Knowledge

Tolman–Oppenheimer–Volkoff limit

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known is PSR J1748-2446ad, rotating at a rate of 716 times per second or 43,000 revolutions per minute, giving a linear (tangential) speed at the surface on the order of 0.24c (i.e., nearly a quarter the speed of light). Star rotation interferes with convective heat loss during supernova collapse, so rotating stars are more likely to collapse directly to form a black hole
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in a (H1,L1)-spectrogram up to 700 Hz with Gaussian equivalent level of confidence greater than 3.3 σ based on causality alone following edge detection applied to (H1,L1)-spectrograms merged by frequency coincidences. Additional confidence derives from the strength of this EE. The observed
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Jayasinghe, T.; Stanek, K. Z.; Thompson, Todd A.; Kochanek, C. S.; Rowan, D. M.; Vallely, P. J.; Strassmeier, K. G.; Weber, M.; Hinkle, J. T.; Hambsch, F-J; Martin, D. V.; Prieto, J. L.; Pessi, T.; Huber, D.; Auchettl, K.; Lopez, L. A.; Ilyin, I.; Badenes, C.; Howard, A. W.; Isaacson, H.; Murphy, S.
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Abeysekara, A. U.; Albert, A.; Alfaro, R.; Alvarez, C.; Álvarez, J. D.; Arceo, R.; Arteaga-Velázquez, J. C.; Avila Rojas, D.; Ayala Solares, H. A.; Belmont-Moreno, E.; Benzvi, S. Y.; Brisbois, C.; Caballero-Mora, K. S.; Capistrán, T.; Carramiñana, A.; Casanova, S.; Castillo, M.; Cotti, U.; Cotzomi,
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Oppenheimer and Volkoff's calculation of the mass limit of neutron stars also neglected to consider the rotation of neutron stars, however we now know that neutron stars are capable of spinning at much faster rates than were known in Oppenheimer and Volkoff's time. The fastest-spinning neutron star
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In a star less massive than the limit, the gravitational compression is balanced by short-range repulsive neutron–neutron interactions mediated by the strong force and also by the quantum degeneracy pressure of neutrons, preventing collapse. If its mass is above the limit, the star will collapse to
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Oppenheimer and Volkoff discounted the influence of heat, stating in reference to work by Landau (1932), 'even 10 degrees... the pressure is determined essentially by the density only and not by the temperature' – yet it has been estimated that temperatures can reach up to approximately >10 K
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This list contains objects that may be neutron stars, black holes, quark stars, or other exotic objects. This list is distinct from the list of least massive black holes due to the undetermined nature of these objects, largely because of indeterminate mass, or other poor observation data.
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Oppenheimer and Volkoff's paper notes that "the effect of repulsive forces, i.e., of raising the pressure for a given density above the value given by the Fermi equation of state ... could tend to prevent the collapse." And indeed, the most massive neutron star detected so far,
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are even more poorly known than those of neutron-degenerate matter, most astrophysicists assume, in the absence of evidence to the contrary, that a neutron star above the limit collapses directly into a black hole.
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during formation of a neutron star, mergers and binary accretion. Another source of heat and therefore collapse-resisting pressure in neutron stars is 'viscous friction in the presence of differential rotation.'
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Orosz, Jerome A.; Jain, Raj K.; Bailyn, Charles D.; McClintock, Jeffrey E.; Remillard, Ronald A. (2002). "Orbital Parameters for the Soft X-Ray Transient 4U 1543-47: Evidence for a Black Hole".
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In the case of a rigidly spinning neutron star, meaning that different levels in the interior of the star all rotate at the same rate, the mass limit is thought to increase by up to 18–20%.
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First discovered microquasar system. Confirmed to have a magnetic field, which is atypical for a black hole; however, it could be the field of the accretion disk, not of the compact object.
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black hole mergers involving black holes in the 7.5–50 solar mass range; it is possible – although unlikely – that these black holes were themselves the result of previous mergers.
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The idea that there should be an absolute upper limit for the mass of a cold (as distinct from thermal pressure supported) self-gravitating body dates back to the 1932 work of
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Hessels, Jason W. T.; Ransom, Scott M.; Stairs, Ingrid H.; Freire, Paulo C. C.; Kaspi, Victoria M.; Camilo, Fernando (2006-03-31). "A Radio Pulsar Spinning at 716 Hz".
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frequencies below 1 kHz indicate a hypermassive magnetar rather than a black hole, spinning down by magnetic winds and interactions with dynamical mass ejecta.
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is the relevant mass per particle. It can be seen that the wavelength cancels out so that one obtains an approximate mass limit formula of the very simple form
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Slany, P.; Stuchlik, Z. (1 October 2008). "Mass estimate of the XTE J1650-500 black hole from the Extended Orbital Resonance Model for high-frequency QPOs".
