jets and electrons

24: 5150:{\displaystyle kU^{5}=k{\frac {dx^{5}}{d\tau }}\to {\frac {q}{mc}},} 1926:

for which Kaluza otherwise inserted a stress–energy tensor by hand.

35: 13875: 12983: 12872: 12867: 12597: 12592: 12529: 12445: 12206: 11556: 11436: 11246: 11239: 10484: 10467: 9411:

Subtle is the Lord ...: The Science and the Life of Albert Einstein

9282:

do not make big contributions to the cross-section observed in the

9213: 8671: 7106:

Brandenberger and Vafa have speculated that in the early universe,

6994: 6898: 6873: 5330:

If there is no gradient in the scalar field, the term quadratic in

1931: 600: 447: 387: 317: 257: 20: 10772: 10427: 10381: 9579: 143: 13548: 13498: 12602: 12582: 12539: 12534: 10808: 7266: 7050: 6986: 3800: 647: 12303: 7338:, except that it is phrased in five dimensions instead of four. 7077:

a compactification of the euclidean time dimension leads to the

11886: 10649:

Overduin, J. M.; Wesson, P. S. (1997). "Kaluza–Klein Gravity".

10412: 9246:, the resulting theory is a super-symmetric Yang–Mills theory. 7778: 6817:, and construction of this compact dimension is referred to as 6805: 6505:, Klein obtained an expression for the 0th mode of such waves: 10608:

Appelquist, Thomas; Chodos, Alan; Freund, Peter G. O. (1987).

10146:

Appelquist, Thomas; Chodos, Alan; Freund, Peter G. O. (1987).

2724:. It shows that the electromagnetic field is a source for the 12574: 11447: 11028: 8413:

The scalar curvature, written in components, then expands to

6978: 6974: 1694: 10526:

Kaluza, Theodor (1921). "Zum Unitätsproblem in der Physik".

9439:

Kaluza, Theodor (1921). "Zum Unitätsproblem in der Physik".

11867: 9235: 7711: 7025: 6982: 6828: 4361:{\displaystyle U^{\nu }\equiv {\frac {dx^{\nu }}{d\tau }},} 605: 7465:{\displaystyle S(g)=\int _{M}R(g)\operatorname {vol} (g),} 6930:, can be then obtained by considering where the action is 6926:

for the bundle, as a whole. The equations of motion, the

10093: 10632:

Proceedings of the Symposium 'The Oskar Klein Centenary'

10465: 8094:{\displaystyle \operatorname {Vert} _{p}P\subset T_{p}P} 10736:

Search for Extra Dimensions using Missing Energy at CDF

10541:

https://archive.org/details/sitzungsberichte1921preussi

9238:. In such a case, the theory is often referred to as a 8198:{\displaystyle \operatorname {Hor} _{p}P\subset T_{p}P} 7069:. This set of possible mass values is often called the 5907:

Kaluza's hypothesis for the matter stress–energy tensor

4147:, which is related to the 5-dimensional length element 10528:

Sitzungsber. Preuss. Akad. Wiss. Berlin. (Math. Phys.)

9513:"The Atomicity of Electricity as a Quantum Theory Law" 9441:

Sitzungsber. Preuss. Akad. Wiss. Berlin. (Math. Phys.)

8308:

The Kaluza–Klein action for such a metric is given by

7091:

Examples of experimental pursuits include work by the

6730: 1323: 925: 10648: 9209:. Compactification does not produce group actions on 9179: 9147: 9120: 9100: 8969: 8867: 8844: 8824: 8687: 8627: 8604: 8572: 8541: 8422: 8317: 8281: 8261: 8241: 8215: 8162: 8130: 8107: 8058: 8026: 8002: 7982: 7953: 7933: 7902: 7870: 7810: 7787: 7747: 7723: 7684: 7573: 7508: 7406: 7275: 7193: 7139: 6680: 6656: 6514: 6463: 6432: 6401: 6243: 6130: 6097: 6077: 5967: 5920: 5739: 5700: 5544: 5514: 5483: 5440: 5366: 5357:

vanishes. But otherwise the expression above implies

5336: 5240: 5210: 5186: 5166: 5079: 4928: 4894: 4673: 4639: 4375: 4314: 4179: 4153: 4068: 3877: 3811: 3764: 3725: 3608: 3574: 3543: 3519: 3393: 3344: 3324: 3297: 3270: 2919: 2886: 2767: 2737: 2699: 2640: 2562: 2456: 2433: 2237: 1998: 1944: 1859: 1810: 1768: 1724: 1718:

To obtain the 5D field equations, the 5D connections

1501: 1475: 1292: 1269: 1065: 894: 871: 844: 812: 773: 10318:

Proceedings of 48th AIAA Joint Propulsion Conference

9413:. Oxford: Oxford University Press. pp. 329–330. 3861:{\displaystyle {\widetilde {U}}^{a}\equiv dx^{a}/ds} 10392: 10288: 10253: 7081:and thus to a discretized thermal energy spectrum. 10697: 10380:Ravndal, F., Oskar Klein and the fifth dimension, 10201: 10172: 9838:Jordan, P. (1948). "Fünfdimensionale Kosmologie". 9185: 9153: 9133: 9106: 9076: 8945: 8850: 8830: 8807: 8655: 8610: 8590: 8554: 8524: 8402: 8296: 8267: 8247: 8227: 8197: 8145: 8113: 8093: 8041: 8008: 7988: 7968: 7939: 7915: 7876: 7853: 7793: 7769: 7729: 7702: 7627: 7550:{\displaystyle {\frac {\delta S(g)}{\delta g}}=0,} 7549: 7464: 7306: 7232: 7170: 6792:, and after Kaluza–Klein decomposition one has an 6709: 6662: 6639: 6497: 6445: 6422:, much like the electrons around a nucleus in the 6414: 6385: 6370: 6223: 6106: 6083: 6060: 5950: 5895: 5722: 5683: 5527: 5496: 5469: 5424:{\displaystyle U^{5}\sim c{\frac {q/m}{G^{1/2}}}.} 5423: 5349: 5319: 5223: 5192: 5172: 5149: 5058: 4907: 4877: 4652: 4622: 4360: 4294: 4162: 4139: 4050: 3860: 3789: 3750: 3708: 3587: 3556: 3525: 3502: 3373: 3330: 3310: 3276: 3253: 2902: 2866: 2750: 2712: 2685: 2627: 2545: 2439: 2413: 2217: 1978: 1914: 1835: 1793: 1754: 1683: 1484: 1439: 1275: 1252: 1045: 877: 857: 830: 798: 9617: 8818:Varying the action with respect to the component 7118:One particular variant of Kaluza–Klein theory is 13920: 7233:{\displaystyle G_{\mu \nu }=8\pi T_{\mu \nu }\,} 10634:. Singapore: World Scientific. pp. 22–35. 7628:{\displaystyle R_{ij}-{\frac {1}{2}}g_{ij}R=0,} 1755:{\displaystyle {\widetilde {\Gamma }}_{bc}^{a}} 13665:Mathematical formulation of the Standard Model 11102:Degenerate Higher-Order Scalar-Tensor theories 10472:Journal of Cosmology and Astroparticle Physics 9197:is five-dimensional. The fifth dimension is a 6769: 5730:is a constant of the five-dimensional motion: 5694:This means that under the cylinder condition, 5204:Yet there is a problem: the term quadratic in 3801:Equations of motion from the Kaluza hypothesis 13514: 12319: 11463: 10793: 10175:Space–Time–Matter, Modern Kaluza–Klein Theory 6117:Then the spacetime component gives a typical 5201:aesthetically unpleasing cylinder condition. 627: 9872: 9734: 6913:defined on the entire bundle. Computing the 6721: 10807: 10459: 10406: 7329: 7113: 3384:The relation above shows that we must have 2880:The field equation for the 4D Ricci tensor 13521: 13507: 12326: 12312: 11470: 11456: 10800: 10786: 10218: 9972: 7316:Friedmann–Lemaître–Robertson–Walker metric 6969:forces by using the symmetry group of the 5911:Kaluza proposed a five-dimensional matter 1695:Field equations from the Kaluza hypothesis 634: 620: 142: 10662: 10483: 10426: 10130: 10035: 9809: 9760: 9578: 9536: 9385: 7229: 6856:. Such generalizations are often called 6710:{\displaystyle \lambda ^{5}\sim 10^{-30}} 5951:{\displaystyle {\widetilde {T}}_{M}^{ab}} 5822: 4596: 4249: 4206: 4123: 4109: 4079: 1638: 1598: 1584: 1554: 1540: 678:and considered an important precursor to 120:Learn how and when to remove this message 10315: 10112: 10014: 9953: 9934: 9915: 7891: 6773: 1979:{\displaystyle {\widetilde {R}}_{ab}=0,} 11406:Gravitational interaction of antimatter 10358:Gauge Theory and Variational Principles 10050: 9833: 9831: 9829: 9730: 9728: 9726: 9682: 9680: 9678: 9564: 8678:and integrating on the fiber, one gets 7307:{\displaystyle {\widetilde {R}}_{ab}=0} 7171:{\displaystyle {\widetilde {R}}_{ab}=0} 6954:. Thus, by applying a single idea: the 13921: 10695: 10576: 10525: 10170: 10010: 10008: 10006: 9837: 9783: 9686: 9639: 9637: 9635: 9633: 9438: 358:de Sitter invariant special relativity 338:N = 4 supersymmetric Yang–Mills theory 56:Please improve this article by adding 13502: 12307: 11451: 11411:Physics in the medieval Islamic world 11334:(2+1)-dimensional topological gravity 10830:Newton's law of universal gravitation 10781: 10545: 10199: 9662: 9643: 9560: 9558: 9556: 9510: 9466: 9434: 9432: 9430: 9428: 9426: 9424: 9422: 9420: 9362:Non-relativistic gravitational fields 7341: 7095:collaboration, which has re-analyzed 6788:is compactified over the compact set 6091:is a density, and the length element 3790:{\displaystyle {\widetilde {R}}_{ab}} 3751:{\displaystyle {\widetilde {G}}_{ab}} 3374:{\displaystyle A^{\mu }\to kA^{\mu }} 1836:{\displaystyle {\widetilde {R}}_{ab}} 1794:{\displaystyle {\widetilde {g}}_{ab}} 799:{\displaystyle {\widetilde {g}}_{ab}} 13901: 12724:Bogomol'nyi–Prasad–Sommerfield bound 11156:Asymptotic safety in quantum gravity 10629: 10612:. Menlo Park, Cal.: Addison–Wesley. 10150:. Menlo Park, Cal.: Addison–Wesley. 10106: 10096:Annales de l'Institut Henri Poincaré 9826: 9723: 9675: 9506: 9504: 9502: 9500: 9462: 9460: 9458: 9408: 7654: 6734: 6498:{\displaystyle p^{5}=h/\lambda ^{5}} 5723:{\displaystyle {\widetilde {U}}_{5}} 3289:electromagnetic stress–energy tensor 757: 288:6D (2,0) superconformal field theory 29: 12042:Tolman–Oppenheimer–Volkoff equation 11995:Friedmann–Lemaître–Robertson–Walker 10087: 10044: 10003: 9630: 9173:In the above, the size of the loop 6835:can essentially be formulated as a 6731:Quantum field theory interpretation 6453:in terms of electric charge, and a 293:Noncommutative quantum field theory 155:particle detector data depicting a 13: 13528: 10908:Gibbons–Hawking–York boundary term 10727: 9567:General Relativity and Gravitation 9553: 9417: 9379: 9249: 9180: 9168: 9148: 9101: 8919: 8858:, one gets the Einstein equations 8751: 8712: 8480: 8016:. The consistency conditions are: 7934: 7833: 7812: 7749: 7386:on this manifold, one defines the 5662: 5635: 5295: 5245: 5025: 4933: 4844: 4705: 4678: 4513: 4463: 4410: 3981: 3901: 3207: 3197: 2823: 2701: 2671: 2661: 2603: 2580: 2374: 2339: 2304: 2242: 2192: 2165: 2135: 2108: 2078: 2065: 2038: 2025: 1890: 1863: 1762:are calculated from the 5D metric 1729: 14: 13960: 13949:Physics beyond the Standard Model 12333: 11812:Hamilton–Jacobi–Einstein equation 11023:Modified Newtonian dynamics, MOND 10939:Classical theories of gravitation 10745:(CDF) particle physics facility.) 9497: 9455: 9312:Classical theories of gravitation 8235:must be isomorphic to the metric 7028:of such standing waves would be 6922:, and, from this, constructs the 5470:{\displaystyle U^{5}>10^{20}c} 4664:plus some electromagnetic terms: 3284:is the standard 4D Ricci scalar. 13900: 13889: 13888: 13633: 12290: 12289: 10119:Advances in Mathematical Physics 6738: 323:Mathematical universe hypothesis 34: 12921:Eleven-dimensional supergravity 10845:History of gravitational theory 10761:Lectures on Kaluza–Klein Theory 10704:. Singapore: World Scientific. 10397: 10386: 10374: 10350: 10309: 10282: 10247: 10212: 10193: 10179:. Singapore: World Scientific. 10164: 10139: 9966: 9947: 9928: 9909: 9866: 9777: 9735:Jordan, P.; Müller, C. (1947). 9094:The original theory identifies 8566:of the fiber bundle projection 7831: 7825: 6938:on the base manifold, with the 6585: 6581: 6386:Quantum interpretation of Klein 1214: 1140: 13816:Causal dynamical triangulation 11619:Mass–energy equivalence (E=mc) 11477: 11151:Causal dynamical triangulation 10840:Poisson's equation for gravity 10752:SUPERSTRINGS! Extra Dimensions 10445:10.1016/j.physletb.2011.02.032 10367:" (1982) D. Reidel Publishing 9656: 9611: 9402: 9061: 9052: 8799: 8793: 8772: 8763: 8739: 8733: 8706: 8691: 8582: 8504: 8495: 8471: 8465: 8441: 8426: 8394: 8379: 8370: 8355: 8336: 8321: 8291: 8285: 8146:{\displaystyle {\widehat {g}}} 8042:{\displaystyle {\widehat {g}}} 7969:{\displaystyle {\widehat {g}}} 7770:{\displaystyle \Omega ^{2}(M)} 7764: 7758: 7694: 7524: 7518: 7456: 7450: 7441: 7435: 7416: 7410: 6582: 5879: 5840: 5126: 5050: 4995: 4869: 4768: 4547: 4533: 4280: 4233: 3355: 3241: 3193: 3003: 2858: 2832: 2713:{\displaystyle \nabla _{\mu }} 2482: 2405: 2300: 1669: 1625: 831:{\displaystyle {g}_{\mu \nu }} 528:Causal dynamical triangulation 1: 13655:Spontaneous symmetry breaking 12369:Second superstring revolution 10743:Collider Detector at Fermilab 10681:10.1016/S0370-1573(96)00046-4 10519: 10502:10.1088/1475-7516/2018/07/048 9665:Compt. Rend. Acad. Sci. Paris 9646:Compt. Rend. Acad. Sci. Paris 9620:Compt. Rend. Acad. Sci. Paris 8656:{\displaystyle \pi ^{*}F=dA.} 7947:. One then considers metrics 7243:with the precise form of the 1056:One can write more precisely 215:Cosmological constant problem 58:secondary or tertiary sources 12863:Generalized complex manifold 12364:First superstring revolution 10610:Modern Kaluza–Klein Theories 10601:10.1016/0550-3213(81)90021-3 10276:10.1016/0375-9601(84)90980-0 10241:10.1016/0550-3213(83)90462-5 10148:Modern Kaluza–Klein Theories 7667:can be understood to be the 7370:, which may be taken as the 7314:can be shown to contain the 7075:Thermal quantum field theory 6415:{\displaystyle \lambda ^{5}} 2903:{\displaystyle R_{\mu \nu }} 248:Cosmic censorship hypothesis 7: 11634:Relativistic Doppler effect 11013:Infinite derivative gravity 9304: 8591:{\displaystyle \pi :P\to M} 7703:{\displaystyle \pi :P\to M} 7320:tests of general relativity 6770:Group theory interpretation 5508:The equation of motion for 670:built around the idea of a 10: 13965: 12461:Non-critical string theory 12105:In computational physics: 11629:Relativity of simultaneity 11201:Unified-field-theoric and 10291:Astronomy and Astrophysics 9386:Nordström, Gunnar (1914). 9332:Compactification (physics) 7560:one obtains precisely the 5434:For elementary particles, 3566:permeability of free space 1843:is calculated from the 5D 18: 13884: 13843: 13821:Canonical quantum gravity 13791: 13758: 13727: 13684: 13673: 13642: 13631: 13536: 13005: 12982: 12959: 12906: 12791: 12699: 12641: 12573: 12522: 12489: 12384: 12341: 12287: 12119: 11984: 11956: 11942:Lense–Thirring precession 11825: 11774: 11736: 11715: 11704: 11662: 11606: 11590: 11532: 11524:Doubly special relativity 11496: 11485: 11424: 11356: 11344:Jackiw–Teitelboim gravity 11314: 11200: 11179: 11123:Canonical quantum gravity 11118:Euclidean quantum gravity 11110: 10957: 10931: 10920: 10853: 10822: 10815: 9597:10.1007/s10714-012-1378-8 9392:Physikalische Zeitschrift 7126:, chiefly promulgated by 6956:principle of least action 3588:{\displaystyle \phi ^{2}} 543:Canonical quantum gravity 368:Black hole thermodynamics 353:Doubly special relativity 136:Beyond the Standard Model 13826:Superfluid vacuum theory 12997:Introduction to M-theory 12691:Wess–Zumino–Witten model 12633:Hanany–Witten transition 12359:History of string theory 11802:Post-Newtonian formalism 11792:Einstein field equations 11728:Mathematical formulation 11552:Hyperbolic orthogonality 11220:Superfluid vacuum theory 11044:Nonsymmetric gravitation 10893:Post-Newtonian formalism 10696:Wesson, Paul S. (2006). 10549:Zeitschrift für Physik A 10200:Pauli, Wolfgang (1958). 10171:Wesson, Paul S. (1999). 10113:Williams, L. L. (2020). 10015:Williams, L. L. (2015). 9895:10.1002/andp.19484370106 9860:10.1002/asna.19482760502 9470:Zeitschrift für Physik A 9373: 9186:{\displaystyle \Lambda } 9154:{\displaystyle \Lambda } 9107:{\displaystyle \Lambda } 8555:{\displaystyle \pi ^{*}} 7940:{\displaystyle \Lambda } 7330:Geometric interpretation 7120:space–time–matter theory 7114:Space–time–matter theory 6936:Einstein field equations 6928:Euler–Lagrange equations 5477:. The term quadratic in 4908:{\displaystyle U^{\nu }} 4653:{\displaystyle U^{\nu }} 3557:{\displaystyle \mu _{0}} 3311:{\displaystyle A^{\mu }} 2751:{\displaystyle A^{\nu }} 858:{\displaystyle A^{\mu }} 709:Einstein field equations 674:beyond the common 4D of 553:Superfluid vacuum theory 403:Gauge gravitation theory 13608:Quantum electrodynamics 13598:Electroweak interaction 12676:Vertex operator algebra 12376:String theory landscape 11513:Galilean transformation 11504:Principle of relativity 11385:Mechanical explanations 11254:Heterotic string theory 11210:Noncommutative geometry 11129:Wheeler–DeWitt equation 10855:General relativity (GR) 10835:Gauss's law for gravity 10809:Theories of gravitation 10733:The CDF Collaboration, 10303:1995A&A...294....1W 9997:10.1103/PhysRev.124.925 8297:{\displaystyle \pi (P)} 6924:Einstein–Hilbert action 2731:The field equation for 2427:The field equation for 752:tensor-algebra software 13586:Quantum chromodynamics 12974:AdS/CFT correspondence 12729:Exceptional Lie groups 12671:Superconformal algebra 12643:Conformal field theory 12514:Montonen–Olive duality 12466:Non-linear sigma model 11598:Lorentz transformation 11226:Logarithmic BEC vacuum 11171:Rainbow gravity theory 11049:Scalar–tensor theories 10823:Newtonian gravity (NG) 9443:(in German): 966–972. 9409:Pais, Abraham (1982). 9261:large extra dimensions 9187: 9155: 9135: 9134:{\displaystyle g_{55}} 9114:with the fiber metric 9108: 9078: 8947: 8852: 8832: 8809: 8657: 8612: 8592: 8556: 8526: 8404: 8298: 8269: 8249: 8229: 8228:{\displaystyle p\in P} 8199: 8147: 8115: 8095: 8043: 8010: 7990: 7970: 7941: 7917: 7878: 7877:{\displaystyle \star } 7855: 7795: 7771: 7731: 7704: 7629: 7551: 7466: 7308: 7259:energy–momentum tensor 7234: 7172: 7010:large extra dimensions 6940:energy–momentum tensor 6885:principal fiber bundle 6801: 6794:effective field theory 6747:This section is empty. 6723:Zeitschrift für Physik 6722: 6711: 6664: 6641: 6499: 6447: 6416: 6372: 6225: 6121:stress–energy tensor: 6108: 6085: 6062: 5952: 5897: 5724: 5685: 5529: 5498: 5471: 5425: 5351: 5321: 5225: 5194: 5180:is particle mass, and 5174: 5151: 5060: 4909: 4879: 4654: 4633:The term quadratic in 4624: 4362: 4296: 4164: 4141: 4052: 3862: 3791: 3752: 3710: 3589: 3558: 3535:gravitational constant 3527: 3504: 3375: 3332: 3312: 3278: 3255: 2904: 2868: 2752: 2714: 2687: 2629: 2547: 2441: 2415: 2219: 1980: 1916: 1837: 1795: 1756: 1685: 1486: 1441: 1277: 1254: 1047: 879: 859: 832: 800: 703:sometimes called the " 533:Causal fermion systems 523:Loop quantum cosmology 468:Large extra dimensions 458:Supersymmetry breaking 363:Causal fermion systems 45:relies excessively on 13702:Cosmological constant 12969:Holographic principle 12936:Type IIB supergravity 12931:Type IIA supergravity 12783:-form electrodynamics 12402:Bosonic string theory 12066:Weyl−Lewis−Papapetrou 11807:Raychaudhuri equation 11746:Equivalence principle 11303:Twistor string theory 11282:Type II string theory 11275:Bosonic string theory 11215:Semiclassical gravity 11180:Unified-field-theoric 10965:Poincaré gauge theory 9811:10.1515/zna-1947-0103 9762:10.1515/zna-1947-0102 9511:Klein, Oskar (1926). 