287:
29:
203:
233:
268:
3722:
2436:
2378:
2967:
173:; the collimated jets about their polar axis; and the asymmetrical jets (relative to the orbital plane). All of those observed properties could be explained in terms of gravitomagnetic effects. Williams's application of Penrose's mechanism can be applied to black holes of any size. Relativistic jets can serve as the largest and brightest form of validations for gravitomagnetism.
1293:
2773:
286:
1714:
3278:
820:
2324:
Some higher-order gravitomagnetic effects can reproduce effects reminiscent of the interactions of more conventional polarized charges. For instance, if two wheels are spun on a common axis, the mutual gravitational attraction between the two wheels will be greater if they spin in opposite directions
133:
field, or velocity-dependent acceleration, is that a moving object near a massive, rotating object will experience acceleration that deviates from that predicted by a purely
Newtonian gravity (gravitoelectric) field. More subtle predictions, such as induced rotation of a falling object and precession
2293:
by â1. These factors variously modify the analogues of the equations for the
Lorentz force. There is no scaling choice that allows all the GEM and EM equations to be perfectly analogous. The discrepancy in the factors arises because the source of the gravitational field is the second order
928:
1562:
1157:
2962:{\displaystyle \mathbf {A} _{\text{g}}=-{\frac {G}{2c^{2}}}{\frac {\mathbf {L} \times \mathbf {r} }{r^{3}}}\quad {\text{with}}\quad \mathbf {L} ={\frac {2}{5}}mR^{2}\mathbf {\omega } \quad {\text{or}}\quad L=I_{\text{ball}}\omega ={\frac {2mR^{2}}{5}}{\frac {2\pi }{T}}\quad }
3818:
Note that the GEM equations are invariant under translations and spatial rotations, just not under boosts and more general curvilinear transformations. Maxwell's equations can be formulated in a way that makes them invariant under all of these coordinate transformations.
2352:
corkscrew-like gravitational field around the object. The reaction forces to dragging at the inner and outer equators would normally be expected to be equal and opposite in magnitude and direction respectively in the simpler case involving only minor-axis spin. When
1956:
3815:, there is no way to calculate the GEM variables of one such frame from the GEM variables of the other, unlike the situation with the variables of electromagnetism. Indeed, their predictions (about what motion is free fall) will probably conflict with each other.
2733:
2186:
3531:
1374:
630:
2340:" rotation) will tend to pull matter through the throat (a case of rotational frame dragging, acting through the throat). In theory, this configuration might be used for accelerating objects (through the throat) without such objects experiencing any
1568:
3138:
2029:
698:
2574:
3387:
690:
2247:
120:
different from that of a freely moving inertial body. This apparent field may be described by two components that act respectively like the electric and magnetic fields of electromagnetism, and by analogy these are called the
420:
826:
469:
3708:. When such fast motion and such strong gravitational fields exist in a system, the simplified approach of separating gravitomagnetic and gravitoelectric forces can be applied only as a very rough approximation.
1429:
2637:
2347:
Consider a toroidal mass with two degrees of rotation (both major axis and minor-axis spin, both turning inside out and revolving). This represents a "special case" in which gravitomagnetic effects generate a
1288:{\displaystyle \mathbf {E} _{\text{g}}:=-{\mbox{grad}}~\phi _{\text{g}}-{\frac {\partial \mathbf {A} _{\text{g}}}{\partial t}}=-\nabla ~\phi _{\text{g}}-{\frac {\partial \mathbf {A} _{\text{g}}}{\partial t}}}
2259:
The literature does not adopt a consistent scaling for the gravitoelectric and gravitomagnetic fields, making comparison tricky. For example, to obtain agreement with
Mashhoon's writings, all instances of
1441:
3699:
516:
1764:
3056:
1875:
2645:
2099:
1095:
Faraday's law of induction (third line of the table) and the
Gaussian law for the gravitomagnetic field (second line of the table) can be solved by the definition of a gravitation potential
554:
3417:
1304:
2765:
1841:
1149:
202:
3577:
562:
267:
3704:
equals about 166 Hz. This would be easy to notice. However, the pulsar is spinning at a quarter of the speed of light at the equator, and its radius is only three times its
1709:{\displaystyle -{\frac {1}{c^{2}}}{\frac {\partial ^{2}\mathbf {A} _{\text{g}}}{\partial t^{2}}}+\nabla ^{2}~\mathbf {A} _{\text{g}}={\frac {4\pi G}{c^{2}}}\rho _{g}\mathbf {v} }
3273:{\displaystyle \mathbf {B} _{\text{g}}=\nabla \times \mathbf {A} _{\text{g}}={\frac {G}{2c^{2}}}{\frac {\mathbf {L} -3(\mathbf {L} \cdot \mathbf {r} /r)\mathbf {r} /r}{r^{3}}},}
2599:
1801:
1120:
815:{\displaystyle \nabla \times \mathbf {B} _{\text{g}}-{\frac {1}{c^{2}}}{\frac {\partial \mathbf {E} _{\text{g}}}{\partial t}}=-{\frac {4\pi G}{c^{2}}}\mathbf {J} _{\text{g}}}
1962:
2995:
301:
of a solid sphere immersed in fluid, analogous directions and senses of rotation as magnetism, analogous interaction to frame dragging for the gravitomagnetic interaction.
3089:
5334:
2494:
129:
fields, since these arise in the same way around a mass that a moving electric charge is the source of electric and magnetic fields. The main consequence of the
3316:
185:
636:
232:
5114:
2192:
322:
produced by a rotating object (or any rotating massâenergy) can, in a particular limiting case, be described by equations that have the same form as in
5169:
4573:
923:{\displaystyle \nabla \times \mathbf {B} -{\frac {1}{c^{2}}}{\frac {\partial \mathbf {E} }{\partial t}}={\frac {1}{\epsilon _{0}c^{2}}}\mathbf {J} }
362:
4594:
4170:
R.K. Williams (2001). "Collimated energyâmomentum extraction from rotating black holes in quasars and microquasars using the
Penrose mechanism".
1431:
into the
Gaussian law for the gravitation field (first line of the table) and AmpĂšre's circuital law (fourth line of the table) and applying the
5471:
426:
4006:
R.K. Williams (1995). "Extracting x rays, Îł rays, and relativistic ee pairs from supermassive Kerr black holes using the
Penrose mechanism".
2310:. This can be traced back to the spin-2 character of the gravitational field, in contrast to the electromagnetism being a spin-1 field. (See
3613:. Such a field is extremely weak and requires extremely sensitive measurements to be detected. One experiment to measure such field was the
1855:
is "small", in a stationary system, the net (Lorentz) force acting on it due to a GEM field is described by the following GEM analog to the
4698:
Causality, electromagnetic induction, and gravitation : a different approach to the theory of electromagnetic and gravitational fields
3783:
1382:
2488:
A rotating spherical body with a homogeneous density distribution produces a stationary gravitomagnetic potential, which is described by:
4049:
R.K. Williams (2004). "Collimated escaping vortical polar ee jets intrinsically produced by rotating black holes and
Penrose processes".
2604:
5277:
1557:{\displaystyle -{\frac {1}{c^{2}}}{\frac {\partial ^{2}\phi _{\text{g}}}{\partial t^{2}}}+\nabla ^{2}~\phi _{\text{g}}=4\pi G\rho _{g}}
19:
This article is about the gravitational analog of electromagnetism as a whole. For the specific gravitational analog of magnetism, see
4108:
5199:
3743:
2453:
93:
5775:
5595:
81:
effects of moving electric charge. The most common version of GEM is valid only far from isolated sources, and for slowly moving
5448:
5754:
5703:
5262:
5135:
3635:
477:
5780:
5247:
5162:
4955:
4912:
4727:
4705:
4683:
4664:
4521:
4494:
4426:
4284:
3936:
3874:
2357:
rotations are applied simultaneously, these two sets of reaction forces can be said to occur at different depths in a radial
1722:
5837:
5525:
5456:
5432:
5405:
1951:{\displaystyle \mathbf {F} _{\text{g}}=m\left(\mathbf {E} _{\text{g}}\ +\mathbf {v} \times 4\mathbf {B} _{\text{g}}\right)}
88:
The analogy and equations differing only by some small factors were first published in 1893, before general relativity, by
3006:
5579:
2728:{\displaystyle \nabla ^{2}\mathbf {A} _{\text{g}}=-{\frac {4\pi G}{c^{2}}}\rho _{g}\mathbf {\omega } \times \mathbf {r} }
3911:
Unified Field
Mechanics: Natural Science Beyond the Veil of Spacetime, Morgan State University, USA, 16â19 November 2014
2364:
Modelling this complex behaviour as a curved spacetime problem has yet to be done and is believed to be very difficult.
