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in New York City; it appeared for the first time in print the following year. Oppenheimer and Snyder used
Einstein's own theory of gravity to prove how black holes could develop for the first time in contemporary physics, but without referencing the aforementioned article by Einstein. Oppenheimer and
1596:
was initially an opponent of the model until the late 1950s, when he was asked to teach a course on general relativity at
Princeton University. Wheeler claimed at a conference in 1958 that the Oppenheimer-Snyder model had neglected the many features of a realistic star. However, he later changed his
836:
studied this topic with their paper "On
Continued Gravitational Contraction" making the opposite argument as Einstein's. They showed when a sufficiently massive star runs out of thermonuclear fuel, it will undergo continued gravitational contraction and become separated from the rest of the universe
1587:
recalled that physicists were initially skeptical of the model, viewing as "truly strange" at the time. He explained further, "It was hard for people of that era to understand the paper because the things that were being smoked out of the mathematics were so different from any mental picture of how
1655:
The world of physics does indeed remember the paper. While
Oppenheimer is remembered in history as the “father of the atomic bomb”, his greatest contribution as a physicist was on the physics of black holes. The work of Oppenheimer and Hartland Snyder helped transform black holes from figments of
1609:
had shown a sufficiently heavy star would undergo continued gravitational contraction in a manner similar to the idealized scenario described by
Oppenheimer and Snyder. Wheeler subsequently played a key role in reviving interest in general relativity in the United States, and popularized the term
1067:
1588:
things should behave in the universe." Oppenheimer himself thought little of this discovery. However, some considered the model's discovery to be more significant than
Oppenheimer did, and model would later be described as forward thinking.
1446:
881:
104:
814:
in 1916, the first known non-trivial exact solution to
Einstein's field equations. In 1939, Einstein published "On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses" in the
1504:
1320:
1257:
1115:
841:, which not even light can escape. This paper predicted the existence of what are today known as black holes. The term "black hole" was coined decades later, in the fall of 1967, by
1350:
791:
During the collapse of a star to a black hole the geometry on the outside of the sphere is the
Schwarzschild geometry. However the geometry inside is, curiously enough, the same
1141:
3228:
1574:
1541:
1610:"black hole" in the late 1960s. Various theoretical physicists pursued this topic and by the late 1960s and early 1970s, advances in observational astronomy, such as
1342:
1170:
474:
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thought it was
Oppenheimer's greatest contribution to science. Lev Davidovich Landau added the Oppenheimer-Snyder paper to his "golden list" of classic papers.
1192:
747:
2325:
1062:{\displaystyle ds^{2}=-d\tau ^{2}+A^{2}(\eta )\left({\frac {dR^{2}}{1-2M{\frac {R_{-}^{2}}{R_{b}^{2}}}{\frac {1}{R_{+}}}}}+R^{2}d\Omega ^{2}\right)}
1707:
126:
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810:
in 1915, initially denied the possibility of black holes, even though they were a genuine implication of the
Schwarzschild metric, obtained by
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Snyder did, however, refer to an earlier article by Oppenheimer and Volkoff on neutron stars, improving upon the work of
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1672:, an interaction between Oppenheimer and his student Snyder occurs as their paper was published on the same day as the
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1999:
Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled on by Hawking Became Loved
1775:
Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled on by Hawking Became Loved
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2180:"'Oppenheimer' fact v. fiction: A nuclear historian breaks down what the movie got right and wrong"
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The Oppenheimer–Snyder model of continued gravitational collapse is described by the line element
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had already been discovered and black holes were no longer considered mere textbook curiosities.
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3075:
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1441:{\displaystyle \tau (\eta ,R)={\frac {1}{2}}{\sqrt {\frac {R_{+}^{3}}{2M}}}(\eta +\sin \eta ).}
842:
614:
599:
444:
206:
2027:
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is a positive quantity, the "boundary radius", representing the boundary of the matter region.
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2002:
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mathematics to real, physical possibilities – something to be found in the cosmos out there.
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would credit the Oppenheimer–Snyder model as one of his inspirations for research.
