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symmetric, non-rotating, non-charged mass. Schwarzschild, in contrast, chose a more elegant "polar-like" coordinate system and was able to produce an exact solution which he first set down in a letter to
Einstein of 22 December 1915, written while he was serving in the war stationed on the Russian front. He concluded the letter by writing: "As you see, the war is kindly disposed toward me, allowing me, despite fierce gunfire at a decidedly terrestrial distance, to take this walk into this your land of ideas." In 1916, Einstein wrote to Schwarzschild on this result:
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Schwarzschild's second paper, which gives what is now known as the "Inner
Schwarzschild solution" (in German: "innere Schwarzschild-Lösung"), is valid within a sphere of homogeneous and isotropic distributed molecules within a shell of radius r=R. It is applicable to solids; incompressible fluids;
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complexity, and because he himself had produced only an approximate solution. Einstein's approximate solution was given in his famous 1915 article on the advance of the perihelion of
Mercury. There, Einstein used rectangular coordinates to approximate the gravitational field around a spherically
1404:
I have read your paper with the utmost interest. I had not expected that one could formulate the exact solution of the problem in such a simple way. I liked very much your mathematical treatment of the subject. Next
Thursday I shall present the work to the Academy with a few words of
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of the city, and the family had ancestors in
Frankfurt from the sixteenth century onwards. The family owned two fabric stores in Frankfurt. His brother Alfred became a painter. The young Schwarzschild attended a Jewish primary school until 11 years of age and then the
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effects near the boundary). When the mass density of this central body exceeds a particular limit, it triggers a gravitational collapse which, if it occurs with spherical symmetry, produces what is known as a
Schwarzschild
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Eisenstaedt, âThe Early
Interpretation of the Schwarzschild Solution,â in D. Howard and J. Stachel (eds), Einstein and the History of General Relativity: Einstein Studies, Vol. 1, pp. 213-234. Boston: Birkhauser,
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the (vectorial) arc element along the world line. Two points on two world lines contribute to the
Lagrangian (are coupled) only if they are a zero Minkowskian distance (connected by a light ray), hence the term
1219:{\displaystyle S=\sum _{i}m_{i}\int _{C_{i}}ds_{i}+{\frac {1}{2}}\sum _{i,j}\iint _{C_{i},C_{j}}q_{i}q_{j}\delta \left(\left\Vert P_{i}P_{j}\right\Vert \right)d\mathbf {s} _{i}d\mathbf {s} _{j}}
1001:
He also introduced a field free variational formulation of electrodynamics (also known as "action at distance" or "direct interparticle action") based only on the world line of particles as
2690:, in "The Collected Papers of Albert Einstein, Volume 8: The Berlin Years: Correspondence, 1914-1918 (English translation supplement)", Translated by Ann M. Hentschel, vol.8a, doc.#169.
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Karl
Schwarzchild appears as a fictionalized character in the story âSchwarzchildâs Singularityâ in the collection "When We Cease to Understand the World" (2020) by
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244:, for the limited case of a single spherical non-rotating mass, which he accomplished in 1915, the same year that Einstein first introduced general relativity. The
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Aktinometrie der Sterne der B. D. bis zur GröĂe 7.5 in der Zone 0° bis +20° Deklination. Teil A. Unter
Mitwirkung von Br. Meyermann, A. KohlschĂŒtter und O. Birck
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332:(secondary school). He received an all-encompassing education, including subjects like Latin, Ancient Greek, music and art, but developed a special interest in
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Schwarzschild, third from left in the automobile; possibly during the Fifth Conference of the International Union for Co-operation in Solar Research, held in
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2157:"Nachforschung der Wahrheit" von der alten Lateinschule zum Lessing-Gymnasium in Frankfurt am Main : Festschrift zum 500-jÀhrigen JubilÀum der Schule
409:, where he took up the post of director of the Astrophysical Observatory. This was then the most prestigious post available for an astronomer in Germany.
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2160:. Bernhard Mieles, Carolin Ritter, Christoph Wolf, Lessing-Gymnasium Frankfurt am Main, Frankfurter SocietÀts-Medien GmbH. Frankfurt am Main. 2020.
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on a surface that is now named after him. In his coordinates, this singularity lies on the sphere of points at a particular radius, called the
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a constant). This formula was important for enabling more accurate photographic measurements of the intensities of faint astronomical sources.
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of star clusters and laid the foundations for a formula linking the intensity of the starlight, exposure time, and the resulting contrast on a
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589:, using photography, and the improvement of optical systems, through the perturbative investigation of geometrical aberrations.
516:(1910â2006) emigrated to Great Britain in 1933. In 1946, she moved to New Zealand, where she became a classics professor at the
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Ueber die Bestimmung von Vertex und Apex nach der Ellipsoidhypothese aus einer geringeren Anzahl beobachteter Eigenbewegungen
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Untersuchungen zur geometrischen Optik I. Einleitung in die Fehlertheorie optischer Instrumente auf Grund des Eikonalbegriffs
233:
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1386:
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Thousands of dissertations, articles, and books have since been devoted to the study of Schwarzschild's solutions to the
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1942:
Slomov, Elena; Loewenthal, Ron; Goldberg, Ilan; Korostishevsky, Michael; Brenner, Sara; Gazit, Ephraim (August 2003).