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we report on a possible detection of extended emission (EE) in gravitational radiation during GRB170817A: a descending chirp with characteristic time-scale
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Microquasar system. Major differences between the spectrum of Cyg X-3 and typical accreting BH can be explained by properties of its companion star.
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contribution would become negligible when compared with the relativistic kinetic contribution (RKC). RKC is determined just by the relevant
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At the upper mass limit, that pressure will equal the pressure needed to resist gravity. The pressure to resist gravity for a body of mass
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Thompson, T. A.; Kochanek, C. S.; Stanek, K. Z.; et al. (2019). "A noninteracting low-mass black hole–giant star binary system".
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Microquasar system. It has a spectrum typical for black holes, however it emits HE and VHE gamma rays similar to neutron stars
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97% chance of prompt collapse into a black hole immediately after merger. Alternative study suggests collapse 2.5 hours later.
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Determination of Black Hole Masses in Galactic Black Hole Binaries Using Scaling of Spectral and Variability Characteristics
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Cherepashchuk, Anatol (2002). "Observational Manifestations of Precession of Accretion Disk in the SS 433 Binary System".
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Foley, Ryan J.; Coulter, David A.; Kilpatrick, Charles D.; Piro, Anthony L.; Ramirez-Ruiz, Enrico; Schwab, Josiah (2020).
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Liu, Jifeng; et al. (27 November 2019). "A wide star–black-hole binary system from radial-velocity measurements".
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Albert, J; et al. (2006). "Variable Very-High-Energy Gamma-Ray Emission from the Microquasar LS I +61 303".
2725:"Precise mass and spin measurements for a stellar-mass black hole through X-ray timing: The case of GRO J1655-40" 504:
are thought to be stellar black holes. These black hole candidates are estimated to have masses between 3 and 20
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Shaposhnikov, Nickolai; Titarchuk, Lev; The Astrophysical Journal, Volume 699, Issue 1, pp. 453-468 (2009)
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Foellmi, C.; Depagne, E.; Dall, T.H.; Mirabel, I.F (12 June 2006). "On the distance of GRO J1655-40".
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Chaty, S.; Mirabel, I. F.; Goldoni, P.; Mereghetti, S.; Duc, P.-A.; Martí, J.; Mignani, R. P. (2002).
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Romani, Roger W.; Kandel, D.; Filippenko, Alexei V.; Brink, Thomas G.; Zheng, WeiKang (2022-08-01).
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particles in sufficiently compressed matter would be forced into energy states so high that their
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Woosley, S. E.; Heger, A.; Weaver, T. A. (2002). "The Evolution and Explosion of Massive Stars".
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must have mass exceeding the Tolman–Oppenheimer–Volkoff limit. Theory predicts that because of
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J.; Coutiño De León, S.; De León, C.; de la Fuente, E.; Díaz-Vélez, J. C.; Dichiara, S.;
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Mass may be underestimated due not accurately measured distance to the companion star.
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Gelino, D. M.; Harrison, T. E. (2003). "GRO J0422+32: The Lowest Mass Black Hole?".
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Gravitational wave data of neutron star merger from LIGO and Virgo interferometers.
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Motta, S. E.; Belloni, T. M.; Stella, L.; Muñoz-Darias, T.; Fender, R. (2014).
2479:"A detached stellar-mass black hole candidate in the globular cluster NGC 3201" 2373: 2338: 1973:
Kaminker, A. D.; Kaurov, A. A.; Potekhin, A. Y.; Yakovlev, D. G. (2014-08-21).
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Intermediate-dispersion spectroscopy and atmosphere model fitting of companion.
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Irrgang, A.; Geier, S.; Kreuzer, S.; Pelisoli, I.; Heber, U. (January 2020).
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Kalogera, V; Baym, G (11 August 1996). "The Maximum Mass of a Neutron Star".
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system. Only mass close to lowest possible allows it not to be a black hole.
464:, or change composition and be supported in some other way (for example, by 4851: 4725: 4693: 4301: 4220: 3755: 3729: 3599: 3594: 3518: 3379:
Casares, J; Ribo, M; Ribas, I; Paredes, J. M; Marti, J; Herrero, A (2005).
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Casares, J. (2006). "Observational Evidence for Stellar-Mass Black Holes".
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Cho, A. (16 February 2018). "A weight limit emerges for neutron stars".
4881: 4811: 4780: 4755: 4708: 4703: 4688: 4354: 4291: 4281: 4182: 4018: 3943: 3858: 3838: 3809: 3760: 3709: 1718:"The heaviest neutron star on record is 2.35 times the mass of the sun" 1621:
Oppenheimer, J. R.; Volkoff, G. M. (1939). "On Massive Neutron Cores".