2181:{\displaystyle {\mathcal {S}}_{\text{g}}=-{\frac {c^{2}}{4\pi G}}\mathbf {E} _{\text{g}}\times 4\mathbf {B} _{\text{g}}}
5760:
5308:
5291:
5232:
5413:
5242:
4642:
4623:
4604:
4583:
4227:
3769:
2475:
2417:
3751:
2395:
5155:
4545:
3526:{\displaystyle B_{\text{g, Earth}}={\frac {G}{5c^{2}}}{\frac {m}{r}}{\frac {2\pi }{T}}={\frac {2\pi rg}{5c^{2}T}},}
1369:{\displaystyle \mathbf {B} _{\text{g}}:={\mbox{rot}}~\mathbf {A} _{\text{g}}=\nabla \times \mathbf {A} _{\text{g}}}
522:
1843:
can also be solved for a rotating spherical body (which is a stationary case) leading to gravitomagnetic moments.
5214:
28:
5520:
5442:
5209:
3747:
2457:
5111:
3879:
625:{\displaystyle \nabla \times \mathbf {E} _{\text{g}}+{\frac {\partial \mathbf {B} _{\text{g}}}{\partial t}}=0}
5713:
5237:
3284:
2741:
2361:
that extends across the rotating torus, making it more difficult to establish that cancellation is complete.
1817:
1125:
162:
3586:
From this calculation it follows that the strength of the Earth's equatorial gravitomagnetic field is about
4996:
L. Filipe Costa; Carlos A. R. Herdeiro (2008). "A gravito-electromagnetic analogy based on tidal tensors".
3964:
3629:(which rotates 716 times per second), assuming a radius of 16 km and a mass of two solar masses, then
3539:
2325:
than in the same direction. This can be expressed as an attractive or repulsive gravitomagnetic component.
62:
5832:
5827:
5498:
5392:
5382:
5257:
3869:
2312:
2582:
1773:
5698:
5340:
5252:
5204:
4211:
3063:
2399:
2388:
323:
134:
of a spinning object are among the last basic predictions of general relativity to be directly tested.
2024:{\displaystyle \mathbf {F} _{\text{e}}=q\left(\mathbf {E} \ +\ \mathbf {v} \times \mathbf {B} \right)}
1098:
5492:
5487:
3906:
5043:
A. Bakopoulos; P. Kanti (2016). "Novel
Ansatzes and Scalar Quantities in Gravito-Electromagnetism".
4267:
5708:
5589:
5418:
4895:
4409:
3805:
3732:
2295:
113:
66:
2978:
77:
is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the
5623:
5556:
3859:
3849:
3736:
2446:
346:, called the "GEM equations", can be derived. GEM equations compared to Maxwell's equations are:
327:
170:
2569:{\displaystyle \nabla ^{2}\mathbf {A} _{\text{g}}=-{\frac {4\pi G}{c^{2}}}\rho _{g}\mathbf {v} }
5540:
5424:
4890:
4652:
4404:
4262:
4239:
B. Mashhoon; F. Gronwald; H.I.M. Lichtenegger (2001), "Gravitomagnetism and the Clock Effect",
3071:
1058:
339:
5672:
5651:
5644:
5584:
5739:
5658:
5637:
5630:
5505:
5360:
5318:
5062:
5015:
4984:
4882:
4869:
Reference Frames and Gravitomagnetism â Proceedings of the XXIII Spanish Relativity Meeting
4839:
4800:
4763:
4459:
4396:
4383:
Reference Frames and Gravitomagnetism â Proceedings of the XXIII Spanish Relativity Meeting
4326:
4254:
4185:
4127:
4068:
4015:
3988:
3884:
3705:
8:
3382:{\displaystyle \mathbf {B} _{\text{g}}={\frac {G}{2c^{2}}}{\frac {\mathbf {L} }{r^{3}}},}
2349:
1808:
1070:
946:
331:
319:
177:
5066:
5019:
4988:
4886:
4843:
4804:
4767:
4463:
4400:
4330:
4258:
4222:
Gravitation and Inertia, I. Ciufolini and J.A. Wheeler, Princeton Physics Series, 1995,
4189:
4131:
4072:
4019:
3992:
685:{\displaystyle \nabla \times \mathbf {E} +{\frac {\partial \mathbf {B} }{\partial t}}=0}
5801:
5267:
5224:
5078:
5052:
5031:
5005:
4974:
4931:
4918:
4872:
4855:
4829:
4779:
4753:
4432:
4386:
4361:
4342:
4316:
4290:
4244:
4175:
4117:
4084:
4058:
3942:
3914:
3864:
3834:
3580:
3392:
3288:
315:
117:
109:
70:
55:
5130:
Measurement of Gravitomagnetic and Acceleration Fields Around Rotating Superconductors
4820:
R.T. Jantzen; P. Carini; D. Bini (1992). "The Many Faces of Gravitoelectromagnetism".
4775:
4338:
1811:. In this way GEM can be regarded as a generalization of Newton's gravitation theory.
5785:
5693:
5437:
5365:
5101:
5082:
4951:
4922:
4908:
4851:
4723:
4715:
4701:
4693:
4679:
4660:
4638:
4619:
4600:
4579:
4527:
4517:
4490:
4436:
4422:
4280:
4223:
4031:
3946:
3932:
3811:
Although GEM may hold approximately in two different reference frames connected by a
3059:
2307:
2303:
1807:
is obtained under non-stationary conditions. GEM therefore predicts the existence of
154:
5035:
4783:
4346:
4294:
184:
satellite experiment, to see whether they are consistent with gravitomagnetism. The
5767:
5461:
5355:
5070:
5023:
4900:
4859:
4847:
4808:
4771:
4467:
4414:
4334:
4272:
4193:
4135:
4088:
4076:
4023:
3960:
3924:
3626:
3601:
3298:-factor by taking into account relativistic calculations. At the equatorial plane,
3294:
is two. This factor of two can be explained completely analogous to the electron's
3092:
2998:
2242:{\displaystyle {\mathcal {S}}=c^{2}\varepsilon _{0}\mathbf {E} \times \mathbf {B} }
1767:
1079:
343:
274:
239:
218:
138:
137:
Indirect validations of gravitomagnetic effects have been derived from analyses of
89:
51:
5466:
5387:
5347:
5313:
5118:
4513:
Inertia and gravitation : the fundamental nature and structure of spaceâtime
3854:
3844:
3614:
2333:
2080:
2067:
1049:
293:
253:
181:
158:
33:
4155:
R.K. Williams (2005). "Gravitomagnetic field and Penrose scattering processes".
5666:
5027:
4904:
4744:
S.J. Clark; R.W. Tucker (2000). "Gauge symmetry and gravito-electromagnetism".
4418:
4307:
S.J. Clark; R.W. Tucker (2000). "Gauge symmetry and gravito-electromagnetism".
3928:
3839:
3607:
3583:. The field direction coincides with the angular moment direction, i.e. north.
2358:
1083:
996:
974:
956:
335:
298:
244:
146:
82:
78:
20:
5074:
4140:
4103:
2298:, as opposed to the source of the electromagnetic field being the first order
415:{\displaystyle \nabla \cdot \mathbf {E} _{\text{g}}=-4\pi G\rho _{\text{g}}\ }
5821:
5603:
5272:
5140:
4531:
4027:
3980:
3812:
2302:
tensor. This difference becomes clearer when one compares non-invariance of
2048:
1856:
1804:
142:
4276:
5561:
5370:
4035:
3829:
2299:
1432:
5147:
4511:
5530:
5129:
4571:
4241:
Gyros, Clocks, Interferometers ...: Testing Relativistic Gravity in Space
4238:
4180:
4063:
3801:
3307:
105:
58:
5124:
464:{\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\epsilon _{0}}}}
5744:
2460: in this section. Unsourced material may be challenged and removed.
2337:
150:
5010:
4979:
4936:
4877:
4834:
4812:
4758:
4471:
4391:
4366:
4321:
4249:
4197:
5749:
5731:
5535:
5512:
1424:{\displaystyle \left(\phi _{\text{g}},\mathbf {A} _{\text{g}}\right)}
1008:
4995:
4212:
https://www.slac.stanford.edu/pubs/slacpubs/14750/slac-pub-14775.pdf
3721:
2767:. The analytical solution outside of the body is (see for example):
2435:
5806:
5616:
5609:
5057:
4965:
M. Tajmar; C.J. de Matos (2001). "Gravitomagnetic Barnett Effect".
4509:
4122:
4080:
3966:
Electromagnetic Theory: A Gravitational and Electromagnetic Analogy
3919:
2044:
1039:
180:
is currently analyzing data from the first direct test of GEM, the
157:, University of Florida, developed a rigorous proof that validated
3983:(1969). "Gravitational collapse: The role of general relativity".