423:
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1926:
472:, a rare and painful autoimmune skin-disease. Nevertheless, he managed to write three outstanding papers, two on the
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1944:"Pemphigus vulgaris in Jewish patients is associated with HLA-A region genes: mapping by microsatellite markers"
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Reimer, Berlin 1916, S. 424-434 (Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften; 1916)
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Reimer, Berlin 1916, S. 189 ff. (Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften; 1916)
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Karl Schwarzschild appears as a character in the science fiction short story "Schwarzschild Radius" (1987) by
3622:
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2049:"Pemphigus vulgaris: Incidence in Jews of different ethnic groups, according to age, sex, and initial lesion"
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the sun and stars viewed as a quasi-isotropic heated gas; and any homogeneous and isotropic distributed gas.
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despite being over 40 years old. He served on both the western and eastern fronts, specifically helping with
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401:. Schwarzschild became the director of the observatory. He married Else Rosenbach, a great-granddaughter of
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484:, and a minor modification of these results gives the well-known solution that now bears his name â the
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Pauli, W.. Theory of Relativity. United States, Dover Publications, 2013.
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in vacuum. In cases where the radius of the central body is less than the Schwarzschild radius,
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Schwarzschild at the Fourth Conference International Union for Cooperation in Solar Research at
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1822:
On the Gravitational Field of a Sphere of Incompressible Liquid, According to Einstein's Theory
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298:
245:
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The entire scientific estate of Karl Schwarzschild is stored in a special collection of the
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in the 1940s and constitutes an alternative but equivalent formulation of electrodynamics.
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and daughter of a professor of surgery at Göttingen, in 1909. Later that year they moved to
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early on. In fact he was something of a child prodigy, having two papers on binary orbits (
257:
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896:{\displaystyle S=(1/2)\int (H^{2}-E^{2})dV+\int \rho (\phi -{\vec {A}}\cdot {\vec {u}})dV}
491:
In March 1916, Schwarzschild left military service because of his illness and returned to
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1997:
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Alfred Schwarzschild (1914â1944) remained in Nazi Germany and was murdered during the
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Untersuchungen zur geometrischen Optik III. Ăber die astrophotographischen Objektive
352:
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2019:
2009:
1955:
1889:
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Zur Elektrodynamik. I. Zwei Formen des Princips der Action in der Elektronentheorie
375:
117:
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393:, where he had the opportunity to work with some significant figures, including
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2292:. Klaus Reinsch, Axel Wittmann, UniversitÀtsverlag Göttingen. Göttingen. 2017.
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287:
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Nicolini, Piero; Kaminski, Matthias; Mureika, Jonas; Bleicher, Marcus (2015).
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Graham, Reg; Taonga, New Zealand Ministry for Culture and Heritage Te Manatu.
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1893:
1613:Ăber das Gravitationsfeld eines Massenpunktes nach der Einsteinâschen Theorie.
30:
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1967:
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While at Vienna in 1897, Schwarzschild developed a formula, now known as the
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2014:
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Karl Schwarzschild (1873-1916) ein Pionier und Wegbereiter der Astrophysik
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A new approach to differential geometry using Clifford's geometric algebra
1813:
On the Gravitational Field of a Point-Mass, According to Einstein's Theory
492:
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3352:
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2434:"Karl Schwarzschild - Important Scientists - The Physics of the Universe"
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Schwarzschild accomplished this while serving in the German army during
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3004:
2999:
2531:"Princeton - News - Princeton Astrophysicist Martin Schwarzschild Dies"
1643:
Untersuchungen zur geometrischen Optik II. Theorie der Spiegelteleskope
1560:
571:
462:
265:
1941:
1783:
Die naturwissenschaftlichen Ergebnisse und Ziele der neueren Mechanik.
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1911, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen
1763:
1908, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen
1751:
1907, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen
1739:
1903, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen
1727:
1903, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen
1715:
1903, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen
1691:
1906, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen
1669:
1907, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen
1620:Ăber das Gravitationsfeld einer Kugel aus inkompressibler FlĂŒssigkeit.
468:
While serving on the front in Russia in 1915, he began to suffer from
2991:
2047:
Pisanti, S.; Sharav, Y.; Kaufman, E.; Posner, L.N. (September 1974).
1679:
Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 6
1657:
Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 4
1647:
Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 4
1637:
Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 4
1339:{\displaystyle \delta \left(\left\Vert P_{i}P_{j}\right\Vert \right)}
567:
496:
480:. His papers on relativity produced the first exact solutions to the
469:
333:
316:
279:
226:
110:
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2884:
2641:"Classical Electrodynamics in Terms of Direct Interparticle Action"
2365:
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Ueber die Helligkeitsverteilung im Schweif des HalleyÂŽschen Kometen
693:
is optical density of exposed photographic emulsion, a function of
183:
2215:, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 29â42,
1919:
Tensors : mathematics of differential geometry and relativity
2639:
Wheeler, John Archibald; Feynman, Richard Phillips (1949-07-01).