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1957:
1937:
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2208:"Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details"
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described it as "one of the great papers in twentieth-century physics."
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1619:
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851:
777:
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241:
167:
99:{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}
854:. Previously, and in the same year, Oppenheimer and three colleagues,
3313:
2960:
2863:
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2330:
2246:
American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer
2028:"Static Solutions of Einstein's Field Equations for Spheres of Fluid"
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250:
3223:
3182:
3080:
2237:
619:
429:
269:
870:. Oppenheimer would not revisit the topic in future publications.
3263:
866:, had investigated the stability of neutron stars, obtaining the
2326:"Oppenheimer: Remembering the physics that first made him great"
1880:
Isaacson, Walter (2007). "Chapter Eleven: Einstein's Universe".
3283:
3273:
3253:
2975:
2574:
2564:
2272:
Subtle Is the Lord: The Science and the Life of Albert Einstein
1615:
2384:
1622:, the first solid black-hole candidate, was discovered by the
821:, claiming to provide "a clear understanding as to why these '
1773:(2015). "Chapter 6: Only Its Gravitational Field Persists".
1069:
The quantities appearing in this expression are as follows:
776:
describing the collapse of an object of extreme mass into a
1997:(2015). "Chapter 9: Why Don't You Call It A Black Hole?".
2295:
2269:
Pais, Abraham (2005). "Chapter 15: The New Dynamics".
2069:(1938). "On the Stability of Stellar Neutron Cores".
1549:
1516:
1456:
1353:
1330:
1265:
1202:
1180:
1151:
1123:
1079:
884:
42:
1684:
1614:, changed the attitude of the scientific community.
1510:This expression is valid both in the matter region
2105:
1568:
1535:
1499:{\displaystyle A(\eta )={\frac {1+\cos \eta }{2}}}
1498:
1440:
1336:
1314:
1251:
1186:
1164:
1135:
1109:
1061:
98:
2064:
1904:
1884:. New York: Simon & Shuster. pp. 250–1.
3359:
2362:"What's Fact and What's Fiction in Oppenheimer?"
1708:Timeline of gravitational physics and relativity
1576:, and continuously transitions between the two.
828:Months after the issuing of Einstein's article,
16:Exact solution to the Einstein field equations
2400:
2199:
1315:{\displaystyle R_{+}=\mathrm {max} (R,R_{b})}
1252:{\displaystyle R_{-}=\mathrm {min} (R,R_{b})}
741:
1737:
2248:. New York: Vintage Books. pp. 89–90.
2236:
795:as in the rest of the observable universe.
2966:Magnetospheric eternally collapsing object
2407:
2393:
1968:. Oxford University Press. pp. 31–2.
1956:
748:
734:
1993:
1936:
1834:
1769:
2275:. Oxford University Press. p. 269.
1911:"On Continued Gravitational Contraction"
1879:
1801:
1597:mind completely after being informed by
1579:
1110:{\displaystyle (\tau ,R,\theta ,\phi )}
3360:
2025:
1802:Hamilton, Andrew (November 13, 2011).
1607:Lawrence Livermore National Laboratory
2388:
2359:
2320:
2318:
2296:Nobel Prize Foundation (March 2021).
2232:
2230:
2228:
2205:
2173:
2171:
2169:
2167:
2165:
2150:from the original on January 16, 2014
1837:"The Reluctant Father of Black Holes"
1830:
1828:
1826:
1824:
1808:JILA, University of Colorado, Boulder
1738:McEvoy, J. P.; Zarate, Oscar (1995).
1660:
1344:is defined implicitly by the equation
825:' do not exist in physical reality."
3342:
2268:
1989:
1987:
1985:
1952:
1950:
1948:
1875:
1873:
1871:
1765:
1763:
1761:
1759:
1733:
1731:
1729:
1727:
1725:
1723:
2177:
1703:Tolman–Oppenheimer–Volkoff equation
847:Goddard Institute for Space Studies
13:
2315:
2225:
2162:
1855:10.1038/scientificamerican0407-4sp
1821:
1601:that a computer simulation ran by
1286:
1283:
1280:
1223:
1220:
1217:
1045:
806:, who had developed his theory of
59:
14:
3384:
1982:
1945:
1868:
1756:
1720:
1194:is a positive quantity, the mass.