2632:{\displaystyle \mathbf {v} =\mathbf {\omega } \times \mathbf {r} }
149:-related effects for extracting energy and momentum from rotating
5178:
3408:
2367:
2341:
986:
165:
could account for the observed high energies and luminosities of
47:
5096:
4546:"2*pi*radius of Earth*earth gravity/(5*c^2*day) â Google Search"
2328:
Gravitomagnetic arguments also predict that a flexible or fluid
5125:
Gravitomagnetic London Moment â New test of General Relativity?
4930:
B. Mashhoon (2003). "Gravitoelectromagnetism: a Brief Review".
4360:
B. Mashhoon (2008). "Gravitoelectromagnetism: A Brief Review".
3112:
2329:
166:
1770:
of the classical gravitation theory is obtained. In a vacuum (
326:. Starting from the basic equation of general relativity, the
5398:
4635:
Spacetime and Geometry: An Introduction to General Relativity
3404:
65:
and an approximation, valid under certain conditions, to the
4819:
4243:, Lecture Notes in Physics, vol. 562, pp. 83â108,
3395:
have equal gravitomagnetic and gravitoelectric components.
3287:
rate. This suggests that the gravitomagnetic analog of the
3102:
2057:
280:, same field profile, and field generation due to rotation.
4510:
Pfister, Herbert, 1936-; King, Markus (24 February 2015).
32:
Diagram regarding the confirmation of gravitomagnetism by
16:
Analogies between Maxwell's and Einstein's field equations
5136:
Test of the LenseâThirring effect with the MGS Mars probe
5105:
4616:
Gravity: An Introduction to Einstein's General Relativity
2738:
has to be solved to obtain the gravitomagnetic potential
1435:
the following inhomogeneous wave-equations are obtained:
3694:{\displaystyle B_{\text{g}}={\frac {2\pi Gm}{5rc^{2}T}}}
2079:
The GEM Poynting vector compared to the electromagnetic
511:{\displaystyle \nabla \cdot \mathbf {B} _{\text{g}}=0\ }
4964:
4572:
M. P. Hobson; G. P. Efstathiou; A. N. Lasenby (2006).
3907:"Pre-metric electromagnetism as a path to unification"
1759:{\displaystyle \partial \phi _{\text{g}}/\partial t=0}
1324:
1180:
186:
Apache Point Observatory Lunar Laser-ranging Operation
5042:
4743:
4306:
3638:
3542:
3420:
3319:
3141:
3074:
3009:
2981:
2776:
2744:
2648:
2607:
2585:
2497:
2398:. Please help to ensure that disputed statements are
2195:
2102:
1965:
1878:
1820:
1776:
1725:
1571:
1444:
1385:
1307:
1160:
1128:
1101:
829:
701:
639:
565:
525:
480:
429:
365:
4948:
Measuring Gravitomagnetism: A Challenging Enterprise
4676:
Measuring Gravitomagnetism: A Challenging Enterprise
3051:{\displaystyle I_{\text{ball}}={\frac {2mR^{2}}{5}}}
1814:
The wave equation for the gravitomagnetic potential
5104:
news on tentative result of European Space Agency (
5102:Gyroscopic Superconducting Gravitomagnetic Effects
4791:R.L. Forward (1963). "Guidelines to Antigravity".
4655:(1990). "Gravity's next prize: Gravitomagnetism".
4575:General Relativity: An Introduction for Physicists
4450:R.L. Forward (1963). "Guidelines to Antigravity".
3693:
3571:
3525:
3381:
3272:
3083:
3050:
2989:
2961:
2759:
2727:
2631:
2593:
2568:
2241:
2180:
2023:
1950:
1835:
1795:
1758:
1708:
1556:
1423:
1368:
1287:
1143:
1114:
922:
814:
684:
624:
548:
510:
463:
414:
4659:. Scientific American Library. pp. 232â233.
3969:. Vol. 1. The Electrician. pp. 455â464.
3625:If the preceding formula is used with the pulsar
2601:the velocity inside the body can be described as
5819:
4599:. Cambridge University Press. pp. 200â207.
4578:. Cambridge University Press. pp. 490â491.
3904:
188:also plans to observe gravitomagnetism effects.
4867:B. Mashhoon (2000). "Gravitoelectromagnetism".
4381:B. Mashhoon (2000). "Gravitoelectromagnetism".
5472:Degenerate Higher-Order Scalar-Tensor theories
4714:
4692:
3782:While Maxwell's equations are invariant under
2368:Gravitomagnetic fields of astronomical objects
5163:
4169:
4154:
4048:
4005:
3880:Speed of gravity § Electrodynamical analogies
549:{\displaystyle \nabla \cdot \mathbf {B} =0\ }
5097:Gravity Probe B: Testing Einstein's Universe
4790:
4651:
4613:
4484:
4449:
4210:Gravitomagnetism in Quantum Mechanics, 2014
3959:
3786:, the GEM equations are not. The fact that
2267:in the GEM equations must be multiplied by â
967:is the gravitomagnetic field, with SI unit s
5177:
4929:
4866:
4592:
4380:
4359:
4104:"Gravitational fields of the magnetic-type"
3750:. Unsourced material may be challenged and
2316:for more on "spin-1" and "spin-2" fields).
945:is the gravitoelectric field (conventional
5170:
5156:
4632:
4157:Annals of the New York Academy of Sciences
3979:
3125:The formula for the gravitomagnetic field
5056:
5009:
4978:
4935:
4894:
4876:
4833:
4757:
4408:
4390:
4365:
4320:
4266:
4248:
4179:
4139:
4121:
4109:International Journal of Modern Physics D
4062:
3918:
3770:Learn how and when to remove this message
2476:Learn how and when to remove this message
2418:Learn how and when to remove this message
4945:
4673:
4101:
2394:Relevant discussion may be found on the
145:had proposed a mechanism that relies on
27:
5776:Gravitational interaction of antimatter
4095:
3804:(instead they are merely a part of the
3310:vanishes, and this formula reduces to:
2760:{\displaystyle \mathbf {A} _{\text{g}}}
2336:rotational acceleration (accelerating "
2319:
1836:{\displaystyle \mathbf {A} _{\text{g}}}
1144:{\displaystyle \mathbf {A} _{\text{g}}}
5820:
1042:of the mass flow), with SI unit kgâ
mâ
s
5781:Physics in the medieval Islamic world
5704:(2+1)-dimensional topological gravity
5200:Newton's law of universal gravitation
5151:
4618:. Addison-Wesley. pp. 296, 303.
3875:Non-Relativistic Gravitational Fields
3711:
3572:{\displaystyle g=G{\frac {m}{r^{2}}}}
94:Newton's law of universal gravitation
5526:Asymptotic safety in quantum gravity
4657:A journey into gravity and spacetime
3748:adding citations to reliable sources
3715:
2458:adding citations to reliable sources
2429:
2371:
2254:
116:makes an apparent field appear in a
5132:M. Tajmar, et al., 17 October 2006.
4174:. Vol. 586. pp. 448â453.
4159:. Vol. 1045. pp. 232â245.
3808:) is the basis of this difference.
2579:Due to the body's angular velocity
13:
5278:GibbonsâHawkingâYork boundary term
5045:General Relativity and Gravitation
4596:Introduction to General Relativity
4560:
4487:Elektromagnetismus und Gravitation
3157:
2650:
2594:{\displaystyle \mathbf {\omega } }
2499:
2198:
2106:
2074:
1796:{\displaystyle \rho _{\text{g}}=0}
1744:
1726:
1639:
1619:
1596:
1510:
1490:
1469:
1348:
1276:
1259:
1237:
1222:
1205:
874:
864:
830:
760:
743:
702:
667:
657:
640:
607:
590:
566:
526:
481:
430:
366:
104:This approximate reformulation of
14:
5849:
5393:Modified Newtonian dynamics, MOND
5309:Classical theories of gravitation
5090:
4489:(2. ed.). Springer-Vieweg.
3720:
3407:'s gravitomagnetic field at its
3360:
3322:
3242:
3226:
3218:
3204:
3165:
3144:
2983:
2854:
2829:
2821:
2779:
2747:
2721:
2661:
2625:
2609:
2562:
2510:
2434:
2376:
2235:
2227:
2168:
2150:
2012:
2004:
1990:
1968:
1933:
1921:
1904:
1881:
1846:
1823:
1702:
1653:
1607:
1406:
1356:
1335:
1310:
1264:
1210:
1163:
1131:
1115:{\displaystyle \phi _{\text{g}}}
916:
868:
837:
802:
748:
710:
661:
647:
595:
574:
533:
489:
437:
374:
285:
266:
231:
201:
5215:History of gravitational theory
4637:. Addison-Wesley. p. 281.
4538:
4516:. Cham: Springer. p. 147.