2396:, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 1â28,
1551:
554:, his research interests were extremely broad, including work in
406:
106:
73:
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Letter from K Schwarzschild to A Einstein dated 22 December 1915
1550:
represents the radius within which all massive bodies, and even
3214:
2553:
1422:
Boundary region of Schwarzschild interior and exterior solution
1722:
Zur Elektrodynamik. II. Die elementare elektrodynamische Kraft
465:
and rising to the rank of second lieutenant in the artillery.
2775:
1800:
Jahresbericht der Deutschen Mathematiker-Vereinigung, Band 16
1788:
Jahresbericht der Deutschen Mathematiker-Vereinigung, Band 13
1698:
Die Beugung und Polarisation des Lichts durch einen Spalt. I.
286:. Various forms of the disease particularly affect people of
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K. Schwarzschild, Nachr. ges. Wiss. Gottingen (1903) 128,132
1831:
On the Permissible Numerical Value of the Curvature of Space
1391:
Einstein himself was pleasantly surprised to learn that the
585:
Some of his particular achievements include measurements of
550:. However, although his best known work lies in the area of
385:
From 1901 until 1909, he was a professor at the prestigious
3195:
304:
3678:
2046:
1600:
Lower Saxony National- and University Library of Göttingen
347:
to study astronomy. After two years he transferred to the
1795:Ăber die astronomische Ausbildung der Lehramtskandidaten.
1734:
Zur Elektrodynamik. III. Ueber die Bewegung des Elektrons
1664:Ăber Differenzformeln zur Durchrechnung optischer Systeme
2602:
K. Schwarzschild, Nachr. ges. Wiss. Gottingen (1903) 125
1996:
Vodo, Dan; Sarig, Ofer; Sprecher, Eli (14 August 2018).
2557:
1st Karl Schwarzschild Meeting on Gravitational Physics
1835:
The Abraham Zelmanov Journal, Volume 1, 2008, pp. 64-73
1554:, must inevitably fall into the central body (ignoring
1430:
Schwarzschild's first (spherically symmetric) solution
495:. Two months later, on May 11, 1916, his struggle with
1826:
The Abraham Zelmanov Journal, 2008, Volume 1, P. 20-32
1817:
The Abraham Zelmanov Journal, 2008, Volume 1, P. 10-19
765:, Schwarzschild is the first to introduce the correct
457:
in 1914, Schwarzschild volunteered for service in the
351:
where he obtained his doctorate in 1896 for a work on
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990:
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713:, the intensity of the source being observed, and
705:
685:
663:
613:
378:). In 1899, he returned to Munich to complete his
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2629:A. D. Fokker, Zeitschrift fĂŒr Physik 58:386, 1929
2605:
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1995:
315:Karl Schwarzschild was born on 9 October 1873 in
3727:
2596:
2462:"How black holes morphed from theory to reality"
3801:German Jewish military personnel of World War I
2620:H. Tetrode, Zeitschrift fĂŒr Physik 10:137, 1922
1563:. This occurs, for example, when the mass of a
526:(1912â1997) became a professor of astronomy at
297:is named in his honour, as is the large crater
2638:
949:are the electric and applied magnetic fields,
3796:Academic staff of the University of Göttingen
3771:Ludwig Maximilian University of Munich alumni
2791:
2390:"Biography of Karl Schwarzschild (1873-1916)"
2387:
2206:
1847:List of things named after Karl Schwarzschild
446:From 1912, Schwarzschild was a member of the
362:in Vienna. His work here concentrated on the
225:; 9 October 1873 â 11 May 1916) was a German
2736:The Light Cone: The Schwarzschild Black Hole
499:may have led to his death at the age of 42.
3776:Members of the Prussian Academy of Sciences
2693:
2338:
2053:Oral Surgery, Oral Medicine, Oral Pathology
1921:. Delhi: Prentice Hall India. p. 205.
1888:. New York: Springer Science. p. 400.
1686:Ăber das Gleichgewicht der SonnenatmosphĂ€re
1395:admitted exact solutions, because of their
769:formalism of the electromagnetic field as
2798:
2784:
2320:: CS1 maint: location missing publisher (
2188:: CS1 maint: location missing publisher (
1493:{\displaystyle R_{s}={\frac {2GM}{c^{2}}}}
509:With his wife Else he had three children:
343:After graduation in 1890, he attended the
319:, the eldest of six boys and one girl, to
2664:
2473:
2364:
2250:"MacTutor History of Mathematics Archive"
2023:
2013:
592:
370:. An integral part of that theory is the
358:From 1897, he worked as assistant at the
2503:
1417:
1369:
433:
422:
411:
2724:MacTutor History of Mathematics Archive
2455:
2453:
1746:Ueber die Eigenbewegungen der Fixsterne
1280:{\displaystyle d\mathbf {s} _{\alpha }}
340:) published before the age of sixteen.
3728:
1574:
349:Ludwig Maximilian University of Munich
323:parents. His father was active in the
275:. He died the following year from the
86:Ludwig Maximilian University of Munich
2779:
2741:Obituary in the Astrophysical Journal
2428:
2426:
2093:. USGS Astrogeology Research Program.