1143:are coordinates for the 2-sphere.
3341:
3332:
3331:
2630:Tolman–Oppenheimer–Volkoff limit
2501:
2206:Donis, Peter (January 9, 2023).
1687:
868:Tolman-Oppenheimer-Volkoff limit
715:
714:
701:
31:
2747:Innermost stable circular orbit
2414:
2353:
2289:
2262:
2099:
2058:
1882:Einstein: His Life and Universe
1628:X-ray space telescope in 1971.
780:. It is named after physicists
3173:Timeline of black hole physics
2019:
1898:
1795:
1466:
1460:
1432:
1414:
1369:
1357:
1309:
1290:
1246:
1227:
1104:
1080:
936:
930:
1:
2941:Nonsingular black hole models
2360:Jones, Nate (July 25, 2023).
1966:J. Robert Oppenheimer: A Life
1713:
1136:{\displaystyle \theta ,\phi }
845:at a conference held by the
788:, who published it in 1939.
7:
3163:Rossi X-ray Timing Explorer
3128:Hypercompact stellar system
3118:Gamma-ray burst progenitors
2026:Tolman, Richard C. (1939).
1740:Introducing Stephen Hawking
1680:
823:Schwarzschild singularities
212:Gravitational time dilation
10:
3389:
2849:Black hole complementarity
2816:Bousso's holographic bound
2801:Quasi-periodic oscillation
2499:
2493:Malament–Hogarth spacetime
2112:"On Massive Neutron Cores"
1835:Bernstein, Jeremy (2007).
1804:"Collapse to a Black Hole"
1569:{\displaystyle R>R_{b}}
1536:{\displaystyle R<R_{b}}
798:
332:Mathisson–Papapetrou–Dixon
173:Pseudo-Riemannian manifold
3327:
3201:
3053:
3015:
2994:
2933:
2892:
2841:
2720:Gravitational singularity
2707:
2600:
2510:
2435:
2422:
2298:"Roger Penrose Interview"
837:by a boundary called the
793:Robertson-Walker geometry
3304:PSO J030947.49+271757.31
3229:SDSS J150243.09+111557.3
2762:Blandford–Znajek process
1543:, and the vacuum region
873:
770:Einstein field equations
766:Oppenheimer–Snyder model
337:Hamilton–Jacobi–Einstein
317:Einstein field equations
140:Mathematical formulation
2560:Active galactic nucleus
2212:Physics Forums Insights
3188:Tidal disruption event
3158:Supermassive dark star
3076:Black holes in fiction
3061:Outline of black holes
2694:Supermassive dark star
2613:Gravitational collapse
2141:10.1103/PhysRev.55.374
2093:10.1103/PhysRev.54.540
2052:10.1103/PhysRev.55.364
1938:10.1103/PhysRev.56.455
1658:
1637:Nobel Prize in Physics
1594:John Archibald Wheeler
1570:
1537:
1500:
1442:
1338:
1316:
1253:
1188:
1166:
1137:
1111:
1063:
843:John Archibald Wheeler
207:Gravitational redshift
100:
3066:Black Hole Initiative
2879:Holographic principle
2003:Yale University Press
1779:Yale University Press
1653:
1571:
1538:
1501:
1443:
1339:
1337:{\displaystyle \eta }
1317:
1254:
1189:
1167:
1165:{\displaystyle R_{b}}
1138:
1112:
1064:
852:Lev Davidovich Landau
830:J. Robert Oppenheimer
818:Annals of Mathematics
782:J. Robert Oppenheimer
768:is a solution to the
495:Weyl−Lewis−Papapetrou
450:Kerr–Newman–de Sitter
270:Einstein–Rosen bridge
202:Gravitational lensing
158:Equivalence principle
101:
2869:Final parsec problem
2828:Schwarzschild radius
1605:and his team at the
1580:Reception and legacy
1547:
1514:
1454:
1351:
1328:
1263:
1200:
1178:
1149:
1121:
1077:
1073:The coordinates are
882:
774:Schwarzschild metric
425:Einstein–Rosen waves
151:Fundamental concepts
40:
3168:Superluminal motion
3143:Population III star
3113:Gravitational waves
3071:Black hole starship
2854:Information paradox
2133:1939PhRv...55..374O
2106:Oppenheimer, J.R.;
2085:1938PhRv...54..540O
2065:Oppenheimer, J.R.;
2044:1939PhRv...55..364T
1929:1939PhRv...56..455O
1905:Oppenheimer, J.R.;
1842:Scientific American
1402:
1005:
990:
379:Kaluza–Klein theory
265:Minkowski spacetime
217:Gravitational waves
3002:Optical black hole
2915:Reissner–Nordström
2874:Firewall (physics)
2779:Gravitational lens
2242:Sherwin, Martin J.