4503:
4478:
4443:
4374:
4353:
4300:
4232:
4216:
2958:
2895:
2889:
2852:
2846:
2445:needs additional citations for
1851:For a test particle whose mass
1379:Inserting this four potentials
1080:speed of propagation of gravity
338:, the gravitational analogs to
92:as a separate theory expanding
5521:Causal dynamical triangulation
5210:Poisson's equation for gravity
4204:
4163:
4148:
4042:
3999:
3987:. Numero Speciale 1: 252â276.
3973:
3953:
3898:
3238:
3214:
1:
5112:In Search of Gravitomagnetism
4746:Classical and Quantum Gravity
4720:Gravitation and Cogravitation
4309:Classical and Quantum Gravity
3891:
1090:
99:
4852:10.1016/0003-4916(92)90297-Y
3403:Therefore, the magnitude of
3306:are perpendicular, so their
3062:of a ball-shaped body (see:
2990:{\displaystyle \mathbf {L} }
1719:For a stationary situation (
309:
193:Physical analogues of fields
7:
5838:Tests of general relativity
5383:Infinite derivative gravity
4967:Indian Journal of Physics B
4793:American Journal of Physics
4776:10.1088/0264-9381/17/19/311
4452:American Journal of Physics
4339:10.1088/0264-9381/17/19/311
3870:Modified Newtonian dynamics
3822:
2313:Relativistic wave equations
1007:is mass current density or
161:. Her model showed how the
10:
5854:
5571:Unified-field-theoric and
5028:10.1103/PhysRevD.78.024021
4905:10.1142/9789812810021_0009
4419:10.1142/9789812810021_0009
4172:AIP Conference Proceedings
3929:10.1142/9789814719063_0023
3283:It is exactly half of the
3064:list of moments of inertia
324:classical electromagnetism
50:between the equations for
18:
5794:
5726:
5714:JackiwâTeitelboim gravity
5684:
5570:
5549:
5493:Canonical quantum gravity
5488:Euclidean quantum gravity
5480:
5327:
5301:
5290:
5223:
5192:
5185:
5075:10.1007/s10714-017-2207-x
4737:
4141:10.1142/S0218271820430014
4051:The Astrophysical Journal
3985:Rivista del Nuovo Cimento
3905:David Delphenich (2015).
3620:
3285:LenseâThirring precession
3121:is the rotational period.
3084:{\displaystyle \omega \ }
1122:and the vector potential
63:Maxwell's field equations
34:Gravity Probe B
5590:Superfluid vacuum theory
5414:Nonsymmetric gravitation
5263:Post-Newtonian formalism
4950:. Nova. pp. 29â39.
4565:
4028:10.1103/PhysRevD.51.5387
3398:
3132:can now be obtained by:
211:â gravitomagnetic field
67:Einstein field equations
61:; specifically: between
5755:Mechanical explanations
5624:Heterotic string theory
5580:Noncommutative geometry
5499:WheelerâDeWitt equation
5225:General relativity (GR)
5205:Gauss's law for gravity
5179:Theories of gravitation
4722:. Electret Scientific.
4700:. Electret Scientific.
4277:10.1007/3-540-40988-2_5
3850:Gravitational radiation
3784:Lorentz transformations
328:Einstein field equation
40:Gravitoelectromagnetism
5596:Logarithmic BEC vacuum
5541:Rainbow gravity theory
5419:Scalarâtensor theories
5193:Newtonian gravity (NG)
5121:, NASA, 20 April 2004.
5117:9 October 2006 at the
4946:L. Iorio, ed. (2007).
4674:L. Iorio, ed. (2007).
3695:
3573:
3527:
3383:
3274:
3085:
3052:
2991:
2963:
2761:
2729:
2633:
2595:
2570:
2243:
2182:
2025:
1952:
1837:
1797:
1760:
1710:
1558:
1425:
1370:
1289:
1145:
1116:
1059:gravitational constant
924:
816:
686:
626:
550:
512:
465:
416:
330:, and assuming a weak
273:... or, equivalently,
171:active galactic nuclei
36:
5673:Twistor string theory
5652:Type II string theory
5645:Bosonic string theory
5585:Semiclassical gravity
5550:Unified-field-theoric
5335:Poincaré gauge theory
4614:J. B. Hartle (2002).
4485:A. Malcherek (2023).
4102:Danehkar, A. (2020).
3696:
3574:
3528:
3384:
3275:
3086:
3053:
2992:
2964:
2762:
2730:
2634:
2596:
2571:
2244:
2183:
2070:of the test particle.
2026:
1953:
1838:
1798:
1761:
1711:
1559:
1426:
1371:
1290:
1146:
1117:
925:
817:
687:
627:
551:
513:
466:
417:
163:LenseâThirring effect
46:, refers to a set of
31:
5740:Aristotelian physics
5709:GaussâBonnet gravity
5659:Little string theory
5638:Type 0 string theory
5631:Type I string theory
5506:Loop quantum gravity
5433:Scalarâtensorâvector
5406:Tensorâvectorâscalar
5361:Gauge theory gravity
5319:Theory of everything
4871:. pp. 121â132.
4593:L. H. Ryder (2009).
4385:. pp. 121â132.
3885:Stationary spacetime
3806:stressâenergy tensor
3744:improve this section
3706:Schwarzschild radius
3636:
3540:
3418:
3317:
3139:
3072:
3007:
2979:
2774:
2742:
2646:
2605:
2583:
2495:
2454:improve this article
2387:factual accuracy is
2320:Higher-order effects
2296:stressâenergy tensor
2193:
2100:
2060:of the test particle
1963:
1876:
1818:
1774:
1723:
1569:
1442:
1383:
1305:
1158:
1126:
1099:
827:
699:
637:
563:
523:
478:
427:
363:
355:Maxwell's equations
5557:KaluzaâKlein theory
5067:2017GReGr..49...44B
5020:2008PhRvD..78b4021C
4989:2000gr.qc....12091D
4887:2001rfg..conf..121M
4844:1992AnPhy.215....1J
4805:1963AmJPh..31..166F
4768:2000CQGra..17.4125C
4633:S. Carroll (2003).
4464:1963AmJPh..31..166F
4401:2001rfg..conf..121M
4331:2000CQGra..17.4125C
4259:2001LNP...562...83M
4190:2001AIPC..586..448W
4132:2020IJMPD..2943001D
4073:2004ApJ...611..952W
4020:1995PhRvD..51.5387W
3993:1969NCimR...1..252P
3860:KaluzaâKlein theory
3393:Gravitational waves
1809:gravitational waves
1071:vacuum permittivity
989:, with SI unit kgâ
m
949:), with SI unit mâ
s
947:gravitational field
340:Maxwell's equations
332:gravitational field
320:gravitational field
178:Stanford University
159:Penrose's mechanism
5833:Effects of gravity
5828:General relativity
5802:Gravitational wave
5685:Generalisations /
5573:quantum-mechanical
5481:Quantum-mechanical
5294:general relativity
5268:Linearized gravity
3865:Linearized gravity
3835:Artificial gravity
3712:Lack of invariance
3691:
3569:
3523:
3379:
3270:
3081:
3048:
2987:
2959:
2757:
2725:
2629:
2591:
2566:
2239:
2178:
2021:
1948:
1833:
1793:
1756:
1706:
1554:
1421:
1366:
1328:
1285:
1184:
1141:
1112:
920:
812:
682:
622:
546:
508:
461:
412:
316:general relativity
118:frame of reference
110:general relativity
71:general relativity
37:
5815:
5814:
5786:Theory of impetus
5722:
5721:
5694:Liouville gravity
5438:Conformal gravity
5366:Composite gravity
5356:Bimetric theories
5286:
5285:
4998:Physical Review D
4957:978-1-60021-002-0
4914:978-981-02-4631-0
4822:Annals of Physics
4813:10.1119/1.1969340
4752:(19): 4125â4157.
4729:978-0-917406-15-7
4707:978-0-917406-09-6
4685:978-1-60021-002-0
4666:978-0-7167-5016-1
4523:978-3-319-15036-9
4496:978-3-658-42701-6
4472:10.1119/1.1969340
4428:978-981-02-4631-0
4315:(19): 4125â4157.
4286:978-3-540-41236-6
4198:10.1063/1.1419591
4014:(10): 5387â5427.