1916:
1881:
1515:is the mass of the central body, and
1255:are the world lines of the particle,
942:{\displaystyle {\vec {E}},{\vec {H}}}
212:
2459:
2450:
2102:
2100:
1998:"The Genetics of Pemphigus Vulgaris"
1346:. The idea was further developed by
502:He rests in his family grave at the
3370:TolmanâOppenheimerâVolkoff equation
3323:FriedmannâLemaĂźtreâRobertsonâWalker
2091:Gazetteer of Planetary Nomenclature
1387:Deriving the Schwarzschild solution
13:
2423:
756:
282:, which he developed while at the
14:
3822:
3140:HamiltonâJacobiâEinstein equation
2706:
2097:
1378:in general relativity, using the
664:{\displaystyle i=f(I\cdot t^{p})}
232:Schwarzschild provided the first
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3701:
3689:
3677:
3665:
3653:
3641:
3618:
3617:
2394:Gesammelte Werke Collected Works
2339:Hertzsprung, Ejnar (June 1917).
2213:Gesammelte Werke Collected Works
2132:"Alfred Schwarzschild Biography"
2108:"The mystery of the dark bodies"
1569:TolmanâOppenheimerâVolkoff limit
1267:
1206:
1191:
146:
29:
3806:20th-century German astronomers
3791:University of Strasbourg alumni
3751:19th-century German astronomers
2759:Biography of Karl Schwarzschild
2681:
2632:
2623:
2614:
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2547:
2523:
2497:
2460:Levy, Adam (January 11, 2021).
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2200:
2148:
1866:Biography of Karl Schwarzschild
1701:, 1902, Mathematische Annalen,
256:, leads to a derivation of the
3811:Deaths from autoimmune disease
2947:Massâenergy equivalence (E=mc)
2805:
2124:
2079:
2040:
1989:
1935:
1910:
1875:
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1328:
1303:
1178:
1153:
962:
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884:
878:
863:
848:
830:
804:
798:
784:
658:
639:
427:Karl Schwarzschild's grave at
1:
2754:Mathematics Genealogy Project
2209:"Karl Schwarzschild Lectures"
1960:10.1016/s0198-8859(03)00092-2
1852:
1365:
570:, stellar structure, stellar
2770:The Abraham Zelmanov Journal
2438:www.physicsoftheuniverse.com
2388:Schwarzschild, Karl (1992),
2207:Schwarzschild, Karl (1992),
2065:10.1016/0030-4220(74)90365-X
1870:The Abraham Zelmanov Journal
1571:(about three solar masses).
978:is the vector potential and
448:Prussian Academy of Sciences
16:German physicist (1873â1916)
7:
3756:German relativity theorists
2962:Relativistic Doppler effect
2402:10.1007/978-3-642-58086-4_1
2221:10.1007/978-3-642-58086-4_2
1840:
1768:K. Schwarzschild, E. Kron:
1248:{\displaystyle C_{\alpha }}
998:is the electric potential.
260:, which is the size of the
10:
3827:
3433:In computational physics:
2957:Relativity of simultaneity
1384:
971:{\displaystyle {\vec {A}}}
733:, the exposure time, with
3781:Scientists from Frankfurt
3615:
3447:
3312:
3284:
3270:LenseâThirring precession
3153:
3102:
3064:
3043:
3032:
2990:
2934:
2918:
2860:
2852:Doubly special relativity
2824:
2813:
2666:10.1103/RevModPhys.21.425
2645:Reviews of Modern Physics
2475:10.1146/knowable-010921-1
2345:The Astrophysical Journal
1894:10.1007/978-0-8176-8283-5
429:Stadtfriedhof (Göttingen)
303:, on the far side of the
250:Schwarzschild coordinates
214:[kaÊlËÊvaÊtsÊÉȘlt]
199:
189:
179:
171:
159:
141:
136:
132:
128:
116:
102:
95:
81:
62:
37:
28:
21:
3786:People from Hesse-Nassau
3766:Jewish German physicists
3130:Post-Newtonian formalism
3120:Einstein field equations
3056:Mathematical formulation
2880:Hyperbolic orthogonality
2729:University of St Andrews
2560:. Springer. p. 10.
2260:(1): 27â28. 2016-01-18.
1593:
558:, observational stellar
548:Einstein field equations
482:Einstein field equations
440:Mount Wilson Observatory
345:University of Strasbourg
238:Einstein field equations
90:University of Strasbourg
2841:Galilean transformation
2832:Principle of relativity
2266:10.1108/rr-08-2015-0205
2136:alfredschwarzschild.com
2015:10.3389/fmed.2018.00226
541:
504:Stadtfriedhof Göttingen
391:University of Göttingen
310:
2926:Lorentz transformation
2087:"Crater Schwarzschild"
1544:
1509:gravitational constant
1494:
1423:
1416:
1382:
1356:John Archibald Wheeler
1340:
1281:
1249:
1220:
992:
972:
943:
897:
747:
727:
707:
687:
665:
615:
593:Physics of photography
463:ballistic calculations
443:
431:
420:
372:Schwarzschild exponent
246:Schwarzschild solution
3761:German Ashkenazi Jews
3394:WeylâLewisâPapapetrou
3135:Raychaudhuri equation
3074:Equivalence principle
2768:by Indranu Suhendro,
2324:) CS1 maint: others (
2192:) CS1 maint: others (
2002:Frontiers in Medicine
1917:Ahsan, Zafar (2015).