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Spectroscopic radial velocity measurements of noninteracting companion.
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Spectroscopic radial velocity measurements of noninteracting companion.
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Initially thought to be first black hole in pair-instability mass gap.
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Theoretical work in 1996 placed the limit at approximately 1.5 to 3.0
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McClintock, J. E.; Remillard, R. A. (2003). "Black Hole Binaries".
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system. Only lowest possible mass allows it not to be a black hole.
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Pooley, D.; Kumar, P.; Wheeler, J. C.; Grossan, B. (2018-05-31).
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van Putten, Maurice H P M; Della Valle, Massimo (January 2019).
2166: 472:). Because the properties of hypothetical, more exotic forms of 60:). Later, more refined analyses have resulted in larger values. 28: 4886: 4876: 4856: 4578: 4177: 4167: 3537: 3487: 3199: 2449:"Strange quark star may have formed from a lucky cosmic merger" 1034: 430: 3987: 2722: 2538:"Near-infrared observations of Galactic black hole candidates" 1972: 2939: 2535: 2250: 43:
stars. Stars more massive than the TOV limit collapse into a
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Burkert, V. D.; Elouadrhiri, L.; Girod, F. X. (2019-05-05).
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Zdziarski, A. A.; Mikolajewska, J.; Belczynski, K. (2013).
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Monthly Notices of the Royal Astronomical Society: Letters
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Monthly Notices of the Royal Astronomical Society: Letters
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Bombaci, I. (1996). "The Maximum Mass of a Neutron Star".
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repulsion predict a neutron star mass limit of 2.2 to 2.9
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Upper bound to the mass of cold, nonrotating neutron stars
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Spectroscopic radial velocity measurements of companion.
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Spectroscopic radial velocity measurements of companion.
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Spectroscopic radial velocity measurements of companion.
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Timeline of white dwarfs, neutron stars, and supernovae
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black hole formed by the collapse of an individual star
2314:"Astronomers Spot A New Class Of Low-Mass Black Holes" 2826: 1516:
Rezzolla, L.; Most, E. R.; Weih, L. R. (2018-01-09).
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all set equal to one, there will be a corresponding
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Proceedings of the International Astronomical Union