3938:978-981-4719-05-6
3780:
3779:
3772:
3689:
3646:
3567:
3518:
3479:
3464:
3454:
3428:
3374:
3355:
3329:
3265:
3198:
3172:
3151:
3080:
3060:moment of inertia
3046:
3017:
2956:
2941:
2909:
2893:
2869:
2850:
2844:
2815:
2786:
2754:
2700:
2668:
2549:
2517:
2486:
2485:
2478:
2428:
2427:
2420:
2308:charge invariance
2304:relativistic mass
2255:Scaling of fields
2252:
2251:
2175:
2157:
2146:
2114:
2034:
2033:
2002:
1996:
1975:
1940:
1916:
1911:
1888:
1830:
1784:
1736:
1689:
1660:
1650:
1633:
1614:
1590:
1529:
1521:
1504:
1485:
1463:
1413:
1398:
1363:
1342:
1332:
1327:
1317:
1283:
1271:
1250:
1242:
1229:
1217:
1196:
1188:
1183:
1170:
1138:
1109:
933:
932:
913:
881:
859:
809:
798:
767:
755:
738:
717:
674:
614:
602:
581:
545:
507:
496:
459:
411:
406:
381:
155:Reva Kay Williams
139:relativistic jets
5845:
5770:
5768:Entropic gravity
5763:
5687:extensions of GR
5675:
5661:
5654:
5647:
5640:
5633:
5626:
5619:
5612:
5598:
5515:
5508:
5501:
5462:Geometrodynamics
5451:
5427:
5408:
5401:
5350:
5343:
5299:
5298:
5190:
5189:
5172:
5165:
5158:
5149:
5148:
5086:
5060:
5039:
5013:
4992:
4982:
4961:
4941:
4939:
4926:
4898:
4880:
4863:
4837:
4816:
4787:
4761:
4733:
4711:
4689:
4670:
4648:
4629:
4610:
4589:
4554:
4553:
4542:
4536:
4535:
4507:
4501:
4500:
4482:
4476:
4475:
4447:
4441:
4440:
4412:
4394:
4378:
4372:
4371:
4369:
4357:
4351:
4350:
4324:
4304:
4298:
4297:
4270:
4252:
4236:
4230:
4220:
4214:
4208:
4202:
4201:
4183:
4181:astro-ph/0111161
4167:
4161:
4160:
4152:
4146:
4145:
4143:
4125:
4099:
4093:
4092:
4066:
4064:astro-ph/0404135
4046:
4040:
4039:
4003:
3997:
3996:
3977:
3971:
3970:
3957:
3951:
3950:
3922:
3902:
3775:
3768:
3764:
3761:
3755:
3724:
3716:
3700:
3698:
3697:
3692:
3690:
3688:
3684:
3683:
3667:
3653:
3648:
3647:
3644:
3627:PSR J1748-2446ad
3612:
3599:
3593:
3591:
3578:
3576:
3575:
3570:
3568:
3566:
3565:
3553:
3532:
3530:
3529:
3524:
3519:
3517:
3513:
3512:
3499:
3485:
3480:
3475:
3467:
3465:
3457:
3455:
3453:
3452:
3451:
3435:
3430:
3429:
3426:
3388:
3386:
3385:
3380:
3375:
3373:
3372:
3363:
3358:
3356:
3354:
3353:
3352:
3336:
3331:
3330:
3327:
3325:
3279:
3277:
3276:
3271:
3266:
3264:
3263:
3254:
3250:
3245:
3234:
3229:
3221:
3207:
3201:
3199:
3197:
3196:
3195:
3179:
3174:
3173:
3170:
3168:
3153:
3152:
3149:
3147:
3093:angular velocity
3090:
3088:
3087:
3082:
3078:
3057:
3055:
3054:
3049:
3047:
3042:
3041:
3040:
3024:
3019:
3018:
3015:
2999:angular momentum
2996:
2994:
2993:
2988:
2986:
2968:
2966:
2965:
2960:
2957:
2952:
2944:
2942:
2937:
2936:
2935:
2919:
2911:
2910:
2907:
2894:
2891:
2888:
2883:
2882:
2870:
2862:
2857:
2851:
2848:
2845:
2843:
2842:
2833:
2832:
2824:
2818:
2816:
2814:
2813:
2812:
2796:
2788:
2787:
2784:
2782:
2766:
2764:
2763:
2758:
2756:
2755:
2752:
2750:
2734:
2732:
2731:
2726:
2724:
2716:
2711:
2710:
2701:
2699:
2698:
2689:
2678:
2670:
2669:
2666:
2664:
2658:
2657:
2638:
2636:
2635:
2630:
2628:
2620:
2612:
2600:
2598:
2597:
2592:
2590:
2575:
2573:
2572:
2567:
2565:
2560:
2559:
2550:
2548:
2547:
2538:
2527:
2519:
2518:
2515:
2513:
2507:
2506:
2481:
2474:
2470:
2467:
2461:
2438:
2430:
2423:
2416:
2412:
2409:
2403:
2400:reliably sourced
2380:
2379:
2372:
2332:mass undergoing
2285:
2283:
2282:
2276:
2273:
2248:
2246:
2245:
2240:
2238:
2230:
2225:
2224:
2215:
2214:
2202:
2201:
2187:
2185:
2184:
2179:
2177:
2176:
2173:
2171:
2159:
2158:
2155:
2153:
2147:
2145:
2134:
2133:
2124:
2116:
2115:
2112:
2110:
2109:
2086:
2085:
2030:
2028:
2027:
2022:
2020:
2016:
2015:
2007:
2000:
1994:
1993:
1977:
1976:
1973:
1971:
1957:
1955:
1954:
1949:
1947:
1943:
1942:
1941:
1938:
1936:
1924:
1914:
1913:
1912:
1909:
1907:
1890:
1889:
1886:
1884:
1862:
1861:
1842:
1840:
1839:
1834:
1832:
1831:
1828:
1826:
1802:
1800:
1799:
1794:
1786:
1785:
1782:
1768:Poisson equation
1765:
1763:
1762:
1757:
1743:
1738:
1737:
1734:
1715:
1713:
1712:
1707:
1705:
1700:
1699:
1690:
1688:
1687:
1678:
1667:
1662:
1661:
1658:
1656:
1648:
1647:
1646:
1634:
1632:
1631:
1630:
1617:
1616:
1615:
1612:
1610:
1604:
1603:
1593:
1591:
1589:
1588:
1576:
1563:
1561:
1560:
1555:
1553:
1552:
1531:
1530:
1527:
1519:
1518:
1517:
1505:
1503:
1502:
1501:
1488:
1487:
1486:
1483:
1477:
1476:
1466:
1464:
1462:
1461:
1449:
1430:
1428:
1427:
1422:
1420:
1416:
1415:
1414:
1411:
1409:
1400:
1399:
1396:
1375:
1373:
1372:
1367:
1365:
1364:
1361:
1359:
1344:
1343:
1340:
1338:
1330:
1329:
1325:
1319:
1318:
1315:
1313:
1294:
1292:
1291:
1286:
1284:
1282:
1274:
1273:
1272:
1269:
1267:
1257:
1252:
1251:
1248:
1240:
1230:
1228:
1220:
1219:
1218:
1215:
1213:
1203:
1198:
1197:
1194:
1186:
1185:
1181:
1172:
1171:
1168:
1166:
1150:
1148:
1147:
1142:
1140:
1139:
1136:
1134:
1121:
1119:
1118:
1113:
1111:
1110:
1107:
929:
927:
926:
921:
919:
914:
912:
911:
910:
901:
900:
887:
882:
880:
872:
871:
862:
860:
858:
857:
845:
840:
821:
819:
818:
813:
811:
810:
807:
805:
799:
797:
796:
787:
776:
768:
766:
758:
757:
756:
753:
751:
741:
739:
737:
736:
724:
719:
718:
715:
713:
691:
689:
688:
683:
675:
673:
665:
664:
655:
650:
631:
629:
628:
623:
615:
613:
605:
604:
603:
600:
598:
588:
583:
582:
579:
577:
555:
553:
552:
547:
543:
536:
517:
515:
514:
509:
505:
498:
497:
494:
492:
470:
468:
467:
462:
460:
458:
457:
445:
440:
421:
419:
418:
413:
409:
408:
407:
404:
383:
382:
379:
377:
349:
348:
344:electromagnetism
289:
279:
270:
260:
251:
240:Electromagnetism
235:
225:
219:angular momentum
216:
209:Gravitomagnetism
205:
114:weak field limit
108:as described by
90:Oliver Heaviside
75:Gravitomagnetism
52:electromagnetism
48:formal analogies
5853:
5852:
5848:
5847:
5846:
5844:
5843:
5842:
5818:
5817:
5816:
5811:
5790:
5766:
5759:
5730:
5728:
5718:
5699:Lovelock theory
5686:
5680:
5671:
5657:
5650:
5643:
5636:
5629:
5622:
5615:
5608:
5594:
5572:
5566:
5545:
5511:
5504:
5497:
5476:
5467:Induced gravity
5447:
5443:Scalar theories
5423:
5404:
5397:
5388:Massive gravity
5348:Teleparallelism
5346:
5341:EinsteinâCartan
5339:
5323:
5314:Quantum gravity
5293:
5292:Alternatives to
5282:
5248:Exact solutions
5219:
5181:
5176:
5144:, January 2007.