9337:Randall–Sundrum model 9266:The observation of a 9188: 9156: 9136: 9109: 9089:Maxwell stress tensor 9087:sometimes called the 9079: 8948: 8853: 8833: 8810: 8658: 8613: 8593: 8557: 8527: 8405: 8299: 8270: 8250: 8230: 8200: 8148: 8116: 8096: 8044: 8011: 7991: 7971: 7942: 7918: 7916:{\displaystyle S^{1}} 7892:Kaluza–Klein geometry 7879: 7856: 7796: 7772: 7732: 7716:electromagnetic field 7705: 7673:principal U(1)-bundle 7630: 7552: 7497:variational principle 7467: 7352:variational principle 7309: 7235: 7173: 7124:induced matter theory 7079:Matsubara frequencies 6905:on the bundle, and a 6777: 6712: 6665: 6642: 6500: 6448: 6446:{\displaystyle U^{5}} 6417: 6373: 6226: 6114:is as defined above. 6109: 6086: 6084:{\displaystyle \rho } 6063: 5953: 5898: 5725: 5686: 5530: 5528:{\displaystyle U^{5}} 5499: 5497:{\displaystyle U^{5}} 5472: 5426: 5352: 5350:{\displaystyle U^{5}} 5322: 5226: 5224:{\displaystyle U^{5}} 5195: 5175: 5152: 5061: 4910: 4880: 4655: 4625: 4363: 4297: 4165: 4142: 4053: 3863: 3792: 3753: 3711: 3590: 3559: 3528: 3505: 3376: 3333: 3313: 3279: 3256: 2905: 2869: 2753: 2715: 2688: 2630: 2548: 2442: 2440:{\displaystyle \phi } 2416: 2220: 1981: 1917: 1838: 1796: 1757: 1686: 1487: 1442: 1278: 1255: 1048: 880: 878:{\displaystyle \phi } 860: 833: 801: 717:electromagnetic field 548:Semiclassical gravity 343:Twistor string theory 333:Randall–Sundrum model 150:Large Hadron Collider 69:"Kaluza–Klein theory" 13811:Loop quantum gravity 13750:Theory of everything 13745:Grand Unified Theory 13719:Neutrino oscillation 13566:Quantum field theory 12888:Hořava–Witten theory 12835:Hyperkähler manifold 12523:Particles and fields 12471:Tachyon condensation 12456:Matrix string theory 12107:Numerical relativity 11948:pulsar timing arrays 11370:Aristotelian physics 11339:Gauss–Bonnet gravity 11289:Little string theory 11268:Type 0 string theory 11261:Type I string theory 11136:Loop quantum gravity 11063:Scalar–tensor–vector 11036:Tensor–vector–scalar 10991:Gauge theory gravity 10949:Theory of everything 10204:Theory of Relativity 10132:10.1155/2020/1263723 10053:Gen. Relativ. Gravit 9234:taking the place of 9177: 9145: 9118: 9098: 8967: 8958:stress–energy tensor 8865: 8842: 8822: 8685: 8625: 8602: 8570: 8539: 8420: 8315: 8279: 8259: 8239: 8213: 8160: 8128: 8105: 8056: 8024: 8000: 7980: 7951: 7931: 7900: 7868: 7808: 7785: 7745: 7721: 7682: 7571: 7506: 7404: 7273: 7254:Ricci-flat condition 7191: 7183:Einstein's equations 7137: 7002:experimental physics 6952:Yang–Mills equations 6878:noncommutative space 6678: 6654: 6512: 6461: 6430: 6399: 6241: 6128: 6095: 6075: 5965: 5918: 5737: 5698: 5542: 5512: 5481: 5438: 5364: 5334: 5238: 5208: 5184: 5164: 5077: 4926: 4892: 4671: 4637: 4373: 4312: 4177: 4151: 4066: 3875: 3809: 3762: 3723: 3606: 3572: 3541: 3517: 3391: 3342: 3322: 3295: 3268: 2917: 2884: 2765: 2735: 2722:covariant derivative 2697: 2638: 2560: 2454: 2431: 2235: 1996: 1942: 1857: 1808: 1766: 1722: 1499: 1473: 1290: 1267: 1063: 892: 869: 842: 810: 771: 660:unified field theory 513:Loop quantum gravity 408:Gauge theory gravity 273:Grand Unified Theory 268:Unified field theory 263:Theory of everything 225:Neutrino oscillation 16:Unified field theory 13929:Theories of gravity 13778:Split supersymmetry 13740:Kaluza–Klein theory 13613:Fermi's interaction 12926:Type I supergravity 12830:Calabi–Yau manifold 12825:Ricci-flat manifold 12804:Kaluza–Klein theory 12545:Ramond–Ramond field 12451:String field theory 11999:Friedmann equations 11893:Hulse–Taylor binary 11855:Gravitational waves 11751:Riemannian geometry 11577:Proper acceleration 11562:Maxwell's equations 11508:Galilean relativity 11187:Kaluza–Klein theory 10710:2006fdpc.book.....W 10673:1997PhR...283..303O 10593:1981NuPhB.186..412W 10562:1926ZPhy...37..895K 10536:1921SPAW.......966K 10494:2018JCAP...07..048P 10437:2011PhLB..697..434C 10326:10.2514/6.2012-3916 10268:1984PhLA..106..410G 10233:1983NuPhB.226...29G 10065:1989GReGr..21..683F 10037:10.1155/2015/901870 9989:1961PhRv..124..925B 9887:1948AnP...437...76L 9852:1948AN....276..193J 9802:1947ZNatA...2....3L 9784:Ludwig, G. (1947). 9753:1947ZNatA...2....1J 9701:1946NW.....33..250J 9689:Naturwissenschaften 9589:2012GReGr..44.2077G 9529:1926Natur.118..516K 9483:1926ZPhy...37..895K 9449:1921SPAW.......966K 9227:for some arbitrary 8155:horizontal subspace 7886:Hodge star operator 7368:Riemannian manifold 7324:cosmological models 7265:In particular, the 7252:following from the 6866:Riemannian manifold 6858:Yang–Mills theories 6674:. Klein found that 6455:de Broglie relation 6270: 6157: 5994: 5947: 5264: 4955: 4888:The term linear in 4721: 4700: 4532: 4485: 4432: 4003: 2264: 2214: 2187: 2157: 2130: 2100: 2060: 1751: 652:Kaluza–Klein theory 283:Kaluza–Klein theory 13939:Physical cosmology 13806:Superstring theory 13576:Strong interaction 12893:K-theory (physics) 12770:ADE classification 12407:Superstring theory 12048:Reissner–Nordström 11966:Brans–Dicke theory 11797:Linearized gravity 11624:Length contraction 11542:Frame of reference 11519:Special relativity 11432:Gravitational wave 11315:Generalisations / 11203:quantum-mechanical 11111:Quantum-mechanical 10924:general relativity 10898:Linearized gravity 10570:10.1007/BF01397481 10363:2021-07-09 at the 10073:10.1007/BF00759078 10024:Journal of Gravity 9875:Annalen der Physik 9709:10.1007/BF01204481 9491:10.1007/BF01397481 9357:Superstring theory 9201:and is called the 9183: 9151: 9131: 9104: 9074: 8943: 8848: 8828: 8805: 8670:and specifically, 8653: 8608: 8588: 8552: 8522: 8400: 8294: 8265: 8245: 8225: 8195: 8143: 8124:The projection of 8111: 8091: 8039: 8020:The projection of 8006: 7986: 7966: 7937: 7913: 7874: 7851: 7791: 7777:of differentiable 7767: 7727: 7700: 7625: 7562:Einstein equations 7547: 7495:. By applying the 7462: 7376:general relativity 7350:, by applying the 7342:Einstein equations 7304: 7230: 7168: 7071:Kaluza–Klein tower 6920:Lagrangian density 6802: 6707: 6660: 6637: 6495: 6443: 6412: 6368: 6244: 6221: 6131: 6107:{\displaystyle ds} 6104: 6081: 6058: 5968: 5948: 5921: 5893: 5720: 5681: 5525: 5494: 5467: 5421: 5347: 5317: 5241: 5221: 5190: 5170: 5147: 5056: 4929: 4905: 4875: 4704: 4674: 4650: 4620: 4509: 4459: 4406: 4358: 4292: 4163:{\displaystyle ds} 4160: 4137: 4048: 3977: 3858: 3787: 3748: 3706: 3585: 3554: 3523: 3500: 3371: 3328: 3308: 3274: 3251: 3249: 2900: 2864: 2748: 2720:is a standard, 4D 2710: 2683: 2625: 2543: 2437: 2411: 2238: 2215: 2188: 2161: 2131: 2104: 2074: 2034: 1976: 1912: 1833: 1791: 1752: 1725: 1681: 1485:{\displaystyle ds} 1482: 1456:Einstein equations 1452:general relativity 1437: 1428: 1273: 1250: 1043: 1034: 875: 855: 828: 796: 696:general relativity 443:Superstring theory 373:Unparticle physics 313:Superstring theory 243:Brans–Dicke theory 13916: 13915: 13839: 13838: 13714:Strong CP problem 13692:Hierarchy problem 13496: 13495: 13278:van Nieuwenhuizen 12814:Why 10 dimensions 12719:Chern–Simons form 12686:Kac–Moody algebra 12666:Conformal algebra 12661:Conformal anomaly 12555:Magnetic monopole 12550:Kalb–Ramond field 12392:Nambu–Goto action 12301: 12300: 12115: 12114: 12094:Ozsváth–Schücking 11700: 11699: 11682:Minkowski diagram 11639:Thomas precession 11582:Relativistic mass 11445: 11444: 11416:Theory of impetus 11352: 11351: 11324:Liouville gravity 11068:Conformal gravity 10996:Composite gravity 10986:Bimetric theories 10916: 10915: 10719:978-981-256-661-4 10641:978-981-02-2332-8 10619:978-0-201-09829-7 10580:Nuclear Physics B 10415:Physics Letters B 10356:David Bleecker, " 10335:978-1-60086-935-8 10186:978-981-02-3588-8 10157:978-0-201-09829-7 9317:Complex spacetime 9240:Yang–Mills theory 9203:compact dimension 9036: 8928: 8892: 8851:{\displaystyle g} 8831:{\displaystyle A} 8760: 8703: 8611:{\displaystyle A} 8598:. The connection 8492: 8438: 8391: 8367: 8333: 8268:{\displaystyle M} 8248:{\displaystyle g} 8140: 8114:{\displaystyle M} 8051:vertical subspace 8036: 8009:{\displaystyle M} 7989:{\displaystyle P} 7963: 7829: 7794:{\displaystyle M} 7730:{\displaystyle F} 7661:Maxwell equations 7659:By contrast, the 7655:Maxwell equations 7598: 7536: 7286: 7150: 7097:particle collider 7073:. Similarly, in 7024:, the invariant 6767: 6766: 6663:{\displaystyle h} 6632: 6579: 6559: 6363: 6329: 6302: 6254: 6216: 6189: 6141: 6053: 6026: 5978: 5931: 5888: 5838: 5794: 5772: 5750: 5711: 5676: 5648: 5623: 5604: 5592: 5579: 5561: 5416: 5279: 5251: 5193:{\displaystyle q} 5173:{\displaystyle m} 5142: 5124: 4967: 4939: 4917:Lorentz force law 4733: 4684: 4662:geodesic equation 4612: 4582: 4519: 4469: 4416: 4401: 4353: 4033: 4014: 3987: 3972: 3954: 3926: 3907: 3888: 3822: 3775: 3736: 3700: 3679: 3667: 3644: 3619: 3526:{\displaystyle G} 3479: 3454: 3437: 3409: 3331:{\displaystyle k} 3277:{\displaystyle R} 3191: 3134: 3067: 3034: 2990: 2969: 2957: 2934: 2910:is obtained from 2807: 2778: 2758:is obtained from 2502: 2467: 2447:is obtained from 2393: 2358: 2323: 2288: 2276: 2248: 2198: 2171: 2141: 2114: 2084: 2044: 2009: 1955: 1904: 1876: 1821: 1779: 1735: 1528: 1464:Lorentz force law 1460:geodesic equation 1424: 1303: 1276:{\displaystyle 5} 1225: 1176: 1151: 1076: 905: 784: 758:Kaluza hypothesis 713:Maxwell equations 658:) is a classical 644: 643: 518:Quantum cosmology 298:Quantum cosmology 220:Strong CP problem 180:Hierarchy problem 130: 129: 122: 104: 13956: 13934:Particle physics 13904: 13903: 13892: 13891: 13682: 13681: 13637: 13636: 13618:Weak hypercharge 13603:Weak interaction 13544:Particle physics 13523: 13516: 13509: 13500: 13499: 13006:String theorists 12946:Lie superalgebra 12898:Twisted K-theory 12856:Spin(7)-manifold 12809:Compactification 12651:Virasoro algebra 12434:Heterotic string 12328: 12321: 12314: 12305: 12304: 12293: 12292: 12076:van Stockum dust 11848:Two-body problem 11766:Mach's principle 11713: 11712: 11654:Terrell rotation 11494: 11493: 11472: 11465: 11458: 11449: 11448: 11400: 11398:Entropic gravity 11393: 11317:extensions of GR 11305: 11291: 11284: 11277: 11270: 11263: 11256: 11249: 11242: 11228: 11145: 11138: 11131: 11092:Geometrodynamics 11081: 11057: 11038: 11031: 10980: 10973: 10929: 10928: 10820: 10819: 10802: 10795: 10788: 10779: 10778: 10749:John M. Pierre, 10723: 10703: 10692: 10666: 10645: 10623: 10604: 10573: 10539: 10514: 10513: 10487: 10463: 10457: 10456: 10430: 10410: 10404: 10401: 10395: 10390: 10384: 10378: 10372: 10354: 10348: 10347: 10313: 10307: 10306: 10286: 10280: 10279: 10251: 10245: 10244: 10216: 10210: 10209: 10207: 10197: 10191: 10190: 10178: 10168: 10162: 10161: 10143: 10137: 10136: 10134: 10110: 10104: 10103: 10091: 10085: 10084: 10048: 10042: 10041: 10039: 10021: 10012: 10001: 10000: 9970: 9964: 9963: 9956:Helv. Phys. Acta 9951: 9945: 9944: 9937:Helv. Phys. Acta 9932: 9926: 9925: 9918:Helv. Phys. Acta 9913: 9907: 9906: 9870: 9864: 9863: 9846:(5–6): 193–208. 9835: 9824: 9823: 9813: 9781: 9775: 9774: 9764: 9732: 9721: 9720: 9684: 9673: 9672: 9660: 9654: 9653: 9641: 9628: 9627: 9615: 9609: 9608: 9582: 9573:(8): 2077–2097. 9562: 9551: 9550: 9540: 9538:10.1038/118516a0 9508: 9495: 9494: 9464: 9453: 9452: 9436: 9415: 9414: 9406: 9400: 9399: 9383: 9293: 9289: 9285: 9272:Feynman diagrams 9207:compactification 9192: 9190: 9189: 9184: 9160: 9158: 9157: 9152: 9140: 9138: 9137: 9132: 9130: 9129: 9113: 9111: 9110: 9105: 9083: 9081: 9080: 9075: 9070: 9069: 9064: 9055: 9050: 9049: 9037: 9029: 9024: 9023: 9011: 9010: 8998: 8997: 8982: 8981: 8952: 8950: 8949: 8944: 8942: 8941: 8929: 8927: 8926: 8914: 8906: 8905: 8893: 8885: 8880: 8879: 8857: 8855: 8854: 8849: 8837: 8835: 8834: 8829: 8814: 8812: 8811: 8806: 8786: 8782: 8781: 8780: 8775: 8766: 8761: 8759: 8758: 8746: 8724: 8723: 8705: 8704: 8696: 8676:Fubini's theorem 8662: 8660: 8659: 8654: 8637: 8636: 8617: 8615: 8614: 8609: 8597: 8595: 8594: 8589: 8561: 8559: 8558: 8553: 8551: 8550: 8531: 8529: 8528: 8523: 8518: 8514: 8513: 8512: 8507: 8498: 8493: 8488: 8487: 8478: 8456: 8455: 8440: 8439: 8431: 8409: 8407: 8406: 8401: 8393: 8392: 8384: 8369: 8368: 8360: 8351: 8350: 8335: 8334: 8326: 8303: 8301: 8300: 8295: 8274: 8272: 8271: 8266: 8254: 8252: 8251: 8246: 8234: 8232: 8231: 8226: 8204: 8202: 8201: 8196: 8191: 8190: 8172: 8171: 8152: 8150: 8149: 8144: 8142: 8141: 8133: 8120: 8118: 8117: 8112: 8100: 8098: 8097: 8092: 8087: 8086: 8068: 8067: 8048: 8046: 8045: 8040: 8038: 8037: 8029: 8015: 8013: 8012: 8007: 7995: 7993: 7992: 7987: 7975: 7973: 7972: 7967: 7965: 7964: 7956: 7946: 7944: 7943: 7938: 7925:invariant metric 7922: 7920: 7919: 7914: 7912: 7911: 7883: 7881: 7880: 7875: 7860: 7858: 7857: 7852: 7841: 7836: 7830: 7827: 7815: 7800: 7798: 7797: 7792: 7781:on the manifold 7776: 7774: 7773: 7768: 7757: 7756: 7736: 7734: 7733: 7728: 7714:. That is, the 7709: 7707: 7706: 7701: 7665:electromagnetism 7634: 7632: 7631: 7626: 7612: 7611: 7599: 7591: 7586: 7585: 7564:for free space: 7556: 7554: 7553: 7548: 7537: 7535: 7527: 7510: 7485:scalar curvature 7471: 7469: 7468: 7463: 7431: 7430: 7313: 7311: 7310: 7305: 7297: 7296: 7288: 7287: 7279: 7239: 7237: 7236: 7231: 7228: 7227: 7206: 7205: 7177: 7175: 7174: 7169: 7161: 7160: 7152: 7151: 7143: 7108:cosmic inflation 6915:scalar curvature 6833:electromagnetism 6819:compactification 6787: 6762: 6759: 6749:You can help by 6742: 6735: 6725: 6716: 6714: 6713: 6708: 6706: 6705: 6690: 6689: 6669: 6667: 6666: 6661: 6646: 6644: 6643: 6638: 6633: 6631: 6623: 6622: 6621: 6617: 6600: 6595: 6594: 6580: 6578: 6577: 6565: 6560: 6558: 6557: 6553: 6540: 6532: 6527: 6526: 6504: 6502: 6501: 6496: 6494: 6493: 6484: 6473: 6472: 6452: 6450: 6449: 6444: 6442: 6441: 6421: 6419: 6418: 6413: 6411: 6410: 6377: 6375: 6374: 6369: 6364: 6362: 6348: 6346: 6345: 6330: 6328: 6320: 6319: 6318: 6305: 6303: 6301: 6293: 6292: 6291: 6278: 6269: 6261: 6256: 6255: 6247: 6230: 6228: 6227: 6222: 6217: 6215: 6207: 6206: 6205: 6192: 6190: 6188: 