1903: 3202:"Cyg X-3: A low-mass black hole or a neutron star" 1858: 1620: 341: 262: 199: 3385:Monthly Notices of the Royal Astronomical Society 3265:Monthly Notices of the Royal Astronomical Society 3206:Monthly Notices of the Royal Astronomical Society 3147:Monthly Notices of the Royal Astronomical Society 3140: 2729:Monthly Notices of the Royal Astronomical Society 2542:Monthly Notices of the Royal Astronomical Society 2402:Monthly Notices of the Royal Astronomical Society 2174:Monthly Notices of the Royal Astronomical Society 1979:Monthly Notices of the Royal Astronomical Society 1609: 1150:and HESS J0632+057, as well as mysterious object 496:can have a mass of no more than approximately 10 4962: 2212: 1515: 429:. More realistic models neutron stars including 2389: 2330: 2160: 3437: 3259:Massi, M; Migliari, S; Chernyakova, M (2017). 2110:Fryer, Chris L.; Heger, Alexander (Oct 2000). 1511: 1509: 920: 4003: 3503: 3141:Koljonen, K. I. I.; MacCarone, T. J. (2017). 3005: 2999: 2896: 2647: 2112:"Core-Collapse Simulations of Rotating Stars" 1765:"The pressure distribution inside the proton" 2244: 1354: 1210: 1166: 1130: 1097: 1066: 1039: 981: 890: 854: 820: 785: 751: 702: 665: 632: 600: 1506: 387:. Oppenheimer and Volkoff assumed that the 200:{\displaystyle P={\frac {1}{\lambda ^{4}}}} 4569:Magnetospheric eternally collapsing object 4010: 3996: 3510: 3496: 3431: 2109: 1811: 1115:and atmosphere model fitting of companion. 3451: 3414: 3396: 3331: 3294: 3276: 3235: 3217: 3176: 3158: 3125: 3107: 3042: 2958: 2862: 2844: 2787: 2758: 2740: 2661: 2608: 2571: 2553: 2529: 2512: 2494: 2431: 2413: 2372: 2354: 2305: 2264: 2231: 2203: 2185: 2127: 2037: 2000: 1990: 1938: 1909: 1835: 1824:Journal for General Philosophy of Science 1693: 1675: 1551: 1533: 1465: 1463: 1443: 1425: 1401: 1368: 871:Precision X-ray timing observations from 3261:"The black hole candidate LS I +61°0303" 1410:"GW170817 Most Likely Made a Black Hole" 356:can be taken to be given roughly by the 2447:Paul Sutter last updated (2022-09-16). 1924: 1325: 4963: 1817: 1574: 1460: 1319: 277:is the density. This will be given by 3991: 3491: 2311: 1968: 1966: 999: 905: 683: 4945: 3972: 1852: 342:{\displaystyle M={\frac {1}{m^{2}}}} 263:{\displaystyle P^{3}=M^{2}\rho ^{4}} 3026: 2337:Abbott, B. P.; et al. (2020). 1469: 1287:Tolman–Oppenheimer–Volkoff equation 375:this limit was first worked out by 121:. Pauli's principle shows that the 13: 1963: 1737: 460:some denser form. It could form a 14: 4997: 2234:"Masses in the Stellar Graveyard" 1664:The Astrophysical Journal Letters 544:List of least massive black holes 528:List of least massive black holes 4944: 4935: 4934: 4233:Tolman–Oppenheimer–Volkoff limit 4104: 3971: 3962: 3961: 3725:Tolman–Oppenheimer–Volkoff limit 3517: 3416:10.1111/j.1365-2966.2005.09617.x 2573:10.1046/j.1365-8711.2002.05267.x 2477:Giesers, B; et al. (2018). 1271: 1257: 21:Tolman–Oppenheimer–Volkoff limit 4350:Innermost stable circular orbit 4017: 3908:Fermi Gamma-ray Space Telescope 3372: 3311: 3252: 3193: 3134: 3083: 3020: 2933: 2890: 2820: 2767: 2716: 2694: 2641: 2588: 2470: 2440: 2103: 2078: 2017: 1918: 1897: 1756: 1731: 454: 214:will be given according to the 4776:Timeline of black hole physics 1710: 1651: 1568: 1348: 1: 4544:Nonsingular black hole models 3934:X-ray pulsar-based navigation 3913:Compton Gamma Ray Observatory 1312: 841:Transient binary X-ray source 3006:Staff Writers (2018-10-04). 2776:Astronomy & Astrophysics 2650:Astronomy & Astrophysics 2088:. 