1674:Invasion of Poland
1661:In popular culture
1635:After winning the
1566:
1533:
1496:
1438:
1388:
1334:
1312:
1249:
1184:
1162:
1133:
1107:
1059:
991:
976:
812:Karl Schwarzschild
808:general relativity
762:general relativity
708:Physics portal
480:Oppenheimer–Snyder
420:Reissner–Nordström
312:Linearized gravity
260:Spacetime diagrams
163:Special relativity
96:
25:General relativity
3355:
3354:
3148:Supermassive star
3138:Naked singularity
3133:Membrane paradigm
2859:Cosmic censorship
2833:Spaghettification
2821:Immirzi parameter
2774:Hawking radiation
2715:Astrophysical jet
2684:Supermassive star
2674:Binary black hole
2608:Stellar evolution
2550:Intermediate-mass
2334:. July 29, 2023.
2282:978-0-192-80672-7
2255:978-0-375-72626-2
2012:978-0-300-21085-9
2001:. New Haven, CT:
1995:Bartusiak, Marcia
1975:978-0-195-32712-0
1891:978-0-7432-6473-0
1788:978-0-300-21085-9
1777:. New Haven, CT:
1771:Bartusiak, Marcia
1749:978-1-874-16625-2
1666:In the 2023 film
1494:
1412:
1411:
1383:
1187:{\displaystyle M}
1026:
1023:
1006:
758:
757:
391:
390:
277:
276:
3380:
3345:
3344:
3335:
3334:
3007:Sonic black hole
2956:Dark-energy star
2811:Bekenstein bound
2796:M–sigma relation
2725:Ring singularity
2505:
2409:
2402:
2395:
2386:
2385:
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2185:Business Insider
2178:McGrath, Jenny.
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2159:
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2149:
2116:
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2055:
2038:(364): 364–373.
2023:
2017:
2016:
1991:
1980:
1979:
1954:
1943:
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1630:Jeremy Bernstein
1612:radio telescopes
1603:Stirling Colgate
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989:
984:
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916:
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832:and his student
750:
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736:
723:
718:
717:
710:
706:
705:
490:van Stockum dust
475:Robertson–Walker
301:
300:
191:
190:
105:
103:
102:
97:
95:
94:
82:
74:
73:
55:
54:
35:
21:
20:
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3383:
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3381:
3379:
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3377:
3358:
3357:
3356:
3351:
3323:
3299:ULAS J1342+0928
3259:SDSS J0849+1114
3244:Phoenix Cluster
3197:
3049:
3011:
2990:
2929:
2888:
2884:No-hair theorem
2837:
2791:Bondi accretion
2757:Penrose process
2703:
2669:Gamma-ray burst
2596:
2506:
2497:
2483:Direct collapse
2431:
2418:
2413:
2383:
2382:
2372:
2370:
2358:
2354:
2344:
2342:
2324:
2323:
2316:
2306:
2304:
2302:The Nobel Prize
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2200:
2190:
2188:
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2153:
2151:
2147:
2120:Physical Review
2114:
2104:
2100:
2072:Physical Review
2063:
2059:
2032:Physical Review
2024:
2020:
2013:
1992:
1983:
1976:
1955:
1946:
1916:Physical Review
1903:
1899:
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1878:
1869:
1859:
1857:
1833:
1822:
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1800:
1796:
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1757:
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1742:. Totem Books.