1868:by Indranu Suhendro,
1545:
1543:{\displaystyle R_{s}}
1495:
1434:contain a coordinate
1421:
1402:
1373:
1341:
1282:
1250:
1221:
993:
991:{\displaystyle \phi }
973:
944:
898:
748:
728:
708:
688:
666:
616:
437:
426:
415:
387:Göttingen Observatory
248:, which makes use of
172:Years of service
3435:Numerical relativity
3276:pulsar timing arrays
2719:"Karl Schwarzschild"
2715:Robertson, Edmund F.
2341:"Karl Schwarzschild"
1882:Snygg, John (2012).
1807:English translations
1681:, Numero 6, S. 1-117
1659:, Nummero 3, S. 1-54
1649:, Nummero 2, S. 1-28
1639:, Nummero 1, S. 1-31
1527:
1449:
1440:Schwarzschild radius
1380:Schwarzschild metric
1292:
1259:
1232:
1007:
982:
953:
909:
775:
737:
717:
697:
677:
627:
605:
528:Princeton University
524:Martin Schwarzschild
486:Schwarzschild metric
474:theory of relativity
258:Schwarzschild radius
254:Schwarzschild metric
166:Imperial German Army
3327:Friedmann equations
3221:HulseâTaylor binary
3183:Gravitational waves
3079:Riemannian geometry
2905:Proper acceleration
2890:Maxwell's equations
2836:Galilean relativity
2734:Roberto B. Salgado
2713:O'Connor, John J.;
2657:1949RvMP...21..425W
2357:1917ApJ....45..285H
1575:Cultural references
556:celestial mechanics
518:University of Otago
453:At the outbreak of
360:Kuffner Observatory
338:celestial mechanics
3746:Jewish astronomers
3376:ReissnerâNordström
3294:BransâDicke theory
3125:Linearized gravity
2952:Length contraction
2870:Frame of reference
2847:Special relativity
2764:2021-03-02 at the
2750:Karl Schwarzschild
1556:quantum tunnelling
1540:
1490:
1424:
1383:
1336:
1277:
1245:
1216:
1094:
1025:
988:
968:
939:
893:
743:
723:
703:
683:
661:
611:
552:general relativity
444:
432:
421:
368:photographic plate
325:business community
295:837 Schwarzschilda
277:autoimmune disease
264:of a non-rotating
242:general relativity
206:Karl Schwarzschild
23:Karl Schwarzschild
3629:
3628:
3443:
3442:
3422:OzsvĂĄthâSchĂŒcking
3028:
3027:
3010:Minkowski diagram
2967:Thomas precession
2910:Relativistic mass
2772:, 2008, Volume 1.
2745:Ejnar Hertzsprung
2506:"Agathe Thornton"
2466:Knowable Magazine
2411:978-3-642-63467-3
2299:978-3-86395-295-2
2254:Reference Reviews
2230:978-3-642-63467-3
2167:978-3-95542-379-7
1903:978-0-8176-8283-5
1872:, 2008, Volume 1.
1488:
1354:in the 1920s and
1079:
1077:
1016:
965:
936:
921:
881:
866:
746:{\displaystyle p}
726:{\displaystyle t}
706:{\displaystyle I}
686:{\displaystyle i}
614:{\displaystyle p}
599:Schwarzschild law
564:quantum mechanics
399:Hermann Minkowski
330:Lessing-Gymnasium
317:Frankfurt on Main
203:
202:
123:Hugo von Seeliger
97:Scientific career
52:Frankfurt am Main
3818:
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3404:van Stockum dust
3176:Two-body problem
3094:Mach's principle
3041:
3040:
2982:Terrell rotation
2822:
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2535:pr.princeton.edu
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2017:
1993:
1987:
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1948:Human Immunology
1939:
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1879:
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1588:BenjamĂn Labatut
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621:in the formula:
620:
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612:
403:Friedrich Wöhler
376:astrophotography
288:Ashkenazi Jewish
229:and astronomer.