6180: 6179: 6178: 6165: 6156: 6148: 6143: 6142: 6134: 6113: 6111: 6110: 6105: 6090: 6088: 6087: 6082: 6067: 6065: 6064: 6059: 6054: 6052: 6044: 6043: 6042: 6029: 6027: 6025: 6017: 6016: 6015: 6002: 5993: 5985: 5980: 5979: 5971: 5957: 5955: 5954: 5949: 5946: 5938: 5933: 5932: 5924: 5902: 5900: 5899: 5894: 5889: 5886: 5878: 5877: 5865: 5864: 5855: 5854: 5839: 5837: 5829: 5817: 5815: 5814: 5802: 5801: 5796: 5795: 5787: 5783: 5782: 5774: 5773: 5765: 5758: 5757: 5752: 5751: 5743: 5729: 5727: 5726: 5721: 5719: 5718: 5713: 5712: 5704: 5690: 5688: 5687: 5682: 5677: 5675: 5674: 5673: 5660: 5659: 5658: 5650: 5649: 5641: 5633: 5631: 5630: 5625: 5624: 5616: 5612: 5611: 5606: 5605: 5597: 5593: 5585: 5580: 5578: 5570: 5569: 5568: 5563: 5562: 5554: 5546: 5534: 5532: 5531: 5526: 5524: 5523: 5503: 5501: 5500: 5495: 5493: 5492: 5476: 5474: 5473: 5468: 5463: 5462: 5450: 5449: 5430: 5428: 5427: 5422: 5417: 5415: 5414: 5410: 5397: 5393: 5384: 5376: 5375: 5356: 5354: 5353: 5348: 5346: 5345: 5326: 5324: 5323: 5318: 5313: 5312: 5303: 5302: 5293: 5292: 5280: 5272: 5263: 5258: 5253: 5252: 5244: 5230: 5228: 5227: 5222: 5220: 5219: 5199: 5197: 5196: 5191: 5179: 5177: 5176: 5171: 5156: 5154: 5153: 5148: 5143: 5141: 5130: 5125: 5123: 5115: 5114: 5113: 5100: 5092: 5091: 5065: 5063: 5062: 5057: 5049: 5048: 5033: 5032: 5023: 5022: 5010: 5009: 4994: 4993: 4981: 4980: 4968: 4960: 4954: 4949: 4941: 4940: 4932: 4914: 4912: 4911: 4906: 4904: 4903: 4884: 4882: 4881: 4876: 4868: 4867: 4852: 4851: 4842: 4841: 4832: 4831: 4819: 4818: 4806: 4805: 4793: 4792: 4780: 4779: 4767: 4766: 4757: 4756: 4747: 4746: 4734: 4726: 4720: 4715: 4699: 4694: 4686: 4685: 4677: 4660:provides the 4D 4659: 4657: 4656: 4651: 4649: 4648: 4629: 4627: 4626: 4621: 4613: 4611: 4603: 4591: 4583: 4581: 4570: 4568: 4567: 4555: 4554: 4545: 4544: 4531: 4526: 4521: 4520: 4512: 4505: 4504: 4495: 4494: 4484: 4479: 4471: 4470: 4462: 4452: 4451: 4442: 4441: 4431: 4426: 4418: 4417: 4409: 4402: 4400: 4392: 4391: 4390: 4377: 4367: 4365: 4364: 4359: 4354: 4352: 4344: 4343: 4342: 4329: 4324: 4323: 4301: 4299: 4298: 4293: 4288: 4287: 4278: 4277: 4262: 4261: 4248: 4247: 4232: 4231: 4219: 4218: 4205: 4204: 4192: 4191: 4170:as given above: 4169: 4167: 4166: 4161: 4146: 4144: 4143: 4138: 4136: 4135: 4122: 4121: 4108: 4107: 4092: 4091: 4078: 4077: 4057: 4055: 4054: 4049: 4041: 4040: 4035: 4034: 4026: 4022: 4021: 4016: 4015: 4007: 4002: 3997: 3989: 3988: 3980: 3973: 3971: 3963: 3962: 3961: 3956: 3955: 3947: 3939: 3934: 3933: 3928: 3927: 3919: 3915: 3914: 3909: 3908: 3900: 3896: 3895: 3890: 3889: 3881: 3867: 3865: 3864: 3859: 3851: 3846: 3845: 3830: 3829: 3824: 3823: 3815: 3796: 3794: 3793: 3788: 3786: 3785: 3777: 3776: 3768: 3757: 3755: 3754: 3749: 3747: 3746: 3738: 3737: 3729: 3715: 3713: 3712: 3707: 3702: 3701: 3693: 3690: 3689: 3681: 3680: 3672: 3668: 3660: 3655: 3654: 3646: 3645: 3637: 3630: 3629: 3621: 3620: 3612: 3594: 3592: 3591: 3586: 3584: 3583: 3563: 3561: 3560: 3555: 3553: 3552: 3532: 3530: 3529: 3524: 3509: 3507: 3506: 3501: 3496: 3495: 3480: 3478: 3477: 3468: 3460: 3455: 3453: 3452: 3440: 3438: 3436: 3435: 3426: 3415: 3410: 3405: 3404: 3395: 3380: 3378: 3377: 3372: 3370: 3369: 3354: 3353: 3337: 3335: 3334: 3329: 3317: 3315: 3314: 3309: 3307: 3306: 3283: 3281: 3280: 3275: 3260: 3258: 3257: 3252: 3250: 3234: 3233: 3215: 3214: 3205: 3204: 3192: 3184: 3179: 3175: 3174: 3173: 3161: 3160: 3148: 3147: 3135: 3127: 3122: 3121: 3109: 3108: 3096: 3095: 3078: 3077: 3068: 3060: 3048: 3047: 3035: 3027: 3022: 3021: 2992: 2991: 2983: 2980: 2979: 2971: 2970: 2962: 2958: 2950: 2945: 2944: 2936: 2935: 2927: 2909: 2907: 2906: 2901: 2899: 2898: 2873: 2871: 2870: 2865: 2857: 2856: 2844: 2843: 2831: 2830: 2821: 2820: 2808: 2800: 2789: 2788: 2780: 2779: 2771: 2757: 2755: 2754: 2749: 2747: 2746: 2719: 2717: 2716: 2711: 2709: 2708: 2692: 2690: 2689: 2684: 2679: 2678: 2669: 2668: 2659: 2658: 2634: 2632: 2631: 2626: 2621: 2620: 2611: 2610: 2598: 2597: 2588: 2587: 2575: 2574: 2552: 2550: 2549: 2544: 2539: 2538: 2526: 2525: 2513: 2512: 2503: 2495: 2475: 2474: 2469: 2468: 2460: 2446: 2444: 2443: 2438: 2420: 2418: 2417: 2412: 2404: 2403: 2395: 2394: 2386: 2382: 2381: 2369: 2368: 2360: 2359: 2351: 2347: 2346: 2334: 2333: 2325: 2324: 2316: 2312: 2311: 2299: 2298: 2290: 2289: 2281: 2277: 2269: 2263: 2258: 2250: 2249: 2241: 2224: 2222: 2221: 2216: 2213: 2208: 2200: 2199: 2191: 2186: 2181: 2173: 2172: 2164: 2156: 2151: 2143: 2142: 2134: 2129: 2124: 2116: 2115: 2107: 2099: 2094: 2086: 2085: 2077: 2073: 2072: 2059: 2054: 2046: 2045: 2037: 2033: 2032: 2020: 2019: 2011: 2010: 2002: 1985: 1983: 1982: 1977: 1966: 1965: 1957: 1956: 1948: 1921: 1919: 1918: 1913: 1905: 1903: 1902: 1901: 1888: 1887: 1886: 1878: 1877: 1869: 1861: 1842: 1840: 1839: 1834: 1832: 1831: 1823: 1822: 1814: 1800: 1798: 1797: 1792: 1790: 1789: 1781: 1780: 1772: 1761: 1759: 1758: 1753: 1750: 1745: 1737: 1736: 1728: 1690: 1688: 1687: 1682: 1677: 1676: 1667: 1666: 1651: 1650: 1637: 1636: 1624: 1623: 1611: 1610: 1597: 1596: 1583: 1582: 1567: 1566: 1553: 1552: 1539: 1538: 1530: 1529: 1521: 1514: 1513: 1491: 1489: 1488: 1483: 1446: 1444: 1443: 1438: 1433: 1432: 1425: 1423: 1422: 1410: 1405: 1404: 1395: 1394: 1385: 1384: 1370: 1369: 1353: 1352: 1338: 1337: 1314: 1313: 1305: 1304: 1296: 1282: 1280: 1279: 1274: 1263:where the index 1259: 1257: 1256: 1251: 1246: 1245: 1233: 1232: 1227: 1226: 1218: 1210: 1209: 1200: 1199: 1187: 1186: 1178: 1177: 1169: 1162: 1161: 1153: 1152: 1144: 1136: 1135: 1126: 1125: 1116: 1115: 1103: 1102: 1087: 1086: 1078: 1077: 1069: 1052: 1050: 1049: 1044: 1039: 1038: 1031: 1030: 1019: 1018: 1009: 1008: 995: 994: 985: 984: 973: 972: 963: 962: 953: 952: 940: 939: 916: 915: 907: 906: 898: 884: 882: 881: 876: 864: 862: 861: 856: 854: 853: 837: 835: 834: 829: 827: 826: 818: 805: 803: 802: 797: 795: 794: 786: 785: 777: 741: 737: 684:Gunnar Nordström 668:electromagnetism 636: 629: 622: 508:Quantum geometry 463:Extra dimensions 146: 132: 131: 125: 118: 114: 111: 105: 103: 62: 38: 30: 13964: 13963: 13959: 13958: 13957: 13955: 13954: 13953: 13919: 13918: 13917: 13912: 13880: 13835: 13793:Quantum gravity 13787: 13754: 13723: 13676: 13669: 13660:Higgs mechanism 13638: 13634: 13629: 13532: 13527: 13497: 13492: 13001: 12978: 12955: 12902: 12850: 12820:Kähler manifold 12787: 12764: 12757: 12750: 12743: 12736: 12695: 12656:Mirror symmetry 12637: 12623:Brane cosmology 12569: 12518: 12485: 12441:N=2 superstring 12427:Type IIB string 12422:Type IIA string 12397:Polyakov action 12380: 12337: 12332: 12302: 12297: 12283: 12111: 12015:BKL singularity 12005:Lemaître–Tolman 11980: 11976:Quantum gravity 11958: 11952: 11938:geodetic effect 11912:(together with 11882:LISA Pathfinder 11821: 11770: 11756:Penrose diagram 11738: 11732: 11707: 11696: 11692:Minkowski space 11658: 11602: 11586: 11534: 11528: 11488: 11481: 11476: 11446: 11441: 11420: 11396: 11389: 11360: 11358: 11348: 11329:Lovelock theory 11316: 11310: 11301: 11287: 11280: 11273: 11266: 11259: 11252: 11245: 11238: 11224: 11202: 11196: 11175: 11141: 11134: 11127: 11106: 11097:Induced gravity 11077: 11073:Scalar theories 11053: 11034: 11027: 11018:Massive gravity 10978:Teleparallelism 10976: 10971:Einstein–Cartan 10969: 10953: 10944:Quantum gravity 10923: 10922:Alternatives to 10912: 10878:Exact solutions 10849: 10811: 10806: 10730: 10728:Further reading 10720: 10651:Physics Reports 10642: 10620: 10556:(12): 895–906. 10522: 10517: 10464: 10460: 10411: 10407: 10402: 10398: 10391: 10387: 10382:arXiv:1309.4113 10379: 10375: 10365:Wayback Machine 10355: 10351: 10336: 10314: 10310: 10287: 10283: 10252: 10248: 10217: 10213: 10198: 10194: 10187: 10169: 10165: 10158: 10144: 10140: 10111: 10107: 10092: 10088: 10049: 10045: 10019: 10013: 10004: 9976:Physical Review 9971: 9967: 9952: 9948: 9933: 9929: 9914: 9910: 9871: 9867: 9836: 9827: 9790:Z. Naturforsch. 9782: 9778: 9741:Z. Naturforsch. 9733: 9724: 9685: 9676: 9661: 9657: 9642: 9631: 9616: 9612: 9563: 9554: 9509: 9498: 9477:(12): 895–906. 9465: 9456: 9437: 9418: 9407: 9403: 9384: 9380: 9376: 9371: 9367:Teleparallelism 9327:Quantum gravity 9307: 9291: 9287: 9283: 9252: 9250:Empirical tests 9178: 9175: 9174: 9171: 9169:Generalizations 9146: 9143: 9142: 9125: 9121: 9119: 9116: 9115: 9099: 9096: 9095: 9065: 9060: 9059: 9051: 9042: 9038: 9028: 9016: 9012: 9003: 8999: 8990: 8986: 8974: 8970: 8968: 8965: 8964: 8960:being given by 8934: 8930: 8922: 8918: 8913: 8898: 8894: 8884: 8872: 8868: 8866: 8863: 8862: 8843: 8840: 8839: 8823: 8820: 8819: 8776: 8771: 8770: 8762: 8754: 8750: 8745: 8729: 8725: 8719: 8715: 8695: 8694: 8686: 8683: 8682: 8632: 8628: 8626: 8623: 8622: 8603: 8600: 8599: 8571: 8568: 8567: 8546: 8542: 8540: 8537: 8536: 8508: 8503: 8502: 8494: 8483: 8479: 8477: 8461: 8457: 8451: 8447: 8430: 8429: 8421: 8418: 8417: 8383: 8382: 8359: 8358: 8346: 8342: 8325: 8324: 8316: 8313: 8312: 8280: 8277: 8276: 8260: 8257: 8256: 8240: 8237: 8236: 8214: 8211: 8210: 8186: 8182: 8167: 8163: 8161: 8158: 8157: 8132: 8131: 8129: 8126: 8125: 8106: 8103: 8102: 8082: 8078: 8063: 8059: 8057: 8054: 8053: 8028: 8027: 8025: 8022: 8021: 8001: 7998: 7997: 7981: 7978: 7977: 7955: 7954: 7952: 7949: 7948: 7932: 7929: 7928: 7907: 7903: 7901: 7898: 7897: 7894: 7869: 7866: 7865: 7837: 7832: 7826: 7811: 7809: 7806: 7805: 7786: 7783: 7782: 7752: 7748: 7746: 7743: 7742: 7739:harmonic 2-form 7722: 7719: 7718: 7683: 7680: 7679: 7669:Hodge equations 7657: 7646: 7604: 7600: 7590: 7578: 7574: 7572: 7569: 7568: 7528: 7511: 7509: 7507: 7504: 7503: 7426: 7422: 7405: 7402: 7401: 7344: 7332: 7289: 7278: 7277: 7276: 7274: 7271: 7270: 7251: 7220: 7216: 7198: 7194: 7192: 7189: 7188: 7153: 7142: 7141: 7140: 7138: 7135: 7134: 7116: 7059:Planck constant 7036: 6779: 6772: 6763: 6757: 6754: 6733: 6698: 6694: 6685: 6681: 6679: 6676: 6675: 6672:Planck constant 6655: 6652: 6651: 6624: 6613: 6609: 6605: 6601: 6599: 6590: 6586: 6573: 6569: 6564: 6549: 6545: 6541: 6533: 6531: 6522: 6518: 6513: 6510: 6509: 6489: 6485: 6480: 6468: 6464: 6462: 6459: 6458: 6437: 6433: 6431: 6428: 6427: 6406: 6402: 6400: 6397: 6396: 6388: 6352: 6347: 6341: 6337: 6321: 6314: 6310: 6306: 6304: 6294: 6287: 6283: 6279: 6277: 6262: 6257: 6246: 6245: 6242: 6239: 6238: 6208: 6201: 6197: 6193: 6191: 6181: 6174: 6170: 6166: 6164: 6149: 6144: 6133: 6132: 6129: 6126: 6125: 6096: 6093: 6092: 6076: 6073: 6072: 6045: 6038: 6034: 6030: 6028: 6018: 6011: 6007: 6003: 6001: 5986: 5981: 5970: 5969: 5966: 5963: 5962: 5939: 5934: 5923: 5922: 5919: 5916: 5915: 5909: 5885: 5873: 5869: 5860: 5856: 5850: 5846: 5830: 5818: 5816: 5810: 5806: 5797: 5786: 5785: 5784: 5775: 5764: 5763: 5762: 5753: 5742: 5741: 5740: 5738: 5735: 5734: 5714: 5703: 5702: 5701: 5699: 5696: 5695: 5669: 5665: 5661: 5651: 5640: 5639: 5638: 5634: 5632: 5626: 5615: 5614: 5613: 5607: 5596: 5595: 5594: 5584: 5571: 5564: 5553: 5552: 5551: 5547: 5545: 5543: 5540: 5539: 5519: 5515: 5513: 5510: 5509: 5488: 5484: 5482: 5479: 5478: 5458: 5454: 5445: 5441: 5439: 5436: 5435: 5406: 5402: 5398: 5389: 5385: 5383: 5371: 5367: 5365: 5362: 5361: 5341: 5337: 5335: 5332: 5331: 5308: 5304: 5298: 5294: 5285: 5281: 5271: 5259: 5254: 5243: 5242: 5239: 5236: 5235: 5215: 5211: 5209: 5206: 5205: 5185: 5182: 5181: 5165: 5162: 5161: 5134: 5129: 5116: 5109: 5105: 5101: 5099: 5087: 5083: 5078: 5075: 5074: 5044: 5040: 5028: 5024: 5018: 5014: 5002: 4998: 4989: 4985: 4973: 4969: 4959: 4950: 4942: 4931: 4930: 4927: 4924: 4923: 4899: 4895: 4893: 4890: 4889: 4863: 4859: 4847: 4843: 4837: 4833: 4827: 4823: 4811: 4807: 4801: 4797: 4785: 4781: 4775: 4771: 4762: 4758: 4752: 4748: 4739: 4735: 4725: 4716: 4708: 4695: 4687: 4676: 4675: 4672: 4669: 4668: 4644: 4640: 4638: 4635: 4634: 4604: 4592: 4590: 4574: 4569: 4563: 4559: 4550: 4546: 4540: 4536: 4527: 4522: 4511: 4510: 4500: 4496: 4490: 4486: 4480: 4472: 4461: 4460: 4447: 4443: 4437: 4433: 4427: 4419: 4408: 4407: 4393: 4386: 4382: 4378: 4376: 4374: 4371: 4370: 4345: 4338: 4334: 4330: 4328: 4319: 4315: 4313: 4310: 4309: 4283: 4279: 4273: 4269: 4257: 4253: 4243: 4239: 4227: 4223: 4214: 4210: 4200: 4196: 4187: 4183: 4178: 4175: 4174: 4152: 4149: 4148: 4131: 4127: 4117: 4113: 4100: 4096: 4087: 4083: 4073: 4069: 4067: 4064: 4063: 4036: 4025: 4024: 4023: 4017: 4006: 4005: 4004: 3998: 3990: 3979: 3978: 3964: 3957: 3946: 3945: 3944: 3940: 3938: 3929: 3918: 3917: 3916: 3910: 3899: 3898: 3897: 3891: 3880: 3879: 3878: 3876: 3873: 3872: 3847: 3841: 3837: 3825: 3814: 3813: 3812: 3810: 3807: 3806: 3803: 3778: 3767: 3766: 3765: 3763: 3760: 3759: 3739: 3728: 3727: 3726: 3724: 3721: 3720: 3692: 3691: 3682: 3671: 3670: 3669: 3659: 3647: 3636: 3635: 3634: 3622: 3611: 3610: 3609: 3607: 3604: 3603: 3579: 3575: 3573: 3570: 3569: 3548: 3544: 3542: 3539: 3538: 3518: 3515: 3514: 3491: 3487: 3473: 3469: 3461: 3459: 3448: 3444: 3439: 3431: 3427: 3416: 3414: 3400: 3396: 3394: 3392: 3389: 3388: 3365: 3361: 3349: 3345: 3343: 3340: 3339: 3323: 3320: 3319: 3302: 3298: 3296: 3293: 3292: 3269: 3266: 3265: 3248: 3247: 3226: 3222: 3210: 3206: 3200: 3196: 3183: 3166: 3162: 3153: 3149: 3140: 3136: 3126: 3114: 3110: 3101: 3097: 3088: 3084: 3083: 3079: 3073: 3069: 3059: 3052: 3040: 3036: 3026: 3014: 3010: 3007: 3006: 2993: 2982: 2981: 2972: 2961: 2960: 2959: 2949: 2937: 2926: 2925: 2924: 2920: 2918: 2915: 2914: 2891: 2887: 2885: 2882: 2881: 2849: 2845: 2839: 2835: 2826: 2822: 2813: 2809: 2799: 2781: 2770: 2769: 2768: 2766: 2763: 2762: 2742: 2738: 2736: 2733: 2732: 2704: 2700: 2698: 2695: 2694: 2674: 2670: 2664: 2660: 2651: 2647: 2639: 2636: 2635: 2616: 2612: 2606: 2602: 2593: 2589: 2583: 2579: 2567: 2563: 2561: 2558: 2557: 2531: 2527: 2518: 2514: 2508: 2504: 2494: 2470: 2459: 2458: 2457: 2455: 2452: 2451: 2432: 2429: 2428: 2396: 2385: 2384: 2383: 2377: 2373: 2361: 2350: 2349: 2348: 2342: 2338: 2326: 2315: 2314: 2313: 2307: 2303: 2291: 2280: 2279: 2278: 2268: 2259: 2251: 2240: 2239: 2236: 2233: 2232: 2209: 2201: 2190: 2189: 2182: 2174: 2163: 2162: 2152: 2144: 2133: 2132: 2125: 2117: 2106: 2105: 2095: 2087: 2076: 2075: 2068: 2064: 2055: 2047: 2036: 2035: 2028: 2024: 2012: 2001: 2000: 1999: 1997: 1994: 1993: 1958: 1947: 1946: 1945: 1943: 1940: 1939: 1897: 1893: 1889: 1879: 1868: 1867: 1866: 1862: 1860: 1858: 1855: 1854: 1824: 