2007-12-29. Archived from 1492:10.1126/science.359.6377.724 7: 4766:Rossi X-ray Timing Explorer 4731:Hypercompact stellar system 4721:Gamma-ray burst progenitors 3903:Rossi X-ray Timing Explorer 3746:Gamma-ray burst progenitors 3127:10.1051/0004-6361/201937343 2709:10.1088/0004-637X/699/1/453 2680:10.1051/0004-6361:200810334 1250: 921:List of objects in mass gap 391:in a neutron star formed a 383:in 1939, using the work of 360:. This even applies in the 27:) is an upper bound to the 10: 5002: 4452:Black hole complementarity 4419:Bousso's holographic bound 4404:Quasi-periodic oscillation 4102: 4096:Malament–Hogarth spacetime 3700:Quasi-periodic oscillation 3096:Astronomy and Astrophysics 2806:10.1051/0004-6361:20054686 1883:10.1103/RevModPhys.74.1015 1329:Astronomy and Astrophysics 1113:Near-infrared spectroscopy 964:Mass determination method 584:Mass determination method 537: 531: 403:, which was less than the 108: 4930: 4804: 4656: 4618: 4597: 4536: 4495: 4444: 4323:Gravitational singularity 4310: 4203: 4113: 4038: 4025: 3957: 3926: 3918:Chandra X-ray Observatory 3893: 3867: 3738: 3640: 3582: 3546: 3525: 3440:The Astrophysical Journal 3061:10.1038/s41586-019-1766-2 2977:10.1038/s41586-018-0565-5 2597:The Astrophysical Journal 2343:The Astrophysical Journal 2116:The Astrophysical Journal 1949:10.1017/S1743921307004590 1862:Reviews of Modern Physics 1837:10.1007/s10838-018-9435-y 1781:10.1038/s41586-018-0060-z 1414:The Astrophysical Journal 1357:The Astrophysical Journal 969: 966: 963: 957: 948: 934: 931: 589: 586: 583: 577: 568: 554: 551: 466:quark degeneracy pressure 119:Pauli exclusion principle 4907:PSO J030947.49+271757.31 4832:SDSS J150243.09+111557.3 4365:Blandford–Znajek process 3685:Neutron-star oscillation 3574:Rotating radio transient 3098:(Letter to the Editor). 2374:10.3847/2041-8213/ab75f5 2312:Kumar, V. (2019-11-03). 1818:Illari, Phyllis (2019). 1695:10.3847/2041-8213/ac8007 1553:10.3847/2041-8213/aaa401 1445:10.3847/2041-8213/aac3d6 1307: 1292:Oppenheimer–Snyder model 763:Near-infrared photometry 4163:Active galactic nucleus 3350:10.1126/science.1128177 3118:2020A&A...633L...5I 2919:10.1023/A:1021356630889 2798:2006A&A...457..249F 2672:2008A&A...492..319S 2283:10.1126/science.aau4005 2238:Northwestern University 2232:Elavsky, F; Geller, A. 2056:10.1126/science.1123430 1342:1996A&A...305..871B 655:In Milky Way outskirts. 629:2MASS J05215658+4359220 142:reduced Planck constant 4791:Tidal disruption event 4761:Supermassive dark star 4679:Black holes in fiction 4664:Outline of black holes 4297:Supermassive dark star 4216:Gravitational collapse 3939:Tempo software program 1645:10.1103/PhysRev.55.374 1603:10.1103/PhysRev.55.364 1575:Tolman, R. C. (1939). 734:main sequence turn-off 449:extremely dense matter 352:In this relationship, 343: 264: 201: 156:gravitational constant 31:of cold, non-rotating 4986:J. Robert Oppenheimer 4669:Black Hole Initiative 4482:Holographic principle 3949:The Magnificent Seven 3237:10.1093/mnrasl/sls035 3178:10.1093/mnras/stx2106 2899:Space Science Reviews 2864:10.1093/mnrasl/sly166 2760:10.1093/mnras/stt2068 2514:10.1093/mnrasl/slx203 2433:10.1093/mnras/staa725 2205:10.1093/mnras/stab907 2002:10.1093/mnras/stu1102 1522:Astrophysical Journal 377:J. Robert Oppenheimer 344: 265: 202: 93:merging neutron stars 4472:Final parsec problem 4431:Schwarzschild radius 3854:Thorne–Żytkow object 3296:10.1093/mnras/stx778 1079:stripped helium star 722:In globular cluster 451:are not well known. 385:Richard Chace Tolman 313: 224: 171: 4771:Superluminal motion 4746:Population III star 4716:Gravitational waves 4674:Black hole starship 4457:Information paradox 3805:Neutron star merger 3665:Chandrasekhar limit 3632:Hulse–Taylor pulsar 3559:Soft gamma repeater 3462:2003ApJ...599.1254G 3407:2005MNRAS.364..899C 3342:2006Sci...312.1771A 3287:2017MNRAS.468.3689M 3228:2013MNRAS.429L.104Z 3169:2017MNRAS.472.2181K 3053:2019Natur.575..618L 2969:2018Natur.562...82A 2911:2002SSRv..102...23C 2855:2019MNRAS.482L..46V 2751:2014MNRAS.437.2554M 2619:1998ApJ...499..375O 2564:2002MNRAS.331.1065C 2505:2018MNRAS.475L..15G 2424:2020MNRAS.494..190F 2365:2020ApJ...892L...3A 2275:2019Sci...366..637T 2196:2021MNRAS.504.2577J 2138:2000ApJ...541.1033F 2048:2006Sci...311.1901H 2032:(5769): 1901–1904. 