5119:Wayback Machine
5093:
4958:
4915:
4740:
4730:
4708:
4686:
4667:
4645:
4626:
4607:
4586:
4568:
4563:
4561:Further reading
4558:
4557:
4544:
4543:
4539:
4524:
4508:
4504:
4497:
4483:
4479:
4448:
4444:
4429:
4379:
4375:
4358:
4354:
4305:
4301:
4287:
4268:10.1.1.340.8408
4237:
4233:
4221:
4217:
4209:
4205:
4168:
4164:
4153:
4149:
4116:(14): 2043001.
4100:
4096:
4047:
4043:
4008:Physical Review
4004:
4000:
3978:
3974:
3958:
3954:
3939:
3903:
3899:
3894:
3889:
3855:Gravity Probe B
3845:Geodetic effect
3825:
3799:
3792:
3776:
3765:
3759:
3756:
3741:
3725:
3714:
3679:
3675:
3668:
3654:
3652:
3643:
3639:
3637:
3634:
3633:
3623:
3615:Gravity Probe B
3597:
3595:
3589:
3587:
3581:Earth's gravity
3561:
3557:
3552:
3541:
3538:
3537:
3508:
3504:
3500:
3486:
3484:
3468:
3466:
3456:
3447:
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3439:
3434:
3425:
3421:
3419:
3416:
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3368:
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3326:
3321:
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3259:
3255:
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3230:
3225:
3217:
3203:
3202:
3200:
3191:
3187:
3183:
3178:
3169:
3164:
3163:
3148:
3143:
3142:
3140:
3137:
3136:
3131:
3073:
3070:
3069:
3036:
3032:
3025:
3023:
3014:
3010:
3008:
3005:
3004:
2982:
2980:
2977:
2976:
2945:
2943:
2931:
2927:
2920:
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2906:
2902:
2890:
2884:
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2800:
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2492:
2482:
2471:
2465:
2462:
2451:
2439:
2424:
2413:
2407:
2404:
2393:
2385:This section's
2381:
2377:
2370:
2322:
2292:
2277:
2274:
2271:
2270:
2268:
2266:
2257:
2234:
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2197:
2196:
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2191:
2190:
2172:
2167:
2166:
2154:
2149:
2148:
2135:
2129:
2125:
2123:
2111:
2105:
2104:
2103:
2101:
2098:
2097:
2081:Poynting vector
2077:
2075:Poynting vector
2068:electric charge
2011:
2003:
1989:
1988:
1984:
1972:
1967:
1966:
1964:
1961:
1960:
1937:
1932:
1931:
1920:
1908:
1903:
1902:
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1897:
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1097:
1096:
1093:
1068:
1050:current density
1037:
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1017:
1006:
984:
966:
944:
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453:
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403:
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378:
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372:
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294:Fluid mechanics
290:
281:
277:
271:
262:
256:
247:
236:
227:
221:
217:due to (total)
212:
206:
195:
194:
182:Gravity Probe B
131:gravitomagnetic
127:gravitomagnetic
123:gravitoelectric
102:
24:
17:
12:
11:
5:
5851:
5841:
5840:
5835:
5830:
5813:
5812:
5810:
5809:
5804:
5798:
5796:
5795:Related topics
5792:
5791:
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5778:
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5752:
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5706:
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5690:
5688:
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5677:
5676:
5667:Twistor theory
5664:
5663:
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5655:
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5634:
5627:
5620:
5613:
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5174:
5167:
5160:
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5146:
5145:
5133:
5127:
5122:
5109:
5099:
5092:
5091:External links
5089:
5088:
5087:
5040:
4993:
4962:
4956:
4943:
4927:
4913:
4896:10.1.1.339.476
4864:
4817:
4799:(3): 166â170.
4788:
4739:
4736:
4735:
4734:
4728:
4716:O.D. Jefimenko
4712:
4706:
4694:O.D. Jefimenko
4690:
4684:
4671:
4665:
4649:
4643:
4630:
4624:
4611:
4605:
4590:
4584:
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4522:
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4477:
4458:(3): 166â170.
4442:
4427:
4410:10.1.1.339.476
4373:
4352:
4299:
4285:
4231:
4215:
4203:
4162:
4147:
4094:
4081:10.1086/422304
4057:(2): 952â963.
4041:
3998:
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3937:
3896:
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3890:
3888:
3887:
3882:
3877:
3872:
3867:
3862:
3857:
3852:
3847:
3842:
3840:Frame-dragging
3837:
3832:
3826:
3824:
3821:
3800:do not form a
3797:
3790:
3778:
3777:
3728:
3726:
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3687:
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2483:
2442:
2440:
2433:
2426:
2425:
2384:
2382:
2375:
2369:
2366:
2359:Coriolis field
2321:
2318:
2290:
2264:
2256:
2253:
2250:
2249:
2237:
2233:
2229:
2223:
2219:
2213:
2209:
2205:
2200:
2188:
2170:
2165:
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2122:
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2019:
2014:
2010:
2006:
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1496:
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1471:
1460:
1456:
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1447:
1419:
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1389:
1377:
1376:
1358:
1353:
1350:
1347:
1337:
1322:
1312:
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1295:
1281:
1278:
1266:
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1255:
1246:
1239:
1236:
1233:
1227:
1224:
1212:
1207:
1201:
1192:
1178:
1175:
1165:
1151:according to:
1133:
1105:
1092:
1089:
1088:
1087:
1084:speed of light
1073:
1066:
1061:
1052:
1043:
1035:
1028:
1022:
1015:
1004:
999:
997:charge density
990:
982:
977:
975:magnetic field
968:
964:
959:
957:electric field
950:
942:
931:
930:
918:
909:
905:
899:
895:
890:
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879:
876:
870:
866:
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852:
848:
843:
839:
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832:
822:
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791:
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783:
780:
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771:
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745:
735:
731:
727:
722:
712:
707:
704:
693:
692:
681:
678:
672:
669:
663:
659:
653:
649:
645:
642:
632:
621:
618:
612:
609:
597:
592:
586:
576:
571:
568:
557:
556:
542:
539:
535:
531:
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518:
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491:
486:
483:
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471:
456:
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448:
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435:
432:
422:
402:
398:
395:
392:
389:
386:
376:
371:
368:
357:
356:
353:
352:GEM equations
336:flat spacetime
334:or reasonably
311:
308:
304:
303:
291:
284:
282:
272:
265:
263:
245:magnetic field
237:
230:
228:
207:
200:
197:
196:
192:
191:
190:
147:frame-dragging
101:
98:
83:test particles
42:, abbreviated
21:frame-dragging
15:
9:
6:
4:
3:
2:
5850:
5839:
5836:
5834:
5831:
5829:
5826:
5825:
5823:
5808:
5805:
5803:
5800:
5799:
5797:
5793:
5787:
5784:
5782:
5779:
5777:
5774:
5769:
5765:
5762:
5761:FatioâLe Sage
5758:
5757:
5756:
5753:
5751:
5748:
5746:
5743:
5741:
5738:
5737:
5735:
5733:
5727:Pre-Newtonian
5725:
5715:
5712:
5710:
5707:
5705:
5702:
5700:
5697:
5695:
5692:
5691:
5689:
5683:
5674:
5670:
5669:
5668:
5665:
5660:
5656:
5653:
5649:
5646:
5642:
5639:
5635:
5632:
5628:
5625:
5621:
5618:
5614:
5611:
5607:
5606:
5605:
5604:String theory
5602:
5597:
5593:
5592:
5591:
5588:
5586:
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5581:
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5575:
5569:
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5483:
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5463:
5460:
5458:
5455:
5450:
5446:
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5444:
5441:
5439:
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5426:
5422:
5421:
5420:
5417:
5415:
5412:
5407:
5403:
5400:
5396:
5395:
5394:
5391:
5389:
5386:
5384:
5381:
5379:
5377:
5373:
5369:
5367:
5364:
5362:
5359:
5357:
5354:
5349:
5345:
5342:
5338:
5337:
5336:
5333:
5332:
5330:
5326:
5320:
5317:
5315:
5312:
5310:
5307:
5306:
5304:
5300:
5297:
5295:
5289:
5279:
5276:
5274:
5273:ADM formalism
5271:
5269:
5266:
5264:
5261:
5259:
5256:
5254:
5251:
5249:
5246:
5244:
5241:
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5231:
5230:
5228:
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5222:
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5211:
5208:
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5201:
5198:
5197:
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5191:
5188:
5184:
5180:
5173:
5168:
5166:
5161:
5159:
5154:
5153:
5150:
5143:
5142:
5141:New Scientist
5137:
5134:
5131:
5128:
5126:
5123:
5120:
5116:
5113:
5110:
5107:
5103:
5100:
5098:
5095:
5094:
5084:
5080:
5076:
5072:
5068:
5064:
5059:
5054:
5050:
5046:
5041:
5037:
5033:
5029:
5025:
5021:
5017:
5012:
5011:gr-qc/0612140
5007:
5004:(2): 024021.