1813: 1812: 1811: 1809: 1806: 1805: 1782: 1771: 1770: 1769: 1767: 1764: 1763: 1746: 1738: 1727: 1726: 1723: 1720: 1719: 1701:field equations 1697: 1672: 1668: 1662: 1658: 1646: 1642: 1632: 1628: 1619: 1615: 1606: 1602: 1592: 1588: 1575: 1571: 1562: 1558: 1548: 1544: 1531: 1520: 1519: 1518: 1509: 1505: 1500: 1497: 1496: 1474: 1471: 1470: 1427: 1426: 1418: 1414: 1409: 1400: 1396: 1390: 1386: 1377: 1373: 1371: 1365: 1361: 1355: 1354: 1348: 1344: 1339: 1330: 1326: 1319: 1318: 1306: 1295: 1294: 1293: 1291: 1288: 1287: 1268: 1265: 1264: 1241: 1237: 1228: 1217: 1216: 1215: 1205: 1201: 1195: 1191: 1179: 1168: 1167: 1166: 1154: 1143: 1142: 1141: 1131: 1127: 1121: 1117: 1111: 1107: 1095: 1091: 1079: 1068: 1067: 1066: 1064: 1061: 1060: 1033: 1032: 1026: 1022: 1020: 1014: 1010: 1004: 1000: 997: 996: 990: 986: 980: 976: 974: 968: 964: 958: 954: 948: 944: 932: 928: 921: 920: 908: 897: 896: 895: 893: 890: 889: 870: 867: 866: 849: 845: 843: 840: 839: 819: 814: 813: 811: 808: 807: 787: 776: 775: 774: 772: 769: 768: 765:free parameters 760: 739: 735: 672:fifth dimension 640: 611: 610: 566: 558: 557: 483: 481:Quantum gravity 473: 472: 428: 418: 417: 398:Massive gravity 303:Brane cosmology 238: 230: 229: 175: 160: 126: 115: 109: 106: 63: 61: 55: 51:primary sources 39: 28: 17: 12: 11: 5: 13962: 13952: 13951: 13946: 13941: 13936: 13931: 13914: 13913: 13911: 13910: 13898: 13885: 13882: 13881: 13879: 13878: 13873: 13868: 13863: 13858: 13853: 13847: 13845: 13841: 13840: 13837: 13836: 13834: 13833: 13831:Twistor theory 13828: 13823: 13818: 13813: 13808: 13803: 13797: 13795: 13789: 13788: 13786: 13785: 13780: 13775: 13770: 13764: 13762: 13756: 13755: 13753: 13752: 13747: 13742: 13737: 13731: 13729: 13725: 13724: 13722: 13721: 13716: 13711: 13710: 13709: 13699: 13694: 13688: 13686: 13679: 13677:Standard Model 13671: 13670: 13668: 13667: 13662: 13657: 13652: 13646: 13644: 13640: 13639: 13632: 13630: 13628: 13627: 13626: 13625: 13620: 13615: 13610: 13605: 13595: 13594: 13593: 13588: 13583: 13573: 13568: 13563: 13562: 13561: 13556: 13551: 13540: 13538: 13534: 13533: 13530:Standard Model 13526: 13525: 13518: 13511: 13503: 13494: 13493: 13491: 13490: 13485: 13480: 13475: 13470: 13465: 13460: 13455: 13450: 13445: 13440: 13435: 13430: 13425: 13420: 13415: 13410: 13405: 13400: 13395: 13390: 13385: 13380: 13375: 13370: 13365: 13360: 13355: 13350: 13345: 13340: 13335: 13330: 13328:Randjbar-Daemi 13325: 13320: 13315: 13310: 13305: 13300: 13295: 13290: 13285: 13280: 13275: 13270: 13265: 13260: 13255: 13250: 13245: 13240: 13235: 13230: 13225: 13220: 13215: 13210: 13205: 13200: 13195: 13190: 13185: 13180: 13175: 13170: 13165: 13160: 13155: 13150: 13145: 13140: 13135: 13130: 13125: 13120: 13115: 13110: 13105: 13100: 13095: 13090: 13085: 13080: 13075: 13070: 13065: 13060: 13055: 13050: 13045: 13040: 13035: 13030: 13025: 13020: 13015: 13009: 13007: 13003: 13002: 13000: 12999: 12994: 12988: 12986: 12980: 12979: 12977: 12976: 12971: 12965: 12963: 12957: 12956: 12954: 12953: 12951:Lie supergroup 12948: 12943: 12938: 12933: 12928: 12923: 12918: 12912: 12910: 12904: 12903: 12901: 12900: 12895: 12890: 12885: 12880: 12875: 12870: 12865: 12860: 12859: 12858: 12853: 12848: 12844: 12843: 12842: 12832: 12822: 12817: 12811: 12806: 12801: 12795: 12793: 12789: 12788: 12786: 12785: 12777: 12772: 12767: 12762: 12755: 12748: 12741: 12734: 12726: 12721: 12716: 12711: 12705: 12703: 12697: 12696: 12694: 12693: 12688: 12683: 12678: 12673: 12668: 12663: 12658: 12653: 12647: 12645: 12639: 12638: 12636: 12635: 12630: 12628:Quiver diagram 12625: 12620: 12615: 12610: 12605: 12600: 12595: 12590: 12585: 12579: 12577: 12571: 12570: 12568: 12567: 12562: 12557: 12552: 12547: 12542: 12537: 12532: 12526: 12524: 12520: 12519: 12517: 12516: 12511: 12506: 12501: 12495: 12493: 12491:String duality 12487: 12486: 12484: 12483: 12478: 12473: 12468: 12463: 12458: 12453: 12448: 12443: 12438: 12437: 12436: 12431: 12430: 12429: 12424: 12417:Type II string 12414: 12404: 12399: 12394: 12388: 12386: 12382: 12381: 12379: 12378: 12373: 12372: 12371: 12366: 12356: 12354:Cosmic strings 12351: 12345: 12343: 12339: 12338: 12331: 12330: 12323: 12316: 12308: 12299: 12298: 12288: 12285: 12284: 12282: 12281: 12274: 12269: 12264: 12259: 12254: 12249: 12244: 12239: 12234: 12229: 12224: 12219: 12214: 12209: 12204: 12202:Choquet-Bruhat 12199: 12194: 12189: 12184: 12179: 12174: 12169: 12164: 12159: 12154: 12149: 12144: 12139: 12134: 12129: 12123: 12121: 12117: 12116: 12113: 12112: 12110: 12109: 12102: 12101: 12096: 12091: 12084: 12083: 12078: 12073: 12068: 12063: 12054:Axisymmetric: 12051: 12050: 12045: 12039: 12028: 12027: 12022: 12017: 12012: 12007: 12002: 11993:Cosmological: 11990: 11988: 11982: 11981: 11979: 11978: 11973: 11968: 11962: 11960: 11954: 11953: 11951: 11950: 11945: 11934:frame-dragging 11931: 11926: 11921: 11918:Einstein rings 11914:Einstein cross 11907: 11896: 11895: 11890: 11884: 11879: 11874: 11861: 11851: 11850: 11845: 11840: 11835: 11829: 11827: 11823: 11822: 11820: 11819: 11817:Ernst equation 11814: 11809: 11804: 11799: 11794: 11789: 11787:BSSN formalism 11784: 11778: 11776: 11772: 11771: 11769: 11768: 11763: 11758: 11753: 11748: 11742: 11740: 11734: 11733: 11731: 11730: 11725: 11719: 11717: 11710: 11702: 11701: 11698: 11697: 11695: 11694: 11689: 11684: 11679: 11674: 11668: 11666: 11660: 11659: 11657: 11656: 11651: 11646: 11644:Ladder paradox 11641: 11636: 11631: 11626: 11621: 11616: 11610: 11608: 11604: 11603: 11601: 11600: 11594: 11592: 11588: 11587: 11585: 11584: 11579: 11574: 11569: 11564: 11559: 11554: 11549: 11547:Speed of light 11544: 11538: 11536: 11530: 11529: 11527: 11526: 11521: 11516: 11510: 11500: 11498: 11491: 11483: 11482: 11475: 11474: 11467: 11460: 11452: 11443: 11442: 11440: 11439: 11434: 11428: 11426: 11425:Related topics 11422: 11421: 11419: 11418: 11413: 11408: 11403: 11402: 11401: 11394: 11382: 11377: 11372: 11366: 11364: 11354: 11353: 11350: 11349: 11347: 11346: 11341: 11336: 11331: 11326: 11320: 11318: 11312: 11311: 11309: 11308: 11307: 11306: 11297:Twistor theory 11294: 11293: 11292: 11285: 11278: 11271: 11264: 11257: 11250: 11243: 11231: 11230: 11229: 11217: 11212: 11206: 11204: 11198: 11197: 11195: 11194: 11189: 11183: 11181: 11177: 11176: 11174: 11173: 11168: 11163: 11158: 11153: 11148: 11147: 11146: 11139: 11132: 11120: 11114: 11112: 11108: 11107: 11105: 11104: 11099: 11094: 11089: 11084: 11083: 11082: 11070: 11065: 11060: 11059: 11058: 11046: 11041: 11040: 11039: 11032: 11020: 11015: 11010: 10998: 10993: 10988: 10983: 10982: 10981: 10974: 10961: 10959: 10955: 10954: 10952: 10951: 10946: 10941: 10935: 10933: 10926: 10918: 10917: 10914: 10913: 10911: 10910: 10905: 10900: 10895: 10890: 10885: 10880: 10875: 10870: 10865: 10859: 10857: 10851: 10850: 10848: 10847: 10842: 10837: 10832: 10826: 10824: 10817: 10813: 10812: 10805: 10804: 10797: 10790: 10782: 10776: 10775: 10765: 10756: 10747: 10729: 10726: 10725: 10724: 10718: 10693: 10657:(5): 303–378. 10646: 10640: 10627: 10618: 10605: 10587:(3): 412–428. 10574: 10543: 10521: 10518: 10516: 10515: 10458: 10421:(5): 434–453. 10405: 10396: 10385: 10373: 10369:(See chapter 9 10349: 10334: 10308: 10281: 10246: 10211: 10192: 10185: 10163: 10156: 10138: 10105: 10086: 10043: 10002: 9983:(3): 925–935. 9965: 9946: 9927: 9908: 9865: 9840:Astron. Nachr. 9825: 9776: 9722: 9695:(8): 250–251. 9674: 9655: 9629: 9610: 9552: 9496: 9454: 9416: 9401: 9377: 9375: 9372: 9370: 9369: 9364: 9359: 9354: 9349: 9344: 9339: 9334: 9329: 9324: 9319: 9314: 9308: 9306: 9303: 9251: 9248: 9244:supersymmetric 9182: 9170: 9167: 9150: 9128: 9124: 9103: 9085: 9084: 9073: 9068: 9063: 9058: 9054: 9048: 9045: 9041: 9035: 9032: 9027: 9022: 9019: 9015: 9009: 9006: 9002: 8996: 8993: 8989: 8985: 8980: 8977: 8973: 8954: 8953: 8940: 8937: 8933: 8925: 8921: 8917: 8912: 8909: 8904: 8901: 8897: 8891: 8888: 8883: 8878: 8875: 8871: 8847: 8827: 8816: 8815: 8804: 8801: 8798: 8795: 8792: 8789: 8785: 8779: 8774: 8769: 8765: 8757: 8753: 8749: 8744: 8741: 8738: 8735: 8732: 8728: 8722: 8718: 8714: 8711: 8708: 8702: 8699: 8693: 8690: 8664: 8663: 8652: 8649: 8646: 8643: 8640: 8635: 8631: 8607: 8587: 8584: 8581: 8578: 8575: 8549: 8545: 8533: 8532: 8521: 8517: 8511: 8506: 8501: 8497: 8491: 8486: 8482: 8476: 8473: 8470: 8467: 8464: 8460: 8454: 8450: 8446: 8443: 8437: 8434: 8428: 8425: 8411: 8410: 8399: 8396: 8390: 8387: 8381: 8378: 8375: 8372: 8366: 8363: 8357: 8354: 8349: 8345: 8341: 8338: 8332: 8329: 8323: 8320: 8306: 8305: 8293: 8290: 8287: 8284: 8264: 8244: 8224: 8221: 8218: 8194: 8189: 8185: 8181: 8178: 8175: 8170: 8166: 8139: 8136: 8122: 8110: 8090: 8085: 8081: 8077: 8074: 8071: 8066: 8062: 8035: 8032: 8005: 7985: 7976:on the bundle 7962: 7959: 7936: 7910: 7906: 7893: 7890: 7873: 7862: 7861: 7850: 7847: 7844: 7840: 7835: 7824: 7821: 7818: 7814: 7790: 7766: 7763: 7760: 7755: 7751: 7726: 7699: 7696: 7693: 7690: 7687: 7656: 7653: 7642: 7636: 7635: 7624: 7621: 7618: 7615: 7610: 7607: 7603: 7597: 7594: 7589: 7584: 7581: 7577: 7558: 7557: 7546: 7543: 7540: 7534: 7531: 7526: 7523: 7520: 7517: 7514: 7499:to the action 7493:volume element 7473: 7472: 7461: 7458: 7455: 7452: 7449: 7446: 7443: 7440: 7437: 7434: 7429: 7425: 7421: 7418: 7415: 7412: 7409: 7343: 7340: 7331: 7328: 7303: 7300: 7295: 7292: 7285: 7282: 7247: 7241: 7240: 7226: 7223: 7219: 7215: 7212: 7209: 7204: 7201: 7197: 7179: 7178: 7167: 7164: 7159: 7156: 7149: 7146: 7115: 7112: 7067:speed of light 7032: 7018:standing waves 6971:Standard Model 6948:field strength 6870:supersymmetric 6771: 6768: 6765: 6764: 6745: 6743: 6732: 6729: 6704: 6701: 6697: 6693: 6688: 6684: 6659: 6648: 6647: 6636: 6630: 6627: 6620: 6616: 6612: 6608: 6604: 6598: 6593: 6589: 6584: 6576: 6572: 6568: 6563: 6556: 6552: 6548: 6544: 6539: 6536: 6530: 6525: 6521: 6517: 6492: 6488: 6483: 6479: 6476: 6471: 6467: 6440: 6436: 6409: 6405: 6387: 6384: 6379: 6378: 6367: 6361: 6358: 6355: 6351: 6344: 6340: 6336: 6333: 6327: 6324: 6317: 6313: 6309: 6300: 6297: 6290: 6286: 6282: 6276: 6273: 6268: 6265: 6260: 6253: 6250: 6232: 6231: 6220: 6214: 6211: 6204: 6200: 6196: 6187: 6184: 6177: 6173: 6169: 6163: 6160: 6155: 6152: 6147: 6140: 6137: 6103: 6100: 6080: 6069: 6068: 6057: 6051: 6048: 6041: 6037: 6033: 6024: 6021: 6014: 6010: 6006: 6000: 5997: 5992: 5989: 5984: 5977: 5974: 5945: 5942: 5937: 5930: 5927: 5908: 5905: 5904: 5903: 5892: 5884: 5881: 5876: 5872: 5868: 5863: 5859: 5853: 5849: 5845: 5842: 5836: 5833: 5828: 5825: 5821: 5813: 5809: 5805: 5800: 5793: 5790: 5781: 5778: 5771: 5768: 5761: 5756: 5749: 5746: 5717: 5710: 5707: 5692: 5691: 5680: 5672: 5668: 5664: 5657: 5654: 5647: 5644: 5637: 5629: 5622: 5619: 5610: 5603: 5600: 5591: 5588: 5583: 5577: 5574: 5567: 5560: 5557: 5550: 5522: 5518: 5491: 5487: 5466: 5461: 5457: 5453: 5448: 5444: 5432: 5431: 5420: 5413: 5409: 5405: 5401: 5396: 5392: 5388: 5382: 5379: 5374: 5370: 5344: 5340: 5328: 5327: 5316: 5311: 5307: 5301: 5297: 5291: 5288: 5284: 5278: 5275: 5270: 5267: 5262: 5257: 5250: 5247: 5218: 5214: 5189: 5169: 5158: 5157: 5146: 5140: 5137: 5133: 5128: 5122: 5119: 5112: 5108: 5104: 5098: 5095: 5090: 5086: 5082: 5067: 5066: 5055: 5052: 5047: 5043: 5039: 5036: 5031: 5027: 5021: 5017: 5013: 5008: 5005: 5001: 4997: 4992: 4988: 4984: 4979: 4976: 4972: 4966: 4963: 4958: 4953: 4948: 4945: 4938: 4935: 4902: 4898: 4886: 4885: 4874: 4871: 4866: 4862: 4858: 4855: 4850: 4846: 4840: 4836: 4830: 4826: 4822: 4817: 4814: 4810: 4804: 4800: 4796: 4791: 4788: 4784: 4778: 4774: 4770: 4765: 4761: 4755: 4751: 4745: 4742: 4738: 4732: 4729: 4724: 4719: 4714: 4711: 4707: 4703: 4698: 4693: 4690: 4683: 4680: 4647: 4643: 4631: 4630: 4619: 4616: 4610: 4607: 4602: 4599: 4595: 4589: 4586: 4580: 4577: 4573: 4566: 4562: 4558: 4553: 4549: 4543: 4539: 4535: 4530: 4525: 4518: 4515: 4508: 4503: 4499: 4493: 4489: 4483: 4478: 4475: 4468: 4465: 4458: 4455: 4450: 4446: 4440: 4436: 4430: 4425: 4422: 4415: 4412: 4405: 4399: 4396: 4389: 4385: 4381: 4368: 4357: 4351: 4348: 4341: 4337: 4333: 4327: 4322: 4318: 4303: 4302: 4291: 4286: 4282: 4276: 4272: 4268: 4265: 4260: 4256: 4252: 4246: 4242: 4238: 4235: 4230: 4226: 4222: 4217: 4213: 4209: 4203: 4199: 4195: 4190: 4186: 4182: 4159: 4156: 4134: 4130: 4126: 4120: 4116: 4112: 4106: 4103: 4099: 4095: 4090: 4086: 4082: 4076: 4072: 4059: 4058: 4047: 4044: 4039: 4032: 4029: 4020: 4013: 4010: 4001: 3996: 3993: 3986: 3983: 3976: 3970: 3967: 3960: 3953: 3950: 3943: 3937: 3932: 3925: 3922: 3913: 3906: 3903: 3894: 3887: 3884: 3857: 3854: 3850: 3844: 3840: 3836: 3833: 3828: 3821: 3818: 3802: 3799: 3784: 3781: 3774: 3771: 3745: 3742: 3735: 3732: 3717: 3716: 3705: 3699: 3696: 3688: 3685: 3678: 3675: 3666: 3663: 3658: 3653: 3650: 3643: 3640: 3633: 3628: 3625: 3618: 3615: 3582: 3578: 3551: 3547: 3522: 3511: 3510: 3499: 3494: 3490: 3486: 3483: 3476: 3472: 3467: 3464: 3458: 3451: 3447: 3443: 3434: 3430: 3425: 3422: 3419: 3413: 3408: 3403: 3399: 3368: 3364: 3360: 3357: 3352: 3348: 3327: 3305: 3301: 3273: 3262: 3261: 3246: 3243: 3240: 3237: 3232: 3229: 3225: 3221: 3218: 3213: 3209: 3203: 3199: 3195: 3190: 3187: 3182: 3178: 3172: 3169: 3165: 3159: 3156: 3152: 3146: 3143: 3139: 3133: 3130: 3125: 3120: 3117: 3113: 3107: 3104: 3100: 3094: 3091: 3087: 3082: 3076: 3072: 3066: 3063: 3058: 3055: 3053: 3051: 3046: 3043: 3039: 3033: 3030: 3025: 3020: 3017: 3013: 3009: 3008: 3005: 3002: 2999: 2996: 2994: 2989: 2986: 2978: 2975: 2968: 2965: 2956: 2953: 2948: 2943: 2940: 2933: 2930: 2923: 2922: 2897: 2894: 2890: 2875: 2874: 2863: 2860: 2855: 2852: 2848: 2842: 2838: 2834: 2829: 2825: 2819: 2816: 2812: 2806: 2803: 2798: 2795: 2792: 2787: 2784: 2777: 2774: 2745: 2741: 2707: 2703: 2682: 2677: 2673: 2667: 2663: 2657: 2654: 2650: 2646: 2643: 2624: 2619: 2615: 2609: 2605: 2601: 2596: 2592: 2586: 2582: 2578: 2573: 2570: 2566: 2554: 2553: 2542: 2537: 2534: 2530: 2524: 2521: 2517: 2511: 2507: 2501: 2498: 2493: 2490: 2487: 2484: 2481: 2478: 2473: 2466: 2463: 2436: 2422: 2421: 2410: 2407: 2402: 2399: 2392: 2389: 2380: 2376: 2372: 2367: 2364: 2357: 2354: 2345: 2341: 2337: 2332: 2329: 2322: 2319: 2310: 2306: 2302: 2297: 2294: 2287: 2284: 2275: 2272: 2267: 2262: 2257: 2254: 2247: 2244: 2226: 2225: 2212: 2207: 2204: 2197: 2194: 2185: 2180: 2177: 2170: 