224:
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118:Doctoral advisor
69:
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3439:
3343:BKL singularity
3333:LemaĂźtreâTolman
3308:
3304:Quantum gravity
3286:
3280:
3266:geodetic effect
3240:(together with
3210:LISA Pathfinder
3149:
3098:
3084:Penrose diagram
3066:
3060:
3035:
3024:
3020:Minkowski space
2986:
2930:
2914:
2862:
2856:
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2809:
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2766:Wayback Machine
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1415:
1411:Albert Einstein
1409:
1393:field equations
1389:
1368:
1360:Richard Feynman
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757:Electrodynamics
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566:, instrumental
544:
514:Agathe Thornton
313:
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137:Military career
109:
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82:Alma mater
77:
76:, German Empire
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3382:Axisymmetric:
3379:
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3356:
3355:
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3335:
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3321:Cosmological:
3318:
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3262:frame-dragging
3259:
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3246:Einstein rings
3242:Einstein cross
3235:
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3145:Ernst equation
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3122:
3117:
3115:BSSN formalism
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2972:Ladder paradox
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2875:Speed of light
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2707:External links
2705:
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1385:Main article:
1376:Kepler problem
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3475:Schwarzschild
3473:
3471:
3468:
3466:
3463:
3461:
3458:
3456:
3453:
3452:
3450:
3446:
3436:
3432:
3431:
3428:
3425:
3423:
3420:
3418:
3414:
3413:
3410:
3407:
3405:
3402:
3400:
3397:
3395:
3392:
3389:
3385:
3381:
3380:
3377:
3374:
3371:
3368:
3366:
3362:
3361:Schwarzschild
3358:
3357:
3354:
3351:
3349:
3346:
3344:
3341:
3339:
3336:
3334:
3331:
3328:
3324:
3320:
3319:
3317:
3315:
3311:
3305:
3302:
3300:
3297:
3295:
3292:
3291:
3289:
3283:
3277:
3274:
3271:
3267:
3263:
3260:
3258:
3257:Shapiro delay
3255:
3253:
3250:
3247:
3243:
3239:
3236:
3233:
3229:
3226:
3225:
3222:
3219:
3216:
3213:
3211:
3208:
3206:
3203:
3201:
3200:collaboration
3197:
3193:
3190:
3188:
3184:
3181:
3180:
3177:
3174:
3172:
3169:
3167:
3166:Event horizon
3164:
3162:
3159:
3158:
3156:
3152:
3146:
3143:
3141:
3138:
3136:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3116:
3113:
3111:
3110:ADM formalism
3108:
3107:
3105:
3101:
3095:
3092:
3090:
3087:
3085:
3082:
3080:
3077:
3075:
3072:
3071:
3069:
3063:
3057:
3054:
3052:
3049:
3048:
3046:
3042:
3039:
3037:
3031:
3021:
3018:
3016:
3015:Biquaternions
3013:
3011:
3008:
3006:
3003:
3001:
2998:
2997:
2995:
2993:
2989:
2983:
2980:
2978:
2975:
2973:
2970:
2968:
2965:
2963:
2960:
2958:
2955:
2953:
2950:
2948:
2945:
2943:
2942:Time dilation
2940:
2939:
2937:
2933:
2927:
2924:
2923:
2921:
2917:
2911:
2908:
2906:
2903:
2901:
2898:
2896:
2895:Proper length
2893:
2891:
2888:
2886:
2883:
2881:
2878:
2876:
2873:
2871:
2868:
2867:
2865:
2859:
2853:
2850:
2848:
2845:
2842:
2839:
2837:
2833:
2830:
2829:
2827:
2823:
2820:
2818:
2812:
2808:
2801:
2796:
2794:
2789:
2787:
2782:
2781:
2778:
2771:
2767:
2763:
2760:
2757:
2755:
2751:
2748:
2746:
2743:, written by
2742:
2739:
2737:
2733:
2730:
2726:
2725:
2720:
2716:
2711:
2710:
2696:
2689:
2684:
2676:
2672:
2667:
2662:
2658:
2654:
2650:
2646:
2642:
2635:
2626:
2617:
2608:
2599:
2590:
2580:
2578:
2569:
2567:9783319200460
2563:
2559:
2558:
2550:
2536:
2532:
2526:
2511:
2510:teara.govt.nz
2507:
2500:
2485:
2481:
2476:
2471:
2467:
2463:
2456:
2454:
2439:
2435:
2429:
2427:
2413:
2407:
2403:
2399:
2395:
2391:
2384:
2376:
2372:
2367:
2362:
2358:
2354:
2350:
2346:
2342:
2335:
2327:
2323:
2317:
2309:
2305:
2301:
2295:
2291:
2290:
2283:
2275:
2271:
2267:
2263:
2259:
2255:
2251:
2245:
2232:
2226:
2222:
2218:
2214:
2210:
2203:
2195:
2191:
2185:
2177:
2173:
2169:
2163:
2159:
2158:
2151:
2137:
2133:
2127:
2113:
2109:
2103:
2101:
2092:
2088:
2082:
2074:
2070:
2066:
2062:
2058:
2054:
2050:
2043:
2035:
2031:
2026:
2021:
2016:
2011:
2007:
2003:
1999:
1992:
1977:
1973:
1969:
1965:
1961:
1957:
1953:
1949:
1945:
1938:
1930:
1928:9788120350885
1924:
1920:
1913:
1905:
1899:
1895:
1891:
1887:
1886:
1878:
1871:
1867:
1862:
1858:
1848:
1845:
1844:
1836:
1832:
1829:
1827:
1823:
1820:
1818:
1814:
1811:
1810:
1806:
1805:
1801:
1797:
1796:
1792:
1789:
1785:
1784:
1780:
1777:
1773:
1772:
1767:
1764:
1760:
1759:
1755:
1752:
1748:
1747:
1743:
1740:
1736:
1735:
1731:
1728:
1724:
1723:
1719:
1716:
1712:
1711:
1707:
1704:
1700:
1699:
1695:
1692:
1688:
1687:
1683:
1680:
1676:
1673:
1670:
1666:
1665:
1661:
1658:
1654:
1651:
1648:
1644:
1641:
1638:
1634:
1631:
1630:
1626:
1625:
1621:
1618:
1615:
1614:
1610:
1609:
1605:
1604:
1603:
1601:
1591:
1589:
1584:
1582:
1581:Connie Willis
1572:
1570:
1566:
1562:
1557:
1553:
1535:
1531:
1522:
1518:
1514:
1510:
1506:
1483:
1479:
1474:
1471:
1468:
1462:
1457:
1453:
1445:
1444:
1443:
1441:
1437:
1433:
1428:
1420:
1412:
1406:
1401:
1398:
1394:
1388:
1381:
1377:
1372:
1363:
1361:
1357:
1353:
1349:
1332:
1322:
1318:
1312:
1308:
1299:
1295:
1272:
1262:
1240:
1236:
1226:
1211:
1201:
1196:
1186:
1182:
1172:
1168:
1162:
1158:
1149:
1145:
1140:
1136:
1130:
1126:
1118:
1114:
1110:
1105:
1101:
1096:
1090:
1087:
1084:
1080:
1074:
1071:
1066:
1061:
1057:
1053:
1046:
1042:
1037:
1031:
1027:
1021:
1017:
1013:
1010:
1002:
999:
985:
959:
930:
924:
915:
903:
890:
887:
875:
869:
860:
854:
851:
845:
842:
839:
836:
833:
825:
821:
817:
812:
808:
801:
795:
791:
787:
781:
778:
770:
768:
764:
761:According to
754:
740:
720:
700:
680:
671:
653:
649:
645:
642:
636:
633:
630:
622:
608:
600:
590:
588:
583:
581:
577:
573:
569:
565:
561:
557:
553:
549:
536:
532:
529:
525:
522:
519:
515:
512:
511:
510:
507:
505:
500:
498:
494:
489:
487:
483:
479:
475:
471:
466:
464:
460:
456:
451:
449:
441:
436:
430:
425:
419:
418:Bonn, Germany
414:
410:
408:
404:
400:
396:
395:David Hilbert
392:
388:
383:
381:
377:
373:
369:
365:
361:
356:
355:'s theories.
354:
350:
346:
341:
339:
335:
331:
326:
322:
318:
308:
306:
302:
301:
300:Schwarzschild
296:
291:
289:
285:
284:Russian front
281:
278:
274:
269:
267:
263:
262:event horizon
259:
255:
251:
247:
243:
239:
235:
230:
228:
221:
215:
207:
198:
195:
192:
188:
185:
182:
178:
174:
170:
167:
164:
158:
155:
154:German Empire
144:
140:
135:
131:
127:
124:
121:
119:
115:
112:
108:
105:
101:
98:
94:
91:
87:
84:
80:
75:
65:
61:
57:
56:German Empire
53:
40:
36:
32:
27:
20:
3720:Solar System
3605:
3474:
3299:KaluzaâKlein
3051:Introduction
2977:Twin paradox
2769:
2722:
2699:Landau 1975.
2695:
2683:
2648:
2644:
2634:
2625:
2616:
2607:
2598:
2589:
2556:
2549:
2538:. Retrieved
2534:
2525:
2514:. Retrieved
2509:
2499:
2487:. Retrieved
2465:
2441:. Retrieved
2437:
2415:, retrieved
2393:
2383:
2348:
2344:
2334:
2288:
2282:
2257:
2253:
2244:
2234:, retrieved
2212:
2202:
2156:
2150:
2139:. Retrieved
2135:
2126:
2115:. Retrieved
2111:
2090:
2081:
2056:
2052:
2042:
2005:
2001:
1991:
1979:. Retrieved
1951:
1947:
1937:
1918:
1912:
1884:
1877:
1869:
1861:
1830:
1821:
1812:
1802:, S. 519-522
1793:
1790:, S. 145-156
1781:
1778:, S. 197-208
1769:
1765:, S. 191-200
1756:
1753:, S. 614-632
1744:
1741:, S. 245-278
1732:
1729:, S. 132-141
1720:
1717:, S. 126-131
1708:
1705:, S. 177-247
1696:
1684:
1674:
1671:, S. 551-570
1662:
1652:
1642:
1632:
1627:Other papers
1619:
1611:
1597:
1585:
1578:
1567:exceeds the
1565:neutron star
1516:
1512:
1504:
1502:
1431:
1429:
1425:
1405:explanation.
1403:
1396:
1390:
1348:Hugo Tetrode
1227:
1003:
1000:
904:
771:
760:
672:
623:
596:
584:
580:spectroscopy
545:
508:
501:
490:
467:
452:
445:
384:
380:Habilitation
357:
342:
314:
299:
292:
270:
231:
205:
204:
190:Battles/wars
96:
68:(1916-05-11)
3741:1916 deaths
3736:1873 births
3708:Outer space
3696:Spaceflight
3388:KerrâNewman
3359:Spherical:
3228:Other tests
3171:Singularity
3103:Formulation
3065:Fundamental
2919:Formulation
2900:Proper time
2861:Fundamental
1436:singularity
1397:prima facie
520:in Dunedin.