1875:2002RvMP...74.1015W 1686:2022ApJ...934L..17R 1637:1939PhRv...55..374O 1595:1939PhRv...55..364T 1544:2018ApJ...852L..25R 1484:2018Sci...359..724C 1436:2018ApJ...859L..23P 1379:1996ApJ...470L..61K 1010:neutron star merger 407:for white dwarfs. 405:Chandrasekhar limit 366:Chandrasekhar limit 37:Chandrasekhar limit 35:, analogous to the 4605:Optical black hole 4518:Reissner–Nordström 4477:Firewall (physics) 4382:Gravitational lens 3849:Pulsar wind nebula 3827:Stellar black hole 1370:astro-ph/9608059v1 1006:Gravitational wave 726:. Companion is 0.8 662:GW190425's remnant 534:Stellar black hole 445:equations of state 364:case (that of the 339: 260: 197: 131:quantum wavelength 4958: 4957: 4751:Supermassive star 4741:Naked singularity 4736:Membrane paradigm 4462:Cosmic censorship 4436:Spaghettification 4424:Immirzi parameter 4377:Hawking radiation 4318:Astrophysical jet 4287:Supermassive star 4277:Binary black hole 4211:Stellar evolution 4153:Intermediate-mass 3985: 3984: 3778:Supernova remnant 3568:Ultra-long period 3037:(7784): 618–621. 2259:(6465): 637–640. 1775:(7705): 396–399. 1478:(6377): 724–725. 1248: 1247: 1002: 918: 917: 908: 832:Orbital resonance 765:of companion and 686: 490:stellar evolution 474:degenerate matter 337: 195: 165:given roughly by 4993: 4948: 4947: 4938: 4937: 4610:Sonic black hole 4559:Dark-energy star 4414:Bekenstein bound 4399:M–sigma relation 4328:Ring singularity 4108: 4012: 4005: 3998: 3989: 3988: 3975: 3974: 3965: 3964: 3751:Asteroseismology 3653:Fast radio burst 3512: 3505: 3498: 3489: 3488: 3482: 3481: 3455: 3453:astro-ph/0308490 3446:(2): 1254–1259. 3435: 3429: 3428: 3418: 3400: 3398:astro-ph/0507549 3376: 3370: 3369: 3335: 3333:astro-ph/0605549 3326:(5781): 1771–3. 3315: 3309: 3308: 3298: 3280: 3256: 3250: 3249: 3239: 3221: 3197: 3191: 3190: 3180: 3162: 3138: 3132: 3131: 3129: 3111: 3087: 3081: 3080: 3046: 3024: 3018: 3017: 3003: 2997: 2996: 2962: 2937: 2931: 2930: 2894: 2888: 2887: 2883: 2881: 2866: 2848: 2824: 2818: 2817: 2791: 2789:astro-ph/0606269 2771: 2765: 2764: 2762: 2744: 2720: 2714: 2698: 2692: 2691: 2665: 2645: 2639: 2638: 2612: 2610:astro-ph/9712018 2592: 2586: 2585: 2575: 2557: 2555:astro-ph/0112329 2548:(4): 1065–1071. 2533: 2527: 2526: 2516: 2498: 2474: 2468: 2467: 2465: 2464: 2455:. Archived from 2444: 2438: 2437: 2435: 2417: 2393: 2387: 2386: 2376: 2358: 2334: 2328: 2327: 2325: 2324: 2309: 2303: 2302: 2268: 2248: 2242: 2241: 2229: 2210: 2209: 2207: 2189: 2180:(2): 2577–2602. 2164: 2158: 2157: 2131: 2129:astro-ph/9907433 2122:(2): 1033–1050. 2107: 2101: 2100: 2098: 2097: 2082: 2076: 2075: 2041: 2039:astro-ph/0601337 2021: 2015: 2014: 2004: 1994: 1985:(4): 3484–3494. 1970: 1961: 1960: 1942: 1940:astro-ph/0612312 1922: 1916: 1915: 1913: 1911:astro-ph/0306213 1901: 1895: 1894: 1869:(4): 1015–1071. 1856: 1850: 1849: 1839: 1815: 1809: 1808: 1760: 1754: 1753: 1751: 1750: 1735: 1729: 1728: 1726: 1725: 1714: 1708: 1707: 1697: 1679: 1655: 1649: 1648: 1618: 1607: 1606: 1572: 1566: 1565: 1555: 1537: 1513: 1504: 1503: 1467: 1458: 1457: 1447: 1429: 1405: 1399: 1398: 1372: 1352: 1346: 1345: 1323: 1297:Bekenstein bound 1281: 1276: 1275: 1267: 1265:Astronomy portal 1262: 1261: 1260: 1221: 1220: 1219: 1218: 1177: 1176: 1175: 1174: 1132: 1108: 1099: 1068: 1041: 1020:interferometers. 