2167: 2160: 2155: 2150: 2147: 2140: 2137: 2128: 2123: 2120: 2113: 2110: 2103: 2098: 2093: 2090: 2083: 2080: 2071: 2067: 2063: 2058: 2053: 2050: 2043: 2040: 2031: 2027: 2023: 2018: 2015: 2008: 2005: 1987: 1986: 1975: 1972: 1969: 1964: 1961: 1954: 1951: 1923: 1922: 1911: 1908: 1900: 1896: 1892: 1885: 1882: 1875: 1872: 1865: 1830: 1827: 1820: 1817: 1788: 1785: 1778: 1775: 1749: 1744: 1741: 1734: 1731: 1696: 1693: 1692: 1691: 1680: 1675: 1671: 1665: 1661: 1657: 1654: 1649: 1645: 1641: 1635: 1631: 1627: 1622: 1618: 1614: 1609: 1605: 1601: 1595: 1591: 1587: 1581: 1578: 1574: 1570: 1565: 1561: 1557: 1551: 1547: 1543: 1537: 1534: 1527: 1524: 1517: 1512: 1508: 1504: 1481: 1478: 1448: 1447: 1436: 1431: 1421: 1417: 1413: 1408: 1403: 1399: 1393: 1389: 1383: 1380: 1376: 1372: 1368: 1364: 1360: 1357: 1356: 1351: 1347: 1343: 1340: 1336: 1333: 1329: 1325: 1324: 1322: 1317: 1312: 1309: 1302: 1299: 1272: 1261: 1260: 1249: 1244: 1240: 1236: 1231: 1224: 1221: 1213: 1208: 1204: 1198: 1194: 1190: 1185: 1182: 1175: 1172: 1165: 1160: 1157: 1150: 1147: 1139: 1134: 1130: 1124: 1120: 1114: 1110: 1106: 1101: 1098: 1094: 1090: 1085: 1082: 1075: 1072: 1054: 1053: 1042: 1037: 1029: 1025: 1021: 1017: 1013: 1007: 1003: 999: 998: 993: 989: 983: 979: 975: 971: 967: 961: 957: 951: 947: 943: 938: 935: 931: 927: 926: 924: 919: 914: 911: 904: 901: 874: 852: 848: 825: 822: 817: 793: 790: 783: 780: 759: 756: 692:Theodor Kaluza 676:space and time 642: 641: 639: 638: 631: 624: 616: 613: 612: 609: 608: 603: 598: 593: 588: 583: 578: 573: 567: 564: 563: 560: 559: 556: 555: 550: 545: 540: 535: 530: 525: 520: 515: 510: 505: 500: 495: 490: 484: 479: 478: 475: 474: 471: 470: 465: 460: 455: 450: 445: 440: 435: 429: 424: 423: 420: 419: 416: 415: 410: 405: 400: 395: 390: 385: 380: 375: 370: 365: 360: 355: 350: 345: 340: 335: 330: 325: 320: 315: 310: 305: 300: 295: 290: 285: 280: 275: 270: 265: 260: 255: 250: 245: 239: 236: 235: 232: 231: 228: 227: 222: 217: 212: 207: 205:Dark radiation 202: 200:Phantom energy 197: 192: 187: 182: 176: 173: 172: 169: 168: 166:Standard Model 162: 161: 147: 139: 138: 128: 127: 42: 40: 33: 15: 9: 6: 4: 3: 2: 13961: 13950: 13947: 13945: 13944:String theory 13942: 13940: 13937: 13935: 13932: 13930: 13927: 13926: 13924: 13909: 13908: 13899: 13897: 13896: 13887: 13886: 13883: 13877: 13874: 13872: 13869: 13867: 13864: 13862: 13859: 13857: 13854: 13852: 13849: 13848: 13846: 13842: 13832: 13829: 13827: 13824: 13822: 13819: 13817: 13814: 13812: 13809: 13807: 13804: 13802: 13801:String theory 13799: 13798: 13796: 13794: 13790: 13784: 13781: 13779: 13776: 13774: 13771: 13769: 13766: 13765: 13763: 13761: 13760:Supersymmetry 13757: 13751: 13748: 13746: 13743: 13741: 13738: 13736: 13733: 13732: 13730: 13726: 13720: 13717: 13715: 13712: 13708: 13705: 13704: 13703: 13700: 13698: 13695: 13693: 13690: 13689: 13687: 13683: 13680: 13678: 13672: 13666: 13663: 13661: 13658: 13656: 13653: 13651: 13648: 13647: 13645: 13641: 13624: 13621: 13619: 13616: 13614: 13611: 13609: 13606: 13604: 13601: 13600: 13599: 13596: 13592: 13589: 13587: 13584: 13582: 13579: 13578: 13577: 13574: 13572: 13569: 13567: 13564: 13560: 13557: 13555: 13552: 13550: 13547: 13546: 13545: 13542: 13541: 13539: 13535: 13531: 13524: 13519: 13517: 13512: 13510: 13505: 13504: 13501: 13489: 13486: 13484: 13481: 13479: 13476: 13474: 13473:Zamolodchikov 13471: 13469: 13468:Zamolodchikov 13466: 13464: 13461: 13459: 13456: 13454: 13451: 13449: 13446: 13444: 13441: 13439: 13436: 13434: 13431: 13429: 13426: 13424: 13421: 13419: 13416: 13414: 13411: 13409: 13406: 13404: 13401: 13399: 13396: 13394: 13391: 13389: 13386: 13384: 13381: 13379: 13376: 13374: 13371: 13369: 13366: 13364: 13361: 13359: 13356: 13354: 13351: 13349: 13346: 13344: 13341: 13339: 13336: 13334: 13331: 13329: 13326: 13324: 13321: 13319: 13316: 13314: 13311: 13309: 13306: 13304: 13301: 13299: 13296: 13294: 13291: 13289: 13286: 13284: 13281: 13279: 13276: 13274: 13271: 13269: 13266: 13264: 13261: 13259: 13256: 13254: 13251: 13249: 13246: 13244: 13241: 13239: 13236: 13234: 13231: 13229: 13226: 13224: 13221: 13219: 13216: 13214: 13211: 13209: 13206: 13204: 13201: 13199: 13196: 13194: 13191: 13189: 13186: 13184: 13181: 13179: 13176: 13174: 13171: 13169: 13166: 13164: 13161: 13159: 13156: 13154: 13151: 13149: 13146: 13144: 13141: 13139: 13136: 13134: 13131: 13129: 13126: 13124: 13121: 13119: 13116: 13114: 13111: 13109: 13106: 13104: 13101: 13099: 13096: 13094: 13091: 13089: 13086: 13084: 13081: 13079: 13076: 13074: 13071: 13069: 13066: 13064: 13061: 13059: 13056: 13054: 13051: 13049: 13046: 13044: 13041: 13039: 13036: 13034: 13031: 13029: 13026: 13024: 13021: 13019: 13016: 13014: 13011: 13010: 13008: 13004: 12998: 12995: 12993: 12992:Matrix theory 12990: 12989: 12987: 12985: 12981: 12975: 12972: 12970: 12967: 12966: 12964: 12962: 12958: 12952: 12949: 12947: 12944: 12942: 12939: 12937: 12934: 12932: 12929: 12927: 12924: 12922: 12919: 12917: 12914: 12913: 12911: 12909: 12908:Supersymmetry 12905: 12899: 12896: 12894: 12891: 12889: 12886: 12884: 12881: 12879: 12876: 12874: 12871: 12869: 12866: 12864: 12861: 12857: 12854: 12852: 12845: 12841: 12838: 12837: 12836: 12833: 12831: 12828: 12827: 12826: 12823: 12821: 12818: 12815: 12812: 12810: 12807: 12805: 12802: 12800: 12797: 12796: 12794: 12790: 12784: 12782: 12778: 12776: 12773: 12771: 12768: 12765: 12758: 12751: 12744: 12737: 12730: 12727: 12725: 12722: 12720: 12717: 12715: 12712: 12710: 12707: 12706: 12704: 12702: 12698: 12692: 12689: 12687: 12684: 12682: 12679: 12677: 12674: 12672: 12669: 12667: 12664: 12662: 12659: 12657: 12654: 12652: 12649: 12648: 12646: 12644: 12640: 12634: 12631: 12629: 12626: 12624: 12621: 12619: 12616: 12614: 12611: 12609: 12606: 12604: 12601: 12599: 12596: 12594: 12591: 12589: 12586: 12584: 12581: 12580: 12578: 12576: 12572: 12566: 12563: 12561: 12560:Dual graviton 12558: 12556: 12553: 12551: 12548: 12546: 12543: 12541: 12538: 12536: 12533: 12531: 12528: 12527: 12525: 12521: 12515: 12512: 12510: 12507: 12505: 12502: 12500: 12497: 12496: 12494: 12492: 12488: 12482: 12479: 12477: 12476:RNS formalism 12474: 12472: 12469: 12467: 12464: 12462: 12459: 12457: 12454: 12452: 12449: 12447: 12444: 12442: 12439: 12435: 12432: 12428: 12425: 12423: 12420: 12419: 12418: 12415: 12413: 12412:Type I string 12410: 12409: 12408: 12405: 12403: 12400: 12398: 12395: 12393: 12390: 12389: 12387: 12383: 12377: 12374: 12370: 12367: 12365: 12362: 12361: 12360: 12357: 12355: 12352: 12350: 12347: 12346: 12344: 12340: 12336: 12335:String theory 12329: 12324: 12322: 12317: 12315: 12310: 12309: 12306: 12296: 12286: 12280: 12279: 12275: 12273: 12270: 12268: 12265: 12263: 12260: 12258: 12255: 12253: 12250: 12248: 12245: 12243: 12240: 12238: 12235: 12233: 12230: 12228: 12225: 12223: 12220: 12218: 12215: 12213: 12210: 12208: 12205: 12203: 12200: 12198: 12195: 12193: 12190: 12188: 12187:Chandrasekhar 12185: 12183: 12180: 12178: 12175: 12173: 12170: 12168: 12165: 12163: 12160: 12158: 12155: 12153: 12150: 12148: 12147:Schwarzschild 12145: 12143: 12140: 12138: 12135: 12133: 12130: 12128: 12125: 12124: 12122: 12118: 12108: 12104: 12103: 12100: 12097: 12095: 12092: 12090: 12086: 12085: 12082: 12079: 12077: 12074: 12072: 12069: 12067: 12064: 12061: 12057: 12053: 12052: 12049: 12046: 12043: 12040: 12038: 12034: 12033:Schwarzschild 12030: 12029: 12026: 12023: 12021: 12018: 12016: 12013: 12011: 12008: 12006: 12003: 12000: 11996: 11992: 11991: 11989: 11987: 11983: 11977: 11974: 11972: 11969: 11967: 11964: 11963: 11961: 11955: 11949: 11946: 11943: 11939: 11935: 11932: 11930: 11929:Shapiro delay 11927: 11925: 11922: 11919: 11915: 11911: 11908: 11905: 11901: 11898: 11897: 11894: 11891: 11888: 11885: 11883: 11880: 11878: 11875: 11873: 11872:collaboration 11869: 11865: 11862: 11860: 11856: 11853: 11852: 11849: 11846: 11844: 11841: 11839: 11838:Event horizon 11836: 11834: 11831: 11830: 11828: 11824: 11818: 11815: 11813: 11810: 11808: 11805: 11803: 11800: 11798: 11795: 11793: 11790: 11788: 11785: 11783: 11782:ADM formalism 11780: 11779: 11777: 11773: 11767: 11764: 11762: 11759: 11757: 11754: 11752: 11749: 11747: 11744: 11743: 11741: 11735: 11729: 11726: 11724: 11721: 11720: 11718: 11714: 11711: 11709: 11703: 11693: 11690: 11688: 11687:Biquaternions 11685: 11683: 11680: 11678: 11675: 11673: 11670: 11669: 11667: 11665: 11661: 11655: 11652: 11650: 11647: 11645: 11642: 11640: 11637: 11635: 11632: 11630: 11627: 11625: 11622: 11620: 11617: 11615: 11614:Time dilation 11612: 11611: 11609: 11605: 11599: 11596: 11595: 11593: 11589: 11583: 11580: 11578: 11575: 11573: 11570: 11568: 11567:Proper length 11565: 11563: 11560: 11558: 11555: 11553: 11550: 11548: 11545: 11543: 11540: 11539: 11537: 11531: 11525: 11522: 11520: 11517: 11514: 11511: 11509: 11505: 11502: 11501: 11499: 11495: 11492: 11490: 11484: 11480: 11473: 11468: 11466: 11461: 11459: 11454: 11453: 11450: 11438: 11435: 11433: 11430: 11429: 11427: 11423: 11417: 11414: 11412: 11409: 11407: 11404: 11399: 11395: 11392: 11391:Fatio–Le Sage 11388: 11387: 11386: 11383: 11381: 11378: 11376: 11373: 11371: 11368: 11367: 11365: 11363: 11357:Pre-Newtonian 11355: 11345: 11342: 11340: 11337: 11335: 11332: 11330: 11327: 11325: 11322: 11321: 11319: 11313: 11304: 11300: 11299: 11298: 11295: 11290: 11286: 11283: 11279: 11276: 11272: 11269: 11265: 11262: 11258: 11255: 11251: 11248: 11244: 11241: 11237: 11236: 11235: 11234:String theory 11232: 11227: 11223: 11222: 11221: 11218: 11216: 11213: 11211: 11208: 11207: 11205: 11199: 11193: 11190: 11188: 11185: 11184: 11182: 11178: 11172: 11169: 11167: 11164: 11162: 11159: 11157: 11154: 11152: 11149: 11144: 11140: 11137: 11133: 11130: 11126: 11125: 11124: 11121: 11119: 11116: 11115: 11113: 11109: 11103: 11100: 11098: 11095: 11093: 11090: 11088: 11085: 11080: 11076: 11075: 11074: 11071: 11069: 11066: 11064: 11061: 11056: 11052: 11051: 11050: 11047: 11045: 11042: 11037: 11033: 11030: 11026: 11025: 11024: 11021: 11019: 11016: 11014: 11011: 11009: 11007: 11003: 10999: 10997: 10994: 10992: 10989: 10987: 10984: 10979: 10975: 10972: 10968: 10967: 10966: 10963: 10962: 10960: 10956: 10950: 10947: 10945: 10942: 10940: 10937: 10936: 10934: 10930: 10927: 10925: 10919: 10909: 10906: 10904: 10903:ADM formalism 10901: 10899: 10896: 10894: 10891: 10889: 10886: 10884: 10881: 10879: 10876: 10874: 10871: 10869: 10866: 10864: 10861: 10860: 10858: 10856: 10852: 10846: 10843: 10841: 10838: 10836: 10833: 10831: 10828: 10827: 10825: 10821: 10818: 10814: 10810: 10803: 10798: 10796: 10791: 10789: 10784: 10783: 10780: 10774: 10770: 10766: 10763: 10762: 10757: 10754: 10753: 10748: 10746: 10744: 10738: 10737: 10732: 10731: 10721: 10715: 10711: 10707: 10702: 10701: 10694: 10690: 10686: 10682: 10678: 10674: 10670: 10665: 10664:gr-qc/9805018 10660: 10656: 10652: 10647: 10643: 10637: 10633: 10628: 10626: 10621: 10615: 10611: 10606: 10602: 10598: 10594: 10590: 10586: 10582: 10581: 10575: 10571: 10567: 10563: 10559: 10555: 10551: 10550: 10544: 10542: 10537: 10533: 10529: 10524: 10523: 10511: 10507: 10503: 10499: 10495: 10491: 10486: 10481: 10477: 10473: 10469: 10462: 10454: 10450: 10446: 10442: 10438: 10434: 10429: 10424: 10420: 10416: 10409: 10400: 10394: 10389: 10383: 10377: 10370: 10366: 10362: 10359: 10353: 10345: 10341: 10337: 10331: 10327: 10323: 10319: 10312: 10304: 10300: 10296: 10292: 10285: 10277: 10273: 10269: 10265: 10261: 10257: 10250: 10242: 10238: 10234: 10230: 10226: 10222: 10221:Nucl. Phys. B 10215: 10206: 10205: 10196: 10188: 10182: 10177: 10176: 10167: 10159: 10153: 10149: 10142: 10133: 10128: 10124: 10120: 10116: 10109: 10101: 10097: 10090: 10082: 10078: 10074: 10070: 10066: 10062: 10058: 10054: 10047: 10038: 10033: 10029: 10025: 10018: 10011: 10009: 10007: 9998: 9994: 9990: 9986: 9982: 9978: 9977: 9969: 9961: 9958:(in German). 9957: 9950: 9942: 9938: 9931: 9923: 9920:(in German). 9919: 9912: 9904: 9900: 9896: 9892: 9888: 9884: 9880: 9876: 9869: 9861: 9857: 9853: 9849: 9845: 9842:(in German). 9841: 9834: 9832: 9830: 9821: 9817: 9812: 9807: 9803: 9799: 9795: 9792:(in German). 9791: 9787: 9780: 9772: 9768: 9763: 9758: 9754: 9750: 9746: 9743:(in German). 9742: 9738: 9731: 9729: 9727: 9718: 9714: 9710: 9706: 9702: 9698: 9694: 9691:(in German). 9690: 9683: 9681: 9679: 9670: 9667:(in French). 9666: 9659: 9651: 9648:(in French). 9647: 9640: 9638: 9636: 9634: 9625: 9622:(in French). 9621: 9614: 9606: 9602: 9598: 9594: 9590: 9586: 9581: 9576: 9572: 9568: 9561: 9559: 9557: 9548: 9544: 9539: 9534: 9530: 9526: 9523:(2971): 516. 9522: 9518: 9514: 9507: 9505: 9503: 9501: 9492: 9488: 9484: 9480: 9476: 9473:(in German). 9472: 9471: 9463: 9461: 9459: 9450: 9446: 9442: 9435: 9433: 9431: 9429: 9427: 9425: 9423: 9421: 9412: 9405: 9397: 9394:(in German). 