476:and one on
459:German army
455:World War I
389:within the
273:World War I
194:World War I
66:11 May 1916
3730:Categories
3540:Zel'dovich
3448:Scientists
3427:Alcubierre
3234:of Mercury
3232:precession
3161:Black hole
3044:Background
3036:relativity
3005:World line
3000:Light cone
2825:Background
2817:relativity
2807:Relativity
2540:2022-05-15
2516:2022-05-15
2512:(in MÄori)
2443:2022-05-15
2417:2021-05-18
2236:2021-05-18
2176:1244019080
2141:2022-05-15
2117:2022-05-15
2112:www.mpg.de
1853:References
1693:, S. 41-53
1606:Relativity
1561:black hole
1366:Relativity
767:Lagrangian
572:statistics
560:photometry
364:photometry
266:black hole
184:Lieutenant
142:Allegiance
44:1873-10-09
3672:Astronomy
3648:Biography
3510:Robertson
3495:Friedmann
3490:Eddington
3480:de Sitter
3314:Solutions
3192:detectors
3187:astronomy
3154:Phenomena
3089:Geodesics
2992:Spacetime
2935:Phenomena
2675:0034-6861
2484:250662997
2375:0004-637X
2316:cite book
2308:981916699
2274:0950-4125
2184:cite book
1968:0198-8859
1296:δ
1273:α
1241:α
1146:δ
1097:∬
1081:∑
1038:∫
1018:∑
986:ϕ
963:→
934:→
919:→
879:→
870:⋅
864:→
855:−
852:ϕ
846:ρ
843:∫
818:−
802:∫
646:⋅
568:astronomy
535:Holocaust
497:pemphigus
493:Göttingen
470:pemphigus
334:astronomy
293:Asteroid
280:pemphigus
227:physicist
175:1914â1916
111:Astronomy
3623:Category
3500:LemaĂźtre
3465:Einstein
3455:Poincaré
3415:Others:
3399:TaubâNUT
3365:interior
3287:theories
3285:Advanced
3252:redshift
3067:concepts
2885:Rapidity
2863:concepts
2762:Archived
2489:25 March
2034:30155467
1976:12878355
1841:See also
1798:, 1907,
1786:, 1904,
1677:, 1910,
1655:, 1906,
1645:, 1906,
1635:, 1906,
1432:does not
1408:â
1329:‖
1304:‖
1179:‖
1154:‖
290:origin.
252:and the
160:Service/
3660:Germany
3634:Portals
3565:Hawking
3560:Penrose
3545:Novikov
3525:Wheeler
3470:Hilbert
3460:Lorentz
3417:pp-wave
3238:lensing
3034:General
2815:Special
2752:at the
2653:Bibcode
2353:Bibcode
2351:: 285.
2073:4528670
2025:6102399
2008:: 226.
1703:Band 55
1552:photons
1519:is the
1507:is the
673:(where
407:Potsdam
236:to the
210:German:
107:Physics
74:Potsdam
3606:others
3595:Thorne
3585:Misner
3570:Taylor
3555:Geroch
3550:Ehlers
3520:Zwicky
3338:Kasner
2673:
2564:
2482:
2408:
2373:
2306:
2296:
2272:
2227:
2174:
2164:
2071:
2032:
2022:
1981:3 July
1974:
1966:
1925:
1900:
1503:where
1228:where
905:where
578:, and
442:, 1910
321:Jewish
162:branch
151:
103:Fields
3684:Stars
3600:Weiss
3580:Bondi
3575:Hulse
3505:Milne
3409:discs
3353:Milne
3348:Gödel
3205:Virgo
2584:1989.
2480:S2CID
1594:Works
3535:Kerr
3485:Weyl
3384:Kerr
3244:and
3198:and
3196:LIGO
2671:ISSN
2562:ISBN
2491:2022
2406:ISBN
2371:ISSN
2326:link
2322:link
2304:OCLC
2294:ISBN
2270:ISSN
2225:ISBN
2194:link
2190:link
2172:OCLC
2162:ISBN
2069:PMID
2030:PMID
1983:2022
1972:PMID
1964:ISSN
1923:ISBN
1898:ISBN
1374:The
1358:and
1350:and
542:Work
397:and
311:Life
305:Moon
180:Rank
63:Died
38:Born
3590:Yau
3215:GEO
2661:doi
2470:doi
2398:doi
2361:doi
2262:doi
2217:doi
2061:doi
2020:PMC
2010:doi
1956:doi
1890:doi
240:of
3732::
3264:/
3230::
3185::
2727:,
2721:,
2717:,
2669:.
2659:.
2649:21
2647:.
2643:.
2576:^
2533:.
2508:.
2478:.
2468:.
2464:.
2452:^
2436:.
2425:^
2404:,
2392:,
2369:.
2359:.
2349:45
2347:.
2343:.
2318:}}
2314:{{
2302:.
2268:.
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2110:.
2099:^
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2028:.
2018:.
2004:.
2000:.
1970:.
1962:.
1952:64
1950:.
1946:.
1896:.
1833:,
1824:,
1815:,
1774:,
1761:,
1749:,
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1583:.
1511:,
1442::
1413:,
582:.
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506:.
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450:.
382:.
307:.
268:.
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3636::
3390:)
3386:(
3372:)
3363:(
3329:)
3325:(
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2570:.
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2472::
2446:.
2400::
2377:.
2363::
2355::
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2196:)
2178:.
2144:.
2120:.
2075:.
2063::
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2012::
2006:5
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1958::
1931:.
1906:.
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