1001: 998: 992: 991: 990: 989: 929: 928: 907: 904: 898: 897: 895: 862: 861: 859: 822: 796: 795: 794: 793: 753: 710: 709: 707: 685: 682: 676: 675: 674: 673: 649:K-type (?) giant 643: 642: 641: 640: 622: 608: 607: 605: 596:V723 Monocerotis 549: 548: 538:Content here is 468:if it becomes a 422: 420: 355: 348: 346: 345: 340: 338: 336: 335: 323: 306: 302: 301: 299: 298: 293: 290: 276: 269: 267: 266: 261: 259: 258: 249: 248: 236: 235: 213: 206: 204: 203: 198: 196: 194: 193: 181: 160: 153: 146: 135: 5001: 5000: 4996: 4995: 4994: 4992: 4991: 4990: 4961: 4960: 4959: 4954: 4926: 4902:ULAS J1342+0928 4862:SDSS J0849+1114 4847:Phoenix Cluster 4800: 4652: 4614: 4593: 4532: 4491: 4487:No-hair theorem 4440: 4394:Bondi accretion 4360:Penrose process 4306: 4272:Gamma-ray burst 4199: 4109: 4100: 4086:Direct collapse 4034: 4021: 4016: 3986: 3981: 3953: 3922: 3895: 3889: 3863: 3734: 3670:Gamma-ray burst 3660:Bondi accretion 3636: 3578: 3564:Anomalous X-ray 3542: 3521: 3516: 3486: 3485: 3436: 3432: 3377: 3373: 3316: 3312: 3257: 3253: 3198: 3194: 3139: 3135: 3088: 3084: 3025: 3021: 3004: 3000: 2953:(7725): 82–85. 2938: 2934: 2895: 2891: 2879: 2877: 2874: 2825: 2821: 2772: 2768: 2721: 2717: 2699: 2695: 2646: 2642: 2593: 2589: 2534: 2530: 2475: 2471: 2462: 2460: 2445: 2441: 2394: 2390: 2335: 2331: 2322: 2320: 2310: 2306: 2249: 2245: 2230: 2213: 2165: 2161: 2108: 2104: 2095: 2093: 2084: 2083: 2079: 2022: 2018: 1971: 1964: 1923: 1919: 1902: 1898: 1857: 1853: 1816: 1812: 1761: 1757: 1748: 1746: 1738:Siegel, Ethan. 1736: 1732: 1723: 1721: 1716: 1715: 1711: 1656: 1652: 1624:Physical Review 1619: 1610: 1582:Physical Review 1573: 1569: 1514: 1507: 1468: 1461: 1406: 1402: 1353: 1349: 1324: 1320: 1315: 1310: 1277: 1270: 1263: 1258: 1256: 1253: 1216: 1214: 1213: 1211: 1172: 1170: 1169: 1167: 1106: 987: 985: 984: 982: 950: 944: 941: 936: 923: 893: 891: 857: 855: 791: 789: 788: 786: 747: 732: 729: 705: 703: 671: 669: 668: 666: 638: 636: 635: 633: 620: 603: 601: 570: 564: 561: 556: 547: 536: 530: 457: 442: 439: 428: 418: 416: 371:In the case of 353: 350: 331: 327: 322: 314: 311: 310: 304: 294: 291: 286: 285: 283: 278: 274: 271: 254: 250: 244: 240: 231: 227: 225: 222: 221: 211: 208: 189: 185: 180: 172: 169: 168: 158: 151: 144: 133: 117:, based on the 111: 101: 98: 83: 80: 76: 73: 69: 66: 58: 55: 17: 12: 11: 5: 4999: 4989: 4988: 4983: 4978: 4973: 4956: 4955: 4953: 4952: 4942: 4931: 4928: 4927: 4925: 4924: 4922:Swift J1644+57 4919: 4914: 4909: 4904: 4899: 4894: 4889: 4884: 4879: 4874: 4872:MS 0735.6+7421 4869: 4864: 4859: 4854: 4849: 4844: 4839: 4837:Sagittarius A* 4834: 4829: 4824: 4819: 4814: 4808: 4806: 4802: 4801: 4799: 4798: 4793: 4788: 4783: 4778: 4773: 4768: 4763: 4758: 4753: 4748: 4743: 4738: 4733: 4728: 4723: 4718: 4713: 4712: 4711: 4706: 4696: 4691: 4686: 4681: 4676: 4671: 4666: 4660: 4658: 4654: 4653: 4651: 4650: 4645: 4640: 4635: 4630: 4624: 4622: 4616: 4615: 4613: 4612: 4607: 4601: 4599: 4595: 4594: 4592: 4591: 4586: 4581: 4576: 4571: 4566: 4561: 4556: 4551: 4546: 4540: 4538: 4534: 4533: 4531: 4530: 4525: 4520: 4515: 4510: 4499: 4497: 4493: 4492: 4490: 4489: 4484: 4479: 4474: 4469: 4464: 4459: 4454: 4448: 4446: 4442: 4441: 4439: 4438: 4433: 4428: 4427: 4426: 4416: 4411: 4409:Thermodynamics 4406: 4401: 4396: 4391: 4390: 4389: 4379: 4374: 4372:Accretion disk 4369: 4368: 4367: 4362: 4352: 4347: 