9393: 9389: 9382: 9378: 9368: 9365: 9363: 9360: 9358: 9355: 9353: 9350: 9348: 9347:String theory 9345: 9343: 9340: 9338: 9335: 9333: 9330: 9328: 9325: 9323: 9320: 9318: 9315: 9313: 9310: 9309: 9302: 9300: 9295: 9281: 9277: 9273: 9269: 9264: 9262: 9258: 9247: 9245: 9241: 9237: 9233: 9230: 9226: 9224: 9217: 9215: 9212: 9208: 9204: 9200: 9199:compact space 9196: 9166: 9164: 9126: 9122: 9092: 9090: 9071: 9066: 9056: 9046: 9043: 9039: 9033: 9030: 9025: 9020: 9017: 9013: 9007: 9004: 9000: 8994: 8991: 8987: 8983: 8978: 8975: 8971: 8963: 8962: 8961: 8959: 8938: 8935: 8931: 8923: 8915: 8910: 8907: 8902: 8899: 8895: 8889: 8886: 8881: 8876: 8873: 8869: 8861: 8860: 8859: 8845: 8825: 8802: 8796: 8790: 8787: 8783: 8777: 8767: 8755: 8747: 8742: 8736: 8730: 8726: 8720: 8716: 8709: 8700: 8697: 8688: 8681: 8680: 8679: 8677: 8673: 8669: 8650: 8647: 8644: 8641: 8638: 8633: 8629: 8621: 8620: 8619: 8605: 8585: 8579: 8576: 8573: 8565: 8547: 8543: 8519: 8515: 8509: 8499: 8489: 8484: 8474: 8468: 8462: 8458: 8452: 8448: 8444: 8435: 8432: 8423: 8416: 8415: 8414: 8397: 8388: 8385: 8376: 8373: 8364: 8361: 8352: 8347: 8343: 8339: 8330: 8327: 8318: 8311: 8310: 8309: 8288: 8282: 8262: 8242: 8222: 8219: 8216: 8208: 8207:tangent space 8192: 8187: 8183: 8179: 8176: 8173: 8168: 8164: 8156: 8137: 8134: 8123: 8108: 8088: 8083: 8079: 8075: 8072: 8069: 8064: 8060: 8052: 8033: 8030: 8019: 8018: 8017: 8003: 7983: 7960: 7957: 7926: 7908: 7904: 7889: 7887: 7871: 7848: 7845: 7842: 7838: 7822: 7819: 7816: 7804: 7803: 7802: 7788: 7780: 7761: 7753: 7741:in the space 7740: 7724: 7717: 7713: 7697: 7691: 7688: 7685: 7678: 7677:circle bundle 7674: 7670: 7666: 7662: 7652: 7650: 7645: 7641: 7622: 7619: 7616: 7613: 7608: 7605: 7601: 7595: 7592: 7587: 7582: 7579: 7575: 7567: 7566: 7565: 7563: 7544: 7541: 7538: 7532: 7529: 7521: 7515: 7512: 7502: 7501: 7500: 7498: 7494: 7490: 7486: 7482: 7478: 7459: 7453: 7447: 7444: 7438: 7432: 7427: 7423: 7419: 7413: 7407: 7400: 7399: 7398: 7396: 7392: 7389: 7385: 7381: 7377: 7373: 7369: 7365: 7361: 7357: 7354:to a certain 7353: 7349: 7339: 7337: 7327: 7325: 7321: 7317: 7301: 7298: 7293: 7290: 7283: 7280: 7269:solutions of 7268: 7263: 7260: 7255: 7250: 7246: 7224: 7221: 7217: 7213: 7210: 7207: 7202: 7199: 7195: 7187: 7186: 7185: 7184: 7165: 7162: 7157: 7154: 7147: 7144: 7133: 7132: 7131: 7129: 7125: 7121: 7111: 7109: 7104: 7102: 7101:warped models 7098: 7094: 7089: 7087: 7082: 7080: 7076: 7072: 7068: 7064: 7060: 7056: 7052: 7048: 7044: 7040: 7035: 7031: 7027: 7023: 7019: 7015: 7014:warped models 7011: 7007: 7003: 6998: 6996: 6992: 6988: 6984: 6980: 6976: 6972: 6968: 6964: 6959: 6957: 6953: 6949: 6945: 6942:given by the 6941: 6937: 6933: 6929: 6925: 6921: 6916: 6912: 6911:bundle metric 6908: 6904: 6900: 6896: 6893: 6889: 6886: 6881: 6879: 6875: 6871: 6867: 6863: 6859: 6855: 6850: 6846: 6845:circle bundle 6842: 6838: 6834: 6830: 6827: 6822: 6820: 6816: 6811: 6807: 6799: 6795: 6791: 6786: 6782: 6776: 6761: 6758:February 2015 6752: 6748: 6744: 6741: 6737: 6736: 6728: 6724: 6718: 6702: 6699: 6695: 6691: 6686: 6682: 6673: 6657: 6634: 6628: 6625: 6618: 6614: 6610: 6606: 6602: 6596: 6591: 6587: 6574: 6570: 6566: 6561: 6554: 6550: 6546: 6542: 6537: 6534: 6528: 6523: 6519: 6515: 6508: 6507: 6506: 6490: 6486: 6481: 6477: 6474: 6469: 6465: 6457:for momentum 6456: 6438: 6434: 6425: 6407: 6403: 6394: 6383: 6365: 6359: 6356: 6353: 6349: 6342: 6338: 6334: 6331: 6325: 6322: 6315: 6311: 6307: 6298: 6295: 6288: 6284: 6280: 6274: 6271: 6266: 6263: 6258: 6251: 6248: 6237: 6236: 6235: 6218: 6212: 6209: 6202: 6198: 6194: 6185: 6182: 6175: 6171: 6167: 6161: 6158: 6153: 6150: 6145: 6138: 6135: 6124: 6123: 6122: 6120: 6115: 6101: 6098: 6078: 6055: 6049: 6046: 6039: 6035: 6031: 6022: 6019: 6012: 6008: 6004: 5998: 5995: 5990: 5987: 5982: 5975: 5972: 5961: 5960: 5959: 5943: 5940: 5935: 5928: 5925: 5914: 5913:stress tensor 5890: 5882: 5874: 5870: 5866: 5861: 5857: 5851: 5847: 5843: 5834: 5831: 5826: 5823: 5819: 5811: 5807: 5803: 5798: 5791: 5788: 5779: 5776: 5769: 5766: 5759: 5754: 5747: 5744: 5733: 5732: 5731: 5715: 5708: 5705: 5678: 5670: 5666: 5655: 5652: 5645: 5642: 5627: 5620: 5617: 5608: 5601: 5598: 5589: 5586: 5581: 5575: 5572: 5565: 5558: 5555: 5548: 5538: 5537: 5536: 5520: 5516: 5506: 5489: 5485: 5464: 5459: 5455: 5451: 5446: 5442: 5418: 5411: 5407: 5403: 5399: 5394: 5390: 5386: 5380: 5377: 5372: 5368: 5360: 5359: 5358: 5342: 5338: 5314: 5309: 5305: 5299: 5289: 5286: 5282: 5276: 5273: 5268: 5265: 5260: 5255: 5248: 5234: 5233: 5232: 5216: 5212: 5202: 5187: 5167: 5144: 5138: 5135: 5131: 5120: 5117: 5110: 5106: 5102: 5096: 5093: 5088: 5084: 5080: 5073: 5072: 5071: 5053: 5045: 5041: 5037: 5034: 5029: 5019: 5015: 5011: 5006: 5003: 4999: 4990: 4986: 4982: 4977: 4974: 4970: 4964: 4961: 4956: 4951: 4946: 4943: 4936: 4922: 4921: 4920: 4918: 4915:provides the 4900: 4896: 4872: 4864: 4860: 4856: 4853: 4848: 4838: 4834: 4828: 4824: 4820: 4815: 4812: 4808: 4802: 4798: 4794: 4789: 4786: 4782: 4776: 4772: 4763: 4759: 4753: 4749: 4743: 4740: 4736: 4730: 4727: 4722: 4717: 4712: 4709: 4701: 4696: 4691: 4688: 4681: 4667: 4666: 4665: 4663: 4645: 4641: 4617: 4614: 4608: 4605: 4600: 4597: 4593: 4587: 4584: 4578: 4575: 4571: 4564: 4560: 4556: 4551: 4541: 4537: 4528: 4523: 4516: 4506: 4501: 4497: 4491: 4487: 4481: 4476: 4473: 4466: 4456: 4453: 4448: 4444: 4438: 4434: 4428: 4423: 4420: 4413: 4403: 4397: 4394: 4387: 4383: 4379: 4369: 4355: 4349: 4346: 4339: 4335: 4331: 4325: 4320: 4316: 4308: 4307: 4306: 4289: 4284: 4274: 4270: 4266: 4263: 4258: 4254: 4250: 4244: 4240: 4236: 4228: 4224: 4220: 4215: 4211: 4207: 4201: 4197: 4193: 4188: 4184: 4180: 4173: 4172: 4171: 4157: 4154: 4132: 4128: 4124: 4118: 4114: 4110: 4104: 4101: 4097: 4093: 4088: 4084: 4080: 4074: 4070: 4045: 4042: 4037: 4030: 4027: 4018: 4011: 4008: 3999: 3994: 3991: 3984: 3974: 3968: 3965: 3958: 3951: 3948: 3941: 3935: 3930: 3923: 3920: 3911: 3904: 3892: 3885: 3882: 3871: 3870: 3869: 3855: 3852: 3848: 3842: 3838: 3834: 3831: 3826: 3819: 3816: 3798: 3782: 3779: 3772: 3769: 3743: 3740: 3733: 3730: 3703: 3697: 3694: 3686: 3683: 3676: 3673: 3664: 3661: 3656: 3651: 3648: 3641: 3638: 3631: 3626: 3623: 3616: 3613: 3602: 3601: 3600: 3597: 3580: 3576: 3567: 3549: 3545: 3536: 3520: 3497: 3492: 3488: 3484: 3481: 3474: 3470: 3465: 3462: 3456: 3449: 3445: 3441: 3432: 3428: 3423: 3420: 3417: 3411: 3406: 3401: 3397: 3387: 3386: 3385: 3382: 3366: 3362: 3358: 3350: 3346: 3325: 3303: 3299: 3290: 3285: 3271: 3244: 3238: 3235: 3230: 3227: 3223: 3219: 3216: 3211: 3201: 3188: 3185: 3180: 3176: 3170: 3167: 3163: 3157: 3154: 3150: 3144: 3141: 3137: 3131: 3128: 3123: 3118: 3115: 3111: 3105: 3102: 3098: 3092: 3089: 3085: 3080: 3074: 3070: 3064: 3061: 3056: 3054: 3049: 3044: 3041: 3037: 3031: 3028: 3023: 3018: 3015: 3011: 3000: 2997: 2995: 2987: 2984: 2976: 2973: 2966: 2963: 2954: 2951: 2946: 2941: 2938: 2931: 2928: 2913: 2912: 2911: 2895: 2892: 2888: 2878: 2861: 2853: 2850: 2846: 2840: 2836: 2827: 2817: 2814: 2810: 2804: 2801: 2796: 2793: 2790: 2785: 2782: 2775: 2772: 2761: 2760: 2759: 2743: 2739: 2729: 2727: 2723: 2705: 2680: 2675: 2665: 2655: 2652: 2648: 2644: 2641: 2622: 2617: 2613: 2607: 2599: 2594: 2590: 2584: 2576: 2571: 2568: 2564: 2540: 2535: 2532: 2528: 2522: 2519: 2515: 2509: 2505: 2499: 2496: 2491: 2488: 2485: 2479: 2476: 2471: 2464: 2461: 2450: 2449: 2448: 2434: 2425: 2408: 2400: 2397: 2390: 2387: 2378: 2370: 2365: 2362: 2355: 2352: 2343: 2335: 2330: 2327: 2320: 2317: 2308: 2295: 2292: 2285: 2282: 2273: 2270: 2265: 2260: 2255: 2252: 2245: 2231: 2230: 2229: 2210: 2205: 2202: 2195: 2183: 2178: 2175: 2168: 2158: 2153: 2148: 2145: 2138: 2126: 2121: 2118: 2111: 2101: 2096: 2091: 2088: 2081: 2069: 2061: 2056: 2051: 2048: 2041: 2029: 2021: 2016: 2013: 2006: 2003: 1992: 1991: 1990: 1973: 1970: 1967: 1962: 1959: 1952: 1949: 1938: 1937: 1936: 1933: 1927: 1909: 1906: 1898: 1894: 1883: 1880: 1873: 1870: 1853: 1852: 1851: 1848: 1846: 1828: 1825: 1818: 1815: 1804: 1801:, and the 5D 1786: 1783: 1776: 1773: 1747: 1742: 1739: 1732: 1716: 1714: 1710: 1706: 1702: 1678: 1673: 1663: 1659: 1655: 1652: 1647: 1643: 1639: 1633: 1629: 1620: 1616: 1612: 1607: 1603: 1599: 1593: 1589: 1585: 1579: 1576: 1572: 1568: 1563: 1559: 1555: 1549: 1545: 1541: 1535: 1532: 1525: 1522: 1515: 1510: 1506: 1502: 1495: 1494: 1493: 1479: 1476: 1467: 1465: 1461: 1457: 1453: 1434: 1429: 1419: 1415: 1411: 1406: 1401: 1397: 1391: 1387: 1381: 1378: 1374: 1366: 1362: 1358: 1349: 1345: 1341: 1334: 1331: 1327: 1320: 1315: 1310: 1307: 1300: 1297: 1286: 1285: 1284: 1270: 1247: 1242: 1238: 1234: 1229: 1222: 1219: 1211: 1206: 1202: 1196: 1192: 1188: 1183: 1180: 1173: 1170: 1163: 1158: 1155: 1148: 1145: 1137: 1132: 1128: 1122: 1118: 1112: 1108: 1104: 1099: 1096: 1092: 1088: 1083: 1080: 1073: 1070: 1059: 1058: 1057: 1040: 1035: 1027: 1023: 1015: 1011: 1005: 1001: 991: 987: 981: 977: 969: 965: 959: 955: 949: 945: 941: 936: 933: 929: 922: 917: 912: 909: 902: 899: 888: 887: 886: 872: 850: 846: 823: 820: 815: 791: 788: 781: 778: 766: 755: 753: 749: 743: 733: 729: 725: 720: 718: 714: 710: 706: 702: 697: 693: 688: 685: 681: 680:string theory 677: 673: 669: 665: 661: 657: 653: 649: 637: 632: 630: 625: 623: 618: 617: 615: 614: 607: 604: 602: 599: 597: 594: 592: 589: 587: 584: 582: 579: 577: 574: 572: 569: 568: 562: 561: 554: 551: 549: 546: 544: 541: 539: 536: 534: 531: 529: 526: 524: 521: 519: 516: 514: 511: 509: 506: 504: 501: 499: 496: 494: 493:String theory 491: 489: 486: 485: 482: 477: 476: 469: 466: 464: 461: 459: 456: 454: 451: 449: 446: 444: 441: 439: 436: 434: 431: 430: 427: 426:Supersymmetry 422: 421: 414: 411: 409: 406: 404: 401: 399: 396: 394: 391: 389: 386: 384: 381: 379: 376: 374: 371: 369: 366: 364: 361: 359: 356: 354: 351: 349: 346: 344: 341: 339: 336: 334: 331: 329: 328:Mirror matter 326: 324: 321: 319: 316: 314: 311: 309: 308:String theory 306: 304: 301: 299: 296: 294: 291: 289: 286: 284: 281: 279: 276: 274: 271: 269: 266: 264: 261: 259: 256: 254: 251: 249: 246: 244: 241: 240: 234: 233: 226: 223: 221: 218: 216: 213: 211: 208: 206: 203: 201: 198: 196: 193: 191: 188: 186: 183: 181: 178: 177: 171: 170: 167: 164: 163: 158: 154: 151: 145: 141: 140: 137: 134: 133: 124: 121: 113: 102: 99: 95: 92: 88: 85: 81: 78: 74: 71: – 70: 66: 65:Find sources: 59: 53: 52: 48: 43:This article 41: 37: 32: 31: 26: 22: 13905: 13893: 13783:Supergravity 13739: 13643:Constituents 13623:Weak isospin 13581:Color charge 13571:Gauge theory 13018:Arkani-Hamed 12916:Supergravity 12883:Moduli space 12803: 12780: 12775:Dirac string 12701:Gauge theory 12681:Loop algebra 12618:Black string 12481:GS formalism 12277: 11971:Kaluza–Klein 11970: 11723:Introduction 11649:Twin paradox 11359:theories and 11192:Supergravity 11186: 11005: 11001: 10863:Introduction 10759: 10758:Chris Pope, 10750: 10740: 10734: 10699: 10654: 10650: 10631: 10624: 10609: 10584: 10578: 10553: 10547: 10527: 10475: 10471: 10461: 10418: 10414: 10408: 10399: 10388: 10376: 10368: 10352: 10317: 10311: 10294: 10290: 10284: 10259: 10255: 10249: 10227:(1): 29–48. 10224: 10220: 10214: 10203: 10195: 10174: 10166: 10147: 10141: 10122: 10118: 10108: 10099: 10095: 10089: 10056: 10052: 10046: 10027: 10023: 9980: 9974: 9968: 9959: 9955: 9949: 9940: 9936: 9930: 9921: 9917: 9911: 9881:(6): 76–84. 9878: 9874: 9868: 9843: 9839: 9793: 9789: 9779: 9744: 9740: 9692: 9688: 9671:: 1881–1882. 9668: 9664: 9658: 9649: 9645: 9623: 9619: 9613: 9570: 9566: 9520: 9516: 9474: 9468: 9440: 9410: 9404: 9395: 9391: 9381: 9352:Supergravity 9342:Matej Pavšič 9299:brane theory 9296: 9265: 9253: 9231: 9222: 9218: 9202: 9194: 9172: 9093: 9086: 8955: 8817: 8665: 8534: 8412: 8307: 7924: 7895: 7863: 7658: 7649:Ricci tensor 7643: 7639: 7637: 7559: 7488: 7480: 7476: 7474: 7394: 7390: 7379: 7359: 7345: 7333: 7264: 7248: 7244: 7242: 7180: 7123: 7119: 7117: 7105: 7090: 7083: 7070: 7062: 7054: 7046: 7042: 7038: 7033: 7029: 7021: 7006:astrophysics 6999: 6960: 6894: 6887: 6882: 6872:manifold or 6868:, or even a 6841:fiber bundle 6837:gauge theory 6826:circle group 6823: 6808:, so that a 6803: 6797: 6789: 6784: 6780: 6755: 6751:adding to it 6746: 6719: 6649: 6392: 6389: 6380: 6233: 6116: 6070: 5958:of the form 5910: 5693: 5507: 5433: 5329: 5203: 5159: 5068: 4887: 4632: 4304: 4060: 3804: 3718: 3598: 3512: 3383: 3286: 3263: 2879: 2876: 2730: 2726:scalar field 2555: 2426: 2423: 2227: 1988: 1928: 1924: 1849: 1803:Ricci tensor 1717: 1713:Academia.edu 1709:ResearchGate 1705:scalar field 1698: 1468: 1449: 1262: 1055: 761: 744: 721: 701:scalar field 689: 655: 651: 645: 503:Quantum foam 488:False vacuum 453:Supergravity 413:CPT symmetry 282: 195:Quintessence 116: 110:January 2023 107: 97: 90: 83: 76: 64: 44: 13844:Experiments 13735:Technicolor 13697:Dark matter 13591:Quark model 13559:Higgs boson 13554:Gauge boson 13378:Silverstein 12878:Orientifold 12613:Black holes 12608:Black brane 12565:Dual photon 12060:Kerr–Newman 12031:Spherical: 11900:Other tests 11843:Singularity 11775:Formulation 11737:Fundamental 11591:Formulation 11572:Proper time 11533:Fundamental 11161:Causal sets 11055:Brans–Dicke 10873:Mathematics 10530:: 966–972. 10125:: 1263723. 9141:and allows 8674:. Applying 7710:with fiber 7663:describing 7128:Paul Wesson 7086:Planck mass 6967:electroweak 6901:M. Given a 6892:gauge group 6849:gauge group 6815:compact set 1845:connections 748:Brans–Dicke 732:Schrödinger 724:Oskar Klein 664:gravitation 565:Experiments 538:Causal sets 383:Graviscalar 378:Graviphoton 278:Technicolor 253:Fifth force 210:Dark photon 190:Dark energy 185:Dark matter 157:Higgs boson 13923:Categories 13851:Gran Sasso 13675:Beyond the 13650:CKM matrix 13537:Background 13398:Strominger 13393:Steinhardt 13388:Staudacher 13303:Polchinski 13253:Nanopoulos 13213:Mandelstam 13193:Kontsevich 13033:Berenstein 12961:Holography 12941:Superspace 12840:K3 surface 12799:Worldsheet 12714:Instantons 12342:Background 12212:Zel'dovich 12120:Scientists 12099:Alcubierre 11906:of Mercury 11904:precession 11833:Black hole 11716:Background 11708:relativity 11677:World line 11672:Light cone 11497:Background 11489:relativity 11479:Relativity 11375:CGHS model 11362:toy models 10520:References 10485:1801.08160 10478:(7): 048. 10262:(9): 410. 10256:Phys. Lett 10059:(7): 683. 10030:: 901870. 9962:: 547–555. 9943:: 537–551. 9796:(1): 3–5. 9747:(1): 1–2. 9652:: 216–218. 9626:: 529–531. 9221:principal 7487:, and vol( 7336:free space 7057:being the 6991:touchstone 6932:stationary 6903:connection 6876:or even a 6778:The space 6424:Bohr model 3338:such that 740:10 cm 736:10 cm 728:Heisenberg 576:Gran Sasso 348:Dark fluid 148:Simulated 80:newspapers 47:references 13433:Veneziano 13313:Rajaraman 13208:Maldacena 13098:Gopakumar 13048:Dijkgraaf 13043:Curtright 12709:Anomalies 12588:NS5-brane 12509:U-duality 12504:S-duality 12499:T-duality 12182:Robertson 12167:Friedmann 12162:Eddington 12152:de Sitter 11986:Solutions 11864:detectors 11859:astronomy 11826:Phenomena 11761:Geodesics 11664:Spacetime 11607:Phenomena 11380:RST model 11166:DGP model 11143:Spin foam 11087:Whitehead 11079:Nordström 11008:) gravity 10958:Classical 10932:Paradigms 10883:Resources 10773:1401.8048 10755:, (2003). 10739:, (2004) 10689:119087814 10510:119197181 10453:122803232 10428:1012.3375 10393:5Dstm.org 10344:122586403 10081:121977988 9924:(2): 130. 