5003:
4999:
4994:
4990:
4986:
4981:
4980:gr-qc/0012091
4976:
4972:
4968:
4963:
4959:
4953:
4949:
4944:
4938:
4937:gr-qc/0311030
4933:
4928:
4924:
4920:
4916:
4910:
4906:
4902:
4897:
4892:
4888:
4884:
4879:
4878:gr-qc/0011014
4874:
4870:
4865:
4861:
4857:
4853:
4849:
4845:
4841:
4836:
4835:gr-qc/0106043
4831:
4827:
4823:
4818:
4814:
4810:
4806:
4802:
4798:
4794:
4789:
4785:
4781:
4777:
4773:
4769:
4765:
4760:
4759:gr-qc/0003115
4755:
4751:
4747:
4742:
4741:
4731:
4725:
4721:
4717:
4713:
4709:
4703:
4699:
4695:
4691:
4687:
4681:
4677:
4672:
4668:
4662:
4658:
4654:
4650:
4646:
4644:9780805387322
4640:
4636:
4631:
4627:
4625:9780805386622
4621:
4617:
4612:
4608:
4606:9780521845632
4602:
4598:
4597:
4591:
4587:
4585:9780521829519
4581:
4577:
4576:
4570:
4569:
4551:
4547:
4541:
4533:
4529:
4525:
4519:
4515:
4514:
4506:
4498:
4492:
4488:
4481:
4473:
4469:
4465:
4461:
4457:
4453:
4446:
4438:
4434:
4430:
4424:
4420:
4416:
4411:
4406:
4402:
4398:
4393:
4392:gr-qc/0011014
4388:
4384:
4377:
4368:
4367:gr-qc/0311030
4363:
4356:
4348:
4344:
4340:
4336:
4332:
4328:
4323:
4322:gr-qc/0003115
4318:
4314:
4310:
4303:
4296:
4292:
4288:
4282:
4278:
4274:
4269:
4264:
4260:
4256:
4251:
4250:gr-qc/9912027
4246:
4242:
4235:
4229:
4228:0-691-03323-4
4225:
4219:
4213:
4207:
4199:
4195:
4191:
4187:
4182:
4177:
4173:
4166:
4158:
4151:
4142:
4137:
4133:
4129:
4124:
4119:
4115:
4111:
4110:
4105:
4098:
4090:
4086:
4082:
4078:
4074:
4070:
4065:
4060:
4056:
4052:
4045:
4037:
4033:
4029:
4025:
4021:
4017:
4013:
4009:
4002:
3994:
3990:
3986:
3982:
3976:
3968:
3967:
3962:
3956:
3948:
3944:
3940:
3934:
3930:
3926:
3921:
3916:
3912:
3908:
3901:
3897:
3886:
3883:
3881:
3878:
3876:
3873:
3871:
3868:
3866:
3863:
3861:
3858:
3856:
3853:
3851:
3848:
3846:
3843:
3841:
3838:
3836:
3833:
3831:
3828:
3827:
3820:
3816:
3814:
3813:Lorentz boost
3809:
3807:
3803:
3796:
3789:
3785:
3774:
3771:
3763:
3753:
3749:
3745:
3739:
3738:
3734:
3729:This section
3727:
3723:
3718:
3717:
3709:
3707:
3685:
3680:
3676:
3672:
3669:
3664:
3661:
3658:
3655:
3649:
3640:
3632:
3631:
3630:
3628:
3618:
3616:
3611:
3610:
3605:
3604:
3584:
3582:
3562:
3558:
3554:
3549:
3546:
3543:
3520:
3514:
3509:
3505:
3501:
3496:
3493:
3490:
3487:
3481:
3476:
3472:
3469:
3461:
3458:
3448:
3444:
3440:
3436:
3431:
3422:
3414:
3413:
3412:
3410:
3406:
3396:
3394:
3376:
3369:
3365:
3349:
3345:
3341:
3337:
3332:
3313:
3312:
3311:
3309:
3305:
3301:
3297:
3293:
3291:
3286:
3267:
3260:
3256:
3251:
3247:
3235:
3231:
3222:
3211:
3208:
3192:
3188:
3184:
3180:
3175:
3160:
3154:
3135:
3134:
3133:
3128:
3120:
3117:
3114:
3110:
3107:
3104:
3100:
3097:
3094:
3075:
3068:
3065:
3061:
3043:
3037:
3033:
3029:
3026:
3020:
3011:
3003:
3000:
2975:
2974:
2973:
2953:
2949:
2946:
2938:
2932:
2928:
2924:
2921:
2915:
2912:
2903:
2899:
2896:
2885:
2879:
2875:
2871:
2866:
2863:
2858:
2839:
2835:
2825:
2809:
2805:
2801:
2797:
2792:
2789:
2770:
2769:
2768:
2717:
2713:
2707:
2703:
2695:
2691:
2686:
2683:
2680:
2674:
2671:
2654:
2642:
2641:
2640:
2639:. Therefore
2621:
2617:
2613:
2587:
2556:
2552:
2544:
2540:
2535:
2532:
2529:
2523:
2520:
2503:
2491:
2490:
2489:
2480:
2477:
2469:
2466:February 2024
2459:
2455:
2449:
2448:
2443:This section
2441:
2437:
2432:
2431:
2422:
2419:
2411:
2401:
2397:
2391:
2390:
2383:
2374:
2373:
2365:
2362:
2360:
2356:
2351:
2345:
2343:
2339:
2335:
2331:
2326:
2317:
2315:
2314:
2309:
2305:
2301:
2297:
2289:
2281:
2263:
2231:
2221:
2217:
2211:
2207:
2203:
2189:
2163:
2160:
2142:
2139:
2136:
2130:
2126:
2120:
2117:
2096:
2095:
2091:
2089:GEM equation
2088:
2087:
2084:
2083:is given by:
2082:
2069:
2065:
2062:
2059:
2055:
2052:
2050:
2049:test particle
2046:
2042:
2039:
2038:
2037:
2017:
2008:
1997:
1985:
1981:
1978:
1959:
1944:
1928:
1925:
1917:
1898:
1894:
1891:
1872:
1871:
1867:
1865:GEM equation
1864:
1863:
1860:
1858:
1857:Lorentz force
1854:
1847:Lorentz force
1844:
1812:
1810:
1806:
1805:wave equation
1790:
1787:
1778:
1769:
1753:
1750:
1747:
1740:
1730:
1696:
1692:
1684:
1680:
1675:
1672:
1669:
1663:
1643:
1635:
1627:
1623:
1600:
1585:
1581:
1577:
1572:
1565:
1549:
1545:
1541:
1538:
1535:
1532:
1523:
1514:
1506:
1498:
1494:
1479:
1473:
1458:
1454:
1450:
1445:
1438:
1437:
1436:
1434:
1417:
1401:
1392:
1387:
1351:
1345:
1320:
1301:
1300:
1299:
1279:
1253:
1244:
1234:
1231:
1225:
1199:
1190:
1176:
1173:
1154:
1153:
1152:
1103:
1085:
1081:
1077:
1074:
1072:
1065:
1062:
1060:
1056:
1053:
1051:
1047:
1044:
1041:
1034:
1027:
1021:
1014:
1010:
1003:
1000:
998:
994:
991:
988:
981:
978:
976:
972:
969:
963:
960:
958:
954:
951:
948:
941:
938:
937:
936:
907:
903:
897:
893:
888:
883:
877:
854:
850:
846:
841:
833:
823:
793:
789:
784:
781:
778:
772:
769:
763:
733:
729:
725:
720:
705:
695:
694:
679:
676:
670:
651:
643:
633:
619:
616:
610:
584:
569:
559:
558:
540:
537:
529:
519:
502:
499:
484:
474:
473:
454:
450:
446:
441:
433:
423:
400:
396:
393:
390:
387:
384:
369:
359:
358:
354:
351:
350:
347:
345:
341:
337:
333:
329:
325:
321:
317:
314:According to
300:
297:â rotational
296:
295:
288:
283:
276:
269:
264:
259:
255:
254:dipole moment
250:
246:
242:
241:
234:
229:
224:
220:
215:
210:
204:
199:
198:
189:
187:
183:
179:
174:
172:
168:
164:
160:
156:
152:
148:
144:
143:Roger Penrose
140:
135:
132:
128:
124:
119:
115:
111:
107:
97:
95:
91:
86:
84:
80:
76:
72:
68:
64:
60:
57:
53:
49:
45:
41:
35:
30:
26:
22:
5729:theories and
5562:Supergravity
5375:
5371:
5233:Introduction
5139:
5048:
5044:
5001:
4997:
4970:
4966:
4947:
4868:
4825:
4821:
4796:
4792:
4749:
4745:
4719:
4697:
4675:
4656:
4653:J.A. Wheeler
4634:
4615:
4595:
4574:
4549:
4540:
4512:
4505:
4486:
4480:
4455:
4451:
4445:
4382:
4376:
4355:
4312:
4308:
4302:
4240:
4234:
4218:
4206:
4171:
4165:
4156:
4150:
4113:
4107:
4097:
4054:
4050:
4044:
4011:
4007:
4001:
3984:
3975:
3965:
3961:O. Heaviside
3955:
3910:
3900:
3830:Anti-gravity
3817:
3810:
3794:
3787:
3781:
3766:
3757:
3742:Please help
3730:
3703:
3624:
3608:
3602:
3585:
3535:
3402:
3391:
3303:
3299:
3295:
3289:
3282:
3126:
3124:
3118:
3108:
3098:
2971:
2737:
2578:
2487:
2472:
2463:
2452:Please help
2447:verification
2444:
2414:
2405:
2386:
2363:
2354:
2346:
2327:
2323:
2311:
2306:to electric
2300:four-current
2287:
2279:
2261:
2258:
2092:EM equation
2078:
2063:
2053:
2040:
2035:
1868:EM equation
1852:
1850:
1813:
1718:
1433:Lorenz gauge
1378:
1297:
1094:
1078:is both the
1075:
1063:
1054:
1048:is electric
1045:
1032:
1025:
1019:
1012:
1001:
992:
987:mass density
979:
970:
961:
952:
939:
934:
313:
292:
257:
248:
238:
222:
213:
208:
175:
136:
130:
126:
122:
103:
87:
74:
56:relativistic
43:
39:
38:
25:
5531:Causal sets
5425:BransâDicke
5243:Mathematics
4973:: 459â461.