1736:
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834:Hartland Snyder
804:Albert Einstein
801:
786:Hartland Snyder
754:
713:
700:
699:
692:
691:
515:
514:
505:
504:
460:Lemaître–Tolman
405:
404:
393:
392:
384:Quantum gravity
371:Advanced theory
298:
297:
296:
279:
278:
227:Geodetic effect
188:
187:
178:
177:
153:
152:
136:
106:
87:
83:
78:
66:
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47:
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17:
12:
11:
5:
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2808:
2806:Thermodynamics
2803:
2798:
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2769:Accretion disk
2766:
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2443:BTZ black hole
2439:
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2198:
2161:
2127:(4): 374–381.
2098:
2067:Serber, Robert
2057:
2018:
2011:
1981:
1974:
1962:Crease, Robert
1944:
1923:(5): 455–459.
1897:
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1695:Physics portal
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856:Richard Tolman
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363:Post-Newtonian
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3294:Markarian 501
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3220:
3219:XTE J1118+480
3217:
3215:
3214:XTE J1650-500
3212:
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3200:
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2900:Schwarzschild
2898:
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2745:
2743:
2742:Photon sphere
2740:
2738:
2737:Event horizon
2735:
2731:
2728:
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2721:
2718:
2716:
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2663:
2662:Related links
2660:
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2649:
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2640:Related links
2638:
2637:
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2628:
2624:
2623:Related links
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2448:Schwarzschild
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2166:
2146:
2142:
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2134:
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2126:
2122:
2121:
2113:
2109:
2108:Volkoff, G.M.
2102:
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2053:
2049:
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2029:
2022:
2014:
2008:
2004:
2000:
1996:
1990:
1988:
1986:
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1971:
1967:
1963:
1959:
1958:Pais, Abraham
1953:
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1641:Roger Penrose
1638:
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1599:Edward Teller
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1590:Freeman Dyson
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921:
917:
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908:
904:
901:
898:
893:
889:
885:
871:
869:
865:
861:
860:Robert Serber
857:
853:
848:
844:
840:
839:event horizon
835:
831:
826:
824:
820:
819:
813:
809:
805:
796:
794:
789:
787:
783:
779:
775:
772:based on the
771:
767:
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751:
746:
744:
739:
737:
732:
731:
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728:
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625:Chandrasekhar
623:
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561:
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541:
540:Schwarzschild
538:
536:
533:
531:
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523:
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518:
517:
509:
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501:
500:Hartle–Thorne
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410:Schwarzschild
408:
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364:
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232:Event horizon
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63:
56:
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48:
44:
34:
30:
29:
26:
23:
22:
19:
3368:Astrophysics
3249:PKS 1302-102
3123:Gravity well
3091:Compact star
3045:Microquasars
3030:Most massive
2934:Alternatives
2699:X-ray binary
2618:Neutron star
2555:Supermassive
2532:Hawking star
2473:Supermassive
2371:. Retrieved
2365:
2355:
2343:. Retrieved
2329:
2305:. Retrieved
2301:
2291:
2271:
2264:
2245:
2215:. Retrieved
2211:
2201:
2189:. Retrieved
2183:
2152:. Retrieved
2124:
2118:
2101:
2076:
2070:
2060:
2035:
2031:
2021:
1998:
1965:
1920:
1914:
1900:
1881:
1858:. Retrieved
1846:
1840:
1813:February 29,
1811:. Retrieved
1807:
1797:
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1646:
1645:
1634:
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1583:
1509:
1347:
877:
827:
816:
802:
790:
765:
759:
685:
645:Raychaudhuri
479:
114:Introduction
18:
3373:Black holes
3239:Centaurus A
3193:Planet Nine
3096:Exotic star
3025:Black holes
2971:Planck star
2920:Kerr–Newman
2635:White dwarf
2585:Radio-Quiet
2543:Microquasar
2416:Black holes
2154:January 15,
1669:Oppenheimer
660:van Stockum
590:Oppenheimer
445:Kerr–Newman
237:Singularity
3362:Categories
3289:Q0906+6930
3279:Hercules A
3209:Cygnus X-1
3178:White hole
3153:Quasi-star
3106:Preon star
3101:Quark star
3086:Big Bounce
2946:Black star
2904:Derivation
2752:Ergosphere
2708:Properties
2689:Quasi-star
2679:Quark star
2590:Radio-Loud
2478:Primordial
2468:Kugelblitz
2217:October 3,
2079:(7): 540.