9903:120176841 9580:1204.3455 9322:DGP model 9276:top quark 9257:top quark 9229:Lie group 9181:Λ 9149:Λ 9102:Λ 9026:− 8956:with the 8920:Λ 8882:− 8791:⁡ 8752:Λ 8743:− 8717:∫ 8713:Λ 8701:^ 8634:∗ 8630:π 8583:→ 8574:π 8548:∗ 8544:π 8481:Λ 8475:− 8453:∗ 8449:π 8436:^ 8389:^ 8377:⁡ 8365:^ 8344:∫ 8331:^ 8283:π 8220:∈ 8209:at point 8180:⊂ 8174:⁡ 8138:^ 8076:⊂ 8070:⁡ 8034:^ 7961:^ 7935:Λ 7872:⋆ 7839:⋆ 7750:Ω 7695:→ 7686:π 7588:− 7530:δ 7513:δ 7491:) is the 7483:) is the 7448:⁡ 7424:∫ 7372:spacetime 7284:~ 7225:ν 7222:μ 7214:π 7203:ν 7200:μ 7148:~ 6944:curvature 6854:Lie group 6700:− 6692:∼ 6683:λ 6597:∼ 6588:λ 6583:⇒ 6571:λ 6487:λ 6404:λ 6343:μ 6335:ρ 6289:μ 6275:ρ 6267:μ 6252:~ 6203:ν 6176:μ 6162:ρ 6154:ν 6151:μ 6139:~ 6079:ρ 5999:ρ 5976:~ 5929:~ 5862:ν 5852:ν 5827:τ 5808:ϕ 5792:~ 5770:~ 5748:~ 5709:~ 5663:∂ 5646:~ 5636:∂ 5621:~ 5602:~ 5559:~ 5378:∼ 5306:ϕ 5300:α 5296:∂ 5290:α 5287:μ 5269:− 5261:μ 5249:~ 5246:Γ 5127:→ 5121:τ 5042:ϕ 5038:⁡ 5030:ν 5026:∂ 5020:α 5012:− 5007:ν 5004:α 4987:ϕ 4978:ν 4975:μ 4952:μ 4947:α 4937:~ 4934:Γ 4901:ν 4861:ϕ 4857:⁡ 4849:ν 4845:∂ 4839:β 4829:α 4821:− 4816:ν 4813:α 4803:β 4790:ν 4787:β 4777:α 4760:ϕ 4744:ν 4741:μ 4718:μ 4713:β 4710:α 4706:Γ 4697:μ 4692:β 4689:α 4682:~ 4679:Γ 4646:ν 4601:τ 4588:⁡ 4579:τ 4565:μ 4529:μ 4517:~ 4514:Γ 4492:α 4482:μ 4477:α 4467:~ 4464:Γ 4449:β 4439:α 4429:μ 4424:β 4421:α 4414:~ 4411:Γ 4398:τ 4388:ν 4350:τ 4340:ν 4326:≡ 4321:ν 4259:ν 4245:ν 4225:ϕ 4212:τ 4133:ν 4119:μ 4105:ν 4102:μ 4094:≡ 4085:τ 4031:~ 4012:~ 3985:~ 3982:Γ 3952:~ 3924:~ 3905:~ 3902:∇ 3886:~ 3832:≡ 3820:~ 3773:~ 3734:~ 3698:~ 3677:~ 3657:− 3642:~ 3632:≡ 3617:~ 3577:ϕ 3546:μ 3489:ϵ 3485:π 3446:μ 3421:π 3367:μ 3356:→ 3351:μ 3304:μ 3239:ϕ 3236:◻ 3231:ν 3228:μ 3220:− 3217:ϕ 3212:ν 3208:∇ 3202:μ 3198:∇ 3189:ϕ 3171:β 3168:α 3158:β 3155:α 3145:ν 3142:μ 3124:− 3119:β 3116:ν 3106:α 3103:μ 3093:β 3090:α 3071:ϕ 3045:ν 3042:μ 3024:− 3019:ν 3016:μ 3004:⇒ 2988:~ 2977:ν 2974:μ 2967:~ 2947:− 2942:ν 2939:μ 2932:~ 2896:ν 2893:μ 2854:β 2851:α 2837:ϕ 2828:μ 2824:∇ 2818:μ 2815:β 2786:α 2776:~ 2744:ν 2706:μ 2702:∇ 2676:ν 2672:∇ 2666:μ 2662:∇ 2656:ν 2653:μ 2645:≡ 2642:◻ 2618:α 2608:β 2604:∂ 2600:− 2595:β 2585:α 2581:∂ 2577:≡ 2572:β 2569:α 2536:β 2533:α 2523:β 2520:α 2506:ϕ 2489:ϕ 2486:◻ 2483:⇒ 2465:~ 2435:ϕ 2391:~ 2375:∂ 2371:− 2356:~ 2340:∂ 2321:~ 2305:∂ 2286:~ 2266:≡ 2246:~ 2243:Γ 2196:~ 2193:Γ 2169:~ 2166:Γ 2159:− 2139:~ 2136:Γ 2112:~ 2109:Γ 2082:~ 2079:Γ 2066:∂ 2062:− 2042:~ 2039:Γ 2026:∂ 2022:≡ 2007:~ 1953:~ 1891:∂ 1874:~ 1864:∂ 1819:~ 1777:~ 1733:~ 1730:Γ 1648:ν 1634:ν 1617:ϕ 1608:ν 1594:μ 1580:ν 1577:μ 1526:~ 1516:≡ 1416:ϕ 1402:β 1392:α 1382:β 1379:α 1367:ν 1359:− 1350:μ 1342:− 1335:ν 1332:μ 1316:≡ 1301:~ 1239:ϕ 1235:≡ 1223:~ 1207:ν 1193:ϕ 1189:≡ 1181:ν 1174:~ 1164:≡ 1159:ν 1149:~ 1133:ν 1123:μ 1109:ϕ 1100:ν 1097:μ 1089:≡ 1084:ν 1081:μ 1074:~ 1024:ϕ 1016:ν 1002:ϕ 992:μ 978:ϕ 970:ν 960:μ 946:ϕ 937:ν 934:μ 918:≡ 903:~ 873:ϕ 851:μ 824:ν 821:μ 782:~ 722:In 1926, 656:KK theory 498:Spin foam 393:Gravitino 25:KK-theory 13895:Category 13876:Tevatron 13728:Theories 13685:Evidence 13549:Fermions 13488:Zwiebach 13443:Verlinde 13438:Verlinde 13413:Townsend 13408:Susskind 13343:Sagnotti 13308:Polyakov 13263:Nekrasov 13228:Minwalla 13223:Martinec 13188:Knizhnik 13183:Klebanov 13178:Kapustin 13143:'t Hooft 13078:Fischler 13013:Aganagić 12984:M-theory 12873:Conifold 12868:Orbifold 12851:manifold 12792:Geometry 12598:M5-brane 12593:M2-brane 12530:Graviton 12446:F-theory 12295:Category 12172:Lemaître 12137:Einstein 12127:Poincaré 12087:Others: 12071:Taub–NUT 12037:interior 11959:theories 11957:Advanced 11924:redshift 11739:concepts 11557:Rapidity 11535:concepts 11437:Graviton 11247:F-theory 11240:M-theory 10816:Standard 10468:GW170817 10361:Archived 9820:94454994 9771:93849549 9717:20091903 9605:13399708 9305:See also 9225:-bundles 9214:fermions 8672:K-theory 8668:homology 8564:pullback 6995:K-theory 6987:fermions 6899:manifold 6874:orbifold 6810:particle 6720:Klein's 5887:constant 1932:geodesic 1462:and the 715:for the 601:Tevatron 448:M-theory 388:Graviton 318:M-theory 258:F-theory 237:Theories 174:Evidence 21:K theory 13907:Commons 13871:Super-K 13707:problem 13418:Trivedi 13403:Sundrum 13368:Shenker 13358:Seiberg 13353:Schwarz 13323:Randall 13283:Novikov 13273:Nielsen 13258:Năstase 13168:Kallosh 13153:Gibbons 13093:Gliozzi 13083:Friedan 13073:Ferrara 13058:Douglas 13053:Distler 12603:S-brane 12583:D-brane 12540:Tachyon 12535:Dilaton 12349:Strings 12237:Hawking 12232:Penrose 12217:Novikov 12197:Wheeler 12142:Hilbert 12132:Lorentz 12089:pp-wave 11910:lensing 11706:General 11487:Special 10868:History 10706:Bibcode 10669:Bibcode 10589:Bibcode 10558:Bibcode 10532:Bibcode 10490:Bibcode 10433:Bibcode 10299:Bibcode 10264:Bibcode 10229:Bibcode 10061:Bibcode 9985:Bibcode 9883:Bibcode 9848:Bibcode 9798:Bibcode 9749:Bibcode 9697:Bibcode 9585:Bibcode 9547:4127863 9525:Bibcode 9479:Bibcode 9445:Bibcode 9280:W boson 8562:is the 8205:of the 8153:to the 8049:to the 7884:is the 7779:2-forms 7647:is the 7382:is the 7364:pseudo- 7267:soliton 7051:integer 6897:over a 6862:pseudo- 6847:, with 6670:is the 3564:is the 3533:is the 648:physics 596:Super-K 94:scholar 13483:Zumino 13478:Zaslow 13463:Yoneya 13453:Witten 13373:Siegel 13348:Scherk 13318:Ramond 13293:Ooguri 13218:Marolf 13173:Kaluza 13158:Kachru 13148:Hořava 13138:Harvey 13133:Hanson 13118:Gubser 13108:Greene 13038:Bousso 13023:Atiyah 12575:Branes 12385:Theory 12278:others 12267:Thorne 12257:Misner 12242:Taylor 12227:Geroch 12222:Ehlers 12192:Zwicky 12010:Kasner 10716: 10687: 10638: 10616: 10508: 10451: 10342: 10332: 10183: 10154: 10102:: 113. 10079: 9901: 9818: 9769: 9715: 9603: 9545: 9517:Nature 9398:: 504. 9292:H → γγ 9288:H → γγ 9284:H → γγ 9211:chiral 9163:radion 8535:where 7864:where 7638:where 7475:where 7388:action 7384:metric 7362:be a ( 7358:. Let 7356:action 7348:action 6963:strong 6907:metric 6843:, the 6806:radius 6650:where 6393:Nature 6119:"dust" 6071:where 5160:where 3537:, and 3513:where 3264:where 2556:where 1989:where 711:, the 705:radion 96: 89: 82: 75: 67: 23:, see 13773:NMSSM 13423:Turok 13333:Roček 13298:Ovrut 13288:Olive 13268:Neveu 13248:Myers 13243:Mukhi 13233:Moore 13203:Linde 13198:Klein 13123:Gukov 13113:Gross 13103:Green 13088:Gates 13068:Dvali 13028:Banks 12272:Weiss 12252:Bondi 12247:Hulse 12177:Milne 12081:discs 12025:Milne 12020:Gödel 11877:Virgo 11029:AQUAL 10888:Tests 10769:arXiv 10685:S2CID 10659:arXiv 10506:S2CID 10480:arXiv 10449:S2CID 10423:arXiv 10340:S2CID 10297:: 1. 10077:S2CID 10020:(PDF) 9899:S2CID 9816:S2CID 9767:S2CID 9713:S2CID 9601:S2CID 9575:arXiv 9543:S2CID 9374:Notes 9268:Higgs 7737:is a 7671:of a 7397:) as 7378:. If 7045:with 6979:SU(2) 6975:SU(3) 6890:with 6839:on a 6831:, as 6796:over 571:ANNIE 438:NMSSM 101:JSTOR 87:books 13768:MSSM 13448:Wess 13428:Vafa 13338:Rohm 13238:Motl 13163:Kaku 13128:Guth 13063:Duff 12207:Kerr 12157:Weyl 12056:Kerr 11916:and 11870:and 11868:LIGO 10714:ISBN 10636:ISBN 10614:ISBN 10476:2018 10330:ISBN 10260:106A 10181:ISBN 10152:ISBN 10123:2020 10028:2015 9278:and 9236:U(1) 8061:Vert 7712:U(1) 7065:the 7061:and 7026:mass 7012:and 7004:and 6983:U(1) 6965:and 6829:U(1) 5452:> 2693:and 2228:and 1711:and 1699:The 730:and 666:and 606:NOvA 433:MSSM 73:news 13866:SNO 13861:LHC 13856:INO 13458:Yau 13383:Sơn 13363:Sen 12262:Yau 11887:GEO 10677:doi 10655:283 10597:doi 10585:186 10566:doi 10498:doi 10470:". 10441:doi 10419:697 10322:doi 10295:294 10272:doi 10237:doi 10225:226 10127:doi 10069:doi 10032:doi 9993:doi 9981:124 9891:doi 9856:doi 9844:276 9806:doi 9757:doi 9705:doi 9669:226 9650:226 9624:224 9593:doi 9533:doi 9521:118 9487:doi 8788:vol 8374:vol 8275:at 8255:on 8165:Hor 7828:and 7675:or 7445:vol 7374:of 7122:or 7093:CDF 7049:an 6753:. 3758:or 662:of 646:In 591:SNO 586:LHC 581:INO 153:CMS 49:to 13925:: 12759:, 12752:, 12745:, 12738:, 11936:/ 11902:: 11857:: 10712:. 10683:. 10675:. 10667:. 10653:. 10595:. 10583:. 10564:. 10554:37 10552:. 10504:. 10496:. 10488:. 10474:. 10447:. 10439:. 10431:. 10417:. 10338:. 10328:. 10293:. 10270:. 10258:. 10235:. 10223:. 10121:. 10117:. 10100:52 10098:. 10075:. 10067:. 10057:21 10055:. 10026:. 10022:. 10005:^ 9991:. 9979:. 9960:23 9941:22 9939:. 9922:14 9897:. 9889:. 9877:. 9854:. 9828:^ 9814:. 9804:. 9794:2a 9788:. 9765:. 9755:. 9745:2a 9739:. 9725:^ 9711:. 9703:. 9693:11 9677:^ 9632:^ 9599:. 9591:. 9583:. 9571:44 9569:. 9555:^ 9541:. 9531:. 9519:. 9515:. 9499:^ 9485:. 9475:37 9457:^ 9419:^ 9396:15 9263:. 9165:. 9127:55 9091:. 7888:. 7849:0. 7651:. 7644:ij 7326:. 7249:μν 7103:. 7088:. 7053:, 7043:Rc 7039:nh 7037:= 6997:. 6981:× 6977:× 6973:, 6880:. 6821:. 6783:× 6703:30 6696:10 5460:20 5456:10 5256:55 5231:, 5035:ln 4919:: 4854:ln 4618:0. 4585:ln 4524:55 4046:0. 3868:: 3381:. 2472:55 1910:0. 1847:. 1492:: 1230:55 650:, 60:. 13522:e 13515:t 13508:v 12849:2 12847:G 12816:? 12781:p 12766:) 12763:8 12761:E 12756:7 12754:E 12749:6 12747:E 12742:4 12740:F 12735:2 12733:G 12731:( 12327:e 12320:t 12313:v 12062:) 12058:( 12044:) 12035:( 12001:) 11997:( 11944:) 11940:( 11920:) 11889:) 11866:( 11515:) 11506:( 11471:e 11464:t 11457:v 11006:R 11004:( 11002:f 10801:e 10794:t 10787:v 10771:: 10764:. 10722:. 10708:: 10691:. 10679:: 10671:: 10661:: 10644:. 10622:. 10603:. 10599:: 10591:: 10572:. 10568:: 10560:: 10538:. 10534:: 10512:. 10500:: 10492:: 10482:: 10455:. 10443:: 10435:: 10425:: 10371:) 10346:. 10324:: 10305:. 10301:: 10278:. 10274:: 10266:: 10243:. 10239:: 10231:: 10189:. 10160:. 10135:. 10129:: 10083:. 10071:: 10063:: 10040:. 10034:: 9999:. 9995:: 9987:: 9905:. 9893:: 9885:: 9879:2 9862:. 9858:: 9850:: 9822:. 9808:: 9800:: 9773:. 9759:: 9751:: 9719:. 9707:: 9699:: 9607:. 9595:: 9587:: 9577:: 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7843:F 7834:d 7823:0 7820:= 7817:F 7813:d 7789:M 7765:) 7762:M 7759:( 7754:2 7725:F 7698:M 7692:P 7689:: 7640:R 7623:, 7620:0 7617:= 7614:R 7609:j 7606:i 7602:g 7596:2 7593:1 7583:j 7580:i 7576:R 7545:, 7542:0 7539:= 7533:g 7525:) 7522:g 7519:( 7516:S 7489:g 7481:g 7479:( 7477:R 7460:, 7457:) 7454:g 7451:( 7442:) 7439:g 7436:( 7433:R 7428:M 7420:= 7417:) 7414:g 7411:( 7408:S 7395:g 7393:( 7391:S 7380:g 7366:) 7360:M 7302:0 7299:= 7294:b 7291:a 7281:R 7245:T 7218:T 7211:8 7208:= 7196:G 7166:0 7163:= 7158:b 7155:a 7145:R 7063:c 7055:h 7047:n 7041:/ 7034:n 7030:M 7022:R 6946:( 6895:G 6888:P 6864:) 6800:. 6798:M 6790:C 6785:C 6781:M 6760:) 6756:( 6687:5 6658:h 6635:, 6629:q 6626:c 6619:2 6615:/ 6611:1 6607:G 6603:h 6592:5 6575:5 6567:h 6562:= 6555:2 6551:/ 6547:1 6543:G 6538:q 6535:c 6529:= 6524:5 6520:U 6516:m 6491:5 6482:/ 6478:h 6475:= 6470:5 6466:p 6439:5 6435:U 6408:5 6366:. 6360:c 6357:m 6354:k 6350:q 6339:U 6332:= 6326:s 6323:d 6316:5 6312:x 6308:d 6299:s 6296:d 6285:x 6281:d 6272:= 6264:5 6259:M 6249:T 6219:. 6213:s 6210:d 6199:x 6195:d 6186:s 6183:d 6172:x 6168:d 6159:= 6146:M 6136:T 6102:s 6099:d 6056:, 6050:s 6047:d 6040:b 6036:x 6032:d 6023:s 6020:d 6013:a 6009:x 6005:d 5996:= 5991:b 5988:a 5983:M 5973:T 5944:b 5941:a 5936:M 5926:T 5891:. 5883:= 5880:) 5875:5 5871:U 5867:+ 5858:U 5848:A 5844:k 5841:( 5835:s 5832:d 5824:d 5820:c 5812:2 5804:= 5799:a 5789:U 5780:a 5777:5 5767:g 5760:= 5755:5 5745:U 5716:5 5706:U 5679:. 5671:a 5667:x 5656:c 5653:b 5643:g 5628:c 5618:U 5609:b 5599:U 5590:2 5587:1 5582:= 5576:s 5573:d 5566:a 5556:U 5549:d 5521:5 5517:U 5490:5 5486:U 5465:c 5447:5 5443:U 5419:. 5412:2 5408:/ 5404:1 5400:G 5395:m 5391:/ 5387:q 5381:c 5373:5 5369:U 5343:5 5339:U 5315:. 5310:2 5283:g 5277:2 5274:1 5266:= 5217:5 5213:U 5188:q 5168:m 5145:, 5139:c 5136:m 5132:q 5118:d 5111:5 5107:x 5103:d 5097:k 5094:= 5089:5 5085:U 5081:k 5054:. 5051:) 5046:2 5016:A 5000:F 4996:( 4991:2 4983:k 4971:g 4965:2 4962:1 4957:= 4944:5 4897:U 4873:. 4870:) 4865:2 4835:A 4825:A 4809:F 4799:A 4795:+ 4783:F 4773:A 4769:( 4764:2 4754:2 4750:k 4737:g 4731:2 4728:1 4723:+ 4702:= 4642:U 4615:= 4609:s 4606:d 4598:d 4594:c 4576:d 4572:d 4561:U 4557:+ 4552:2 4548:) 4542:5 4538:U 4534:( 4507:+ 4502:5 4498:U 4488:U 4474:5 4457:2 4454:+ 4445:U 4435:U 4404:+ 4395:d 4384:U 4380:d 4356:, 4347:d 4336:x 4332:d 4317:U 4290:. 4285:2 4281:) 4275:5 4271:x 4267:d 4264:+ 4255:x 4251:d 4241:A 4237:k 4234:( 4229:2 4221:+ 4216:2 4208:d 4202:2 4198:c 4194:= 4189:2 4185:s 4181:d 4158:s 4155:d 4129:x 4125:d 4115:x 4111:d 4098:g 4089:2 4081:d 4075:2 4071:c 4043:= 4038:c 4028:U 4019:b 4009:U 4000:a 3995:c 3992:b 3975:+ 3969:s 3966:d 3959:a 3949:U 3942:d 3936:= 3931:a 3921:U 3912:b 3893:b 3883:U 3856:s 3853:d 3849:/ 3843:a 3839:x 3835:d 3827:a 3817:U 3783:b 3780:a 3770:R 3744:b 3741:a 3731:G 3704:, 3695:R 3687:b 3684:a 3674:g 3665:2 3662:1 3652:b 3649:a 3639:R 3627:b 3624:a 3614:G 3581:2 3550:0 3521:G 3498:, 3493:0 3482:4 3475:2 3471:c 3466:G 3463:2 3457:= 3450:0 3442:1 3433:4 3429:c 3424:G 3418:8 3412:= 3407:2 3402:2 3398:k 3363:A 3359:k 3347:A 3326:k 3300:A 3272:R 3245:, 3242:) 3224:g 3194:( 3186:1 3181:+ 3177:) 3164:F 3151:F 3138:g 3132:4 3129:1 3112:F 3099:F 3086:g 3081:( 3075:2 3065:2 3062:1 3057:= 3050:R 3038:g 3032:2 3029:1 3012:R 3001:0 2998:= 2985:R 2964:g 2955:2 2952:1 2929:R 2889:R 2862:. 2859:) 2847:F 2841:3 2833:( 2811:g 2805:2 2802:1 2797:= 2794:0 2791:= 2783:5 2773:R 2740:A 2681:, 2649:g 2623:, 2614:A 2591:A 2565:F 2541:, 2529:F 2516:F 2510:3 2500:4 2497:1 2492:= 2480:0 2477:= 2462:R 2409:. 2406:) 2401:c 2398:b 2388:g 2379:d 2366:b 2363:d 2353:g 2344:c 2336:+ 2331:c 2328:d 2318:g 2309:b 2301:( 2296:d 2293:a 2283:g 2274:2 2271:1 2261:a 2256:c 2253:b 2211:d 2206:c 2203:a 2184:c 2179:d 2176:b 2154:d 2149:b 2146:a 2127:c 2122:d 2119:c 2102:+ 2097:c 2092:a 2089:c 2070:b 2057:c 2052:b 2049:a 2030:c 2017:b 2014:a 2004:R 1974:, 1971:0 1968:= 1963:b 1960:a 1950:R 1907:= 1899:5 1895:x 1884:b 1881:a 1871:g 1829:b 1826:a 1816:R 1787:b 1784:a 1774:g 1748:a 1743:c 1740:b 1679:. 1674:2 1670:) 1664:5 1660:x 1656:d 1653:+ 1644:x 1640:d 1630:A 1626:( 1621:2 1613:+ 1604:x 1600:d 1590:x 1586:d 1573:g 1569:= 1564:b 1560:x 1556:d 1550:a 1546:x 1542:d 1536:b 1533:a 1523:g 1511:2 1507:s 1503:d 1480:s 1477:d 1435:. 1430:] 1420:2 1412:1 1407:+ 1398:A 1388:A 1375:g 1363:A 1346:A 1328:g 1321:[ 1311:b 1308:a 1298:g 1271:5 1248:, 1243:2 1220:g 1212:, 1203:A 1197:2 1184:5 1171:g 1156:5 1146:g 1138:, 1129:A 1119:A 1113:2 1105:+ 1093:g 1071:g 1041:. 1036:] 1028:2 1012:A 1006:2 988:A 982:2 966:A 956:A 950:2 942:+ 930:g 923:[ 913:b 910:a 900:g 847:A 816:g 792:b 789:a 779:g 654:( 635:e 628:t 621:v 123:) 117:( 112:) 108:( 98:· 91:· 84:· 77:· 54:. 27:.

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Knowledge

Kaluza–Klein theory

Index