4828:(1): 1â50.
3913:: 215â220.
3802:four-vector
3308:dot product
176:A group at
151:black holes
106:gravitation
59:gravitation
5822:Categories
5745:CGHS model
5732:toy models
5108:) research
5058:1610.09819
4550:google.com
4123:2006.13287
3981:R. Penrose
3920:1512.05183
3892:References
3592:10 Hz
2338:smoke ring
2334:minor axis
1859:equation:
1091:Potentials
299:fluid drag
100:Background
5750:RST model
5536:DGP model
5513:Spin foam
5457:Whitehead
5449:Nordström
5378:) gravity
5328:Classical
5302:Paradigms
5253:Resources
5083:119232668
5051:(3): 44.
4923:263798773
4891:CiteSeerX
4532:904397831
4437:263798773
4405:CiteSeerX
4263:CiteSeerX
3947:118596433
3760:July 2024
3731:does not
3659:π
3617:mission.
3491:π
3473:π
3223:⋅
3209:−
3161:×
3158:∇
3076:ω
2950:π
2913:ω
2886:ω
2826:×
2793:−
2718:×
2714:ω
2704:ρ
2684:π
2675:−
2651:∇
2622:×
2618:ω
2588:ω
2553:ρ
2533:π
2524:−
2500:∇
2396:talk page
2232:×
2218:ε
2161:×
2140:π
2121:−
2009:×
1926:×
1779:ρ
1745:∂
1731:ϕ
1727:∂
1693:ρ
1673:π
1640:∇
1620:∂
1597:∂
1573:−
1546:ρ
1539:π
1524:ϕ
1511:∇
1491:∂
1480:ϕ
1470:∂
1446:−
1393:ϕ
1352:×
1349:∇
1277:∂
1260:∂
1254:−
1245:ϕ
1238:∇
1235:−
1223:∂
1206:∂
1200:−
1191:ϕ
1177:−
1104:ϕ
1009:mass flux
894:ϵ
875:∂
865:∂
842:−
834:×
831:∇
782:π
773:−
761:∂
744:∂
721:−
706:×
703:∇
668:∂
658:∂
644:×
641:∇
608:∂
591:∂
570:×
567:∇
530:⋅
527:∇
485:⋅
482:∇
451:ϵ
447:ρ
434:⋅
431:∇
401:ρ
394:π
388:−
370:⋅
367:∇
310:Equations
252:due to a
5807:Graviton
5617:F-theory
5610:M-theory
5186:Standard
5115:Archived
5036:14846902
4784:15724290
4718:(2006).
4696:(1992).
4678:. Nova.
4347:15724290
4295:32411999
4036:10018300
3963:(1893).
3823:See also
3600:10
3427:g, Earth
2408:May 2013
2389:disputed
2342:g-forces
2330:toroidal
2045:velocity
1082:and the
1040:velocity
1031:, where
79:magnetic
5238:History
5063:Bibcode
5016:Bibcode
4985:Bibcode
4883:Bibcode
4860:6691986
4840:Bibcode
4801:Bibcode
4764:Bibcode
4460:Bibcode
4397:Bibcode
4327:Bibcode
4255:Bibcode
4186:Bibcode
4128:Bibcode
4089:1350543
4069:Bibcode
4016:Bibcode
3989:Bibcode
3752:removed
3737:sources
3409:equator
3292:-factor
3111:is the
3101:is the
3091:is the
3058:is the
3001:vector;
2997:is the
2972:where:
2284:
2269:
2066:is the
2056:is the
2047:of the
2043:is the
2036:where:
1069:is the
1057:is the
1038:is the
973:is the
955:is the
935:where:
275:current
167:quasars
112:in the
5081:
5034:
4954:
4921:
4911:
4893:
4858:
4782:
4738:Papers
4726:
4704:
4682:
4663:
4641:
4622:
4603:
4582:
4530:
4520:
4493:
4435:
4425:
4407:
4345:
4293:
4283:
4265:
4226:
4087:
4034:
3945:
3935:
3788:ρ
3621:Pulsar
3536:where
3113:radius
3079:
2350:chiral
2001:
1995:
1915:
1766:) the
1649:
1520:
1331:
1241:
1187:
544:
506:
410:
318:, the
5399:AQUAL
5258:Tests
5079:S2CID
5053:arXiv
5032:S2CID
5006:arXiv
4975:arXiv
4932:arXiv
4919:S2CID
4873:arXiv
4856:S2CID
4830:arXiv
4780:S2CID
4754:arXiv
4566:Books
4433:S2CID
4387:arXiv
4362:arXiv
4343:S2CID
4317:arXiv
4291:S2CID
4245:arXiv
4176:arXiv
4118:arXiv
4085:S2CID
4059:arXiv
3943:S2CID
3915:arXiv
3594:, or
3588:1.012
3405:Earth
3399:Earth
125:and
4952:ISBN
4909:ISBN
4724:ISBN
4702:ISBN
4680:ISBN
4661:ISBN
4639:ISBN
4620:ISBN
4601:ISBN
4580:ISBN
4528:OCLC
4518:ISBN
4491:ISBN
4423:ISBN
4281:ISBN
4224:ISBN
4032:PMID
3933:ISBN
3793:and
3735:any
3733:cite
3411:is:
3302:and
3103:mass
3016:ball
2908:ball
2849:with
2355:both
2286:and
2058:mass
1803:) a
1298:and
1182:grad
342:for
169:and
69:for
54:and
5106:esa
5071:doi
5024:doi
4901:doi
4848:doi
4826:215
4809:doi
4772:doi
4468:doi
4415:doi
4335:doi
4273:doi
4194:doi
4136:doi
4077:doi
4055:611
4024:doi
3925:doi
3746:by
3596:3.1
3579:is
2456:by
1326:rot
995:is
985:is
261:...
44:GEM
5824::
5138:,
5077:.
5069:.
5061:.
5049:49
5047:.
5030:.
5022:.
5014:.
5002:78
5000:.
4983:.
4971:75
4969:.
4942:in
4917:.
4907:.
4899:.
4889:.
4881:.
4854:.
4846:.
4838:.
4824:.
4807:.
4797:31
4795:.
4778:.
4770:.
4762:.
4750:17
4748:.
4548:.
4526:.
4466:.
4456:31
4454:.
4431:.
4421:.
4413:.
4403:.
4395:.
4341:.
4333:.
4325:.
4313:17
4311:.
4289:,
4279:,
4271:,
4261:,
4253:,
4192:.
4184:.
4134:.
4126:.
4114:29
4112:.
4106:.
4083:.
4075:.
4067:.
4053:.
4030:.
4022:.
4012:51
4010:.
3941:.
3931:.
3923:.
3909:.
3066:);
2892:or
2344:.
1321::=
1174::=
1018:=
243:â
153:.
141:.
96:.
85:.
73:.
5376:R
5374:(
5372:f
5171:e
5164:t
5157:v
5085:.
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