1907:Snyder, H.
1714:References
1620:Cygnus X-1
1585:Kip Thorne
778:black hole
513:Scientists
345:Formalisms
293:Formalisms
242:Black hole
168:World line
3314:AT2018hyz
2961:Gravastar
2951:Dark star
2784:Microlens
2657:Hypernova
2652:Micronova
2647:Supernova
2601:Formation
2373:August 2,
2345:August 2,
2340:0971-751X
2331:The Hindu
2307:August 5,
2238:Bird, Kai
2191:August 2,
1860:August 3,
1648:The Hindu
1639:in 2020,
1488:η
1485:
1464:η
1430:η
1427:
1418:η
1361:η
1355:τ
1332:η
1209:−
1131:ϕ
1125:θ
1102:ϕ
1096:θ
1084:τ
1046:Ω
982:−
966:−
934:η
909:τ
902:−
605:Robertson
570:Friedmann
565:Eddington
555:Nordström
545:de Sitter
402:Solutions
327:Geodesics
322:Friedmann
304:Equations
290:Equations
251:Spacetime
186:Phenomena
92:ν
89:μ
80:κ
71:ν
68:μ
60:Λ
52:ν
49:μ
3337:Category
3224:A0620-00
3183:Wormhole
3081:Big Bang
2981:Fuzzball
2864:ER = EPR
2730:Theorems
2528:Electron
2523:Extremal
2453:Rotating
2244:(2006).
2145:Archived
2110:(1939).
1964:(2006).
1909:(1939).
1849:: 4–11.
1681:See also
721:Category
585:Lemaître
550:Reissner
535:Poincaré
520:Einstein
465:Taub–NUT
430:Wormhole
414:interior
127:Timeline
3347:Commons
3309:P172+18
3264:TON 618
3202:Notable
3054:Related
3040:Quasars
3035:Nearest
2995:Analogs
2925:Hayward
2893:Metrics
2538:Stellar
2463:Virtual
2458:Charged
2427:Outline
2367:Vulture
2129:Bibcode
2081:Bibcode
2040:Bibcode
1925:Bibcode
1616:Pulsars
799:History
640:Hawking
635:Penrose
610:Bardeen
600:Wheeler
530:Hilbert
525:Lorentz
485:pp-wave
122:History
3284:3C 273
3274:NeVe 1
3254:OJ 287
2976:Q star
2842:Issues
2575:Blazar
2565:Quasar
2338:
2279:
2252:
2009:
1972:
1888:
1785:
1746:
1117:where
862:, and
764:, the
719:
686:others
680:Thorne
670:Newman
650:Taylor
630:Ehlers
615:Walker
580:Zwicky
455:Kasner
3017:Lists
2518:Micro
2488:Rogue
2436:Types
2148:(PDF)
2115:(PDF)
1625:Uhuru
874:Model
655:Hulse
595:Gödel
575:Milne
470:Milne
435:Gödel
132:Tests
2986:Geon
2910:Kerr
2511:Size
2375:2023
2347:2023
2336:ISSN
2309:2023
2277:ISBN
2250:ISBN
2219:2023
2193:2023
2156:2014
2007:ISBN
1970:ISBN
1886:ISBN
1862:2023
1815:2024
1783:ISBN
1744:ISBN
1554:>
1521:<
1259:and
784:and
665:Taub
620:Kerr
560:Weyl
440:Kerr
358:BSSN
2580:OVV
2570:LQG
2137:doi
2089:doi
2048:doi
1933:doi
1851:doi
1482:cos
1424:sin
760:In
675:Yau
353:ADM
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