4342: 4337: 4336: 4335: 4330: 4320: 4314: 4312: 4308: 4307: 4305: 4304: 4299: 4294: 4289: 4284: 4279: 4274: 4269: 4268: 4267: 4262: 4257: 4247: 4246: 4245: 4235: 4230: 4229: 4228: 4218: 4213: 4207: 4205: 4201: 4200: 4198: 4197: 4196: 4195: 4190: 4185: 4180: 4175: 4170: 4165: 4155: 4150: 4149: 4148: 4138: 4137: 4136: 4133: 4128: 4117: 4115: 4111: 4110: 4103: 4101: 4099: 4098: 4093: 4088: 4083: 4078: 4073: 4068: 4063: 4058: 4053: 4048: 4046:BTZ black hole 4042: 4040: 4036: 4035: 4033: 4032: 4026: 4023: 4022: 4015: 4014: 4007: 4000: 3992: 3983: 3982: 3980: 3979: 3969: 3958: 3955: 3954: 3952: 3951: 3946: 3941: 3936: 3930: 3928: 3924: 3923: 3921: 3920: 3915: 3910: 3905: 3899: 3897: 3891: 3890: 3888: 3887: 3882: 3877: 3871: 3869: 3865: 3864: 3862: 3861: 3856: 3851: 3846: 3841: 3836: 3835: 3834: 3824: 3823: 3822: 3812: 3807: 3802: 3797: 3792: 3787: 3786: 3785: 3780: 3770: 3769: 3768: 3763: 3753: 3748: 3742: 3740: 3736: 3735: 3733: 3732: 3727: 3722: 3717: 3712: 3707: 3702: 3697: 3692: 3687: 3682: 3680:Neutron matter 3677: 3672: 3667: 3662: 3657: 3656: 3655: 3644: 3642: 3638: 3637: 3635: 3634: 3629: 3624: 3619: 3614: 3613: 3612: 3607: 3602: 3592: 3586: 3584: 3583:Binary pulsars 3580: 3579: 3577: 3576: 3571: 3570: 3569: 3566: 3561: 3550: 3548: 3547:Single pulsars 3544: 3543: 3541: 3540: 3535: 3529: 3527: 3523: 3522: 3515: 3514: 3507: 3500: 3492: 3484: 3483: 3470:10.1086/379311 3430: 3391:(3): 899–908. 3371: 3310: 3251: 3192: 3133: 3082: 3019: 2998: 2932: 2889: 2872: 2839:(1): L46–L49. 2819: 2782:(1): 249–255. 2766: 2715: 2693: 2656:(2): 319–322. 2640: 2627:10.1086/305620 2603:(1): 375–384. 2587: 2528: 2489:(1): L15–L19. 2469: 2439: 2408:(1): 190–198. 2388: 2329: 2304: 2243: 2211: 2159: 2146:10.1086/309446 2102: 2077: 2016: 1962: 1917: 1896: 1851: 1810: 1755: 1730: 1709: 1650: 1631:(4): 374–381. 1608: 1589:(4): 364–373. 1567: 1505: 1459: 1400: 1387:10.1086/310296 1347: 1317: 1316: 1314: 1311: 1309: 1306: 1305: 1304: 1299: 1294: 1289: 1283: 1282: 1279:Physics portal 1268: 1252: 1249: 1246: 1245: 1243: 1237: 1230: 1225: 1222: 1208: 1198: 1197: 1195: 1189: 1186: 1181: 1178: 1164: 1158: 1157: 1155: 1144: 1141: 1136: 1133: 1128: 1122: 1121: 1119: 1116: 1110: 1103: 1102:24,100 ± 3,600 1100: 1095: 1089: 1088: 1086: 1083: 1081: 1072: 1069: 1064: 1058: 1057: 1055: 1052: 1050: 1045: 1042: 1037: 1031: 1030: 1028: 1021: 1003: 996: 993: 979: 972: 971: 968: 965: 962: 956: 947: 942: 939: 933: 922: 919: 916: 915: 913: 911: 909: 902: 899: 888: 882: 881: 879: 876: 869: 866: 863: 852: 846: 845: 843: 838: 834:modeling from 829: 826: 823: 818: 812: 811: 809: 806: 803: 800: 799:30,000 ± 3,500 797: 783: 779: 778: 776: 770: 767:Eddington flux 760: 757: 754: 749: 740: 739: 737: 730: 727: 720: 717: 714: 711: 700: 696: 695: 693: 690: 687: 680: 677: 663: 659: 658: 656: 653: 650: 647: 644: 630: 626: 625: 623: 618: 615: 612: 609: 598: 592: 591: 588: 585: 582: 576: 567: 562: 559: 553: 529: 526: 502:X-ray binaries 456: 453: 440: 437: 426: 413:PSR J0952–0607 381:George Volkoff 334: 330: 326: 321: 318: 309: 257: 253: 247: 243: 239: 234: 230: 220: 216:virial theorem 192: 188: 184: 179: 176: 167: 149:speed of light 110: 107: 99: 96: 81: 78: 74: 71: 67: 64: 56: 53: 15: 9: 6: 4: 3: 2: 4998: 4987: 4984: 4982: 4979: 4977: 4976:Neutron stars 4974: 4972: 4969: 4968: 4966: 4951: 4943: 4941: 4933: 4932: 4929: 4923: 4920: 4918: 4915: 4913: 4910: 4908: 4905: 4903: 4900: 4898: 4897:Markarian 501 4895: 4893: 4890: 4888: 4885: 4883: 4880: 4878: 4875: 4873: 4870: 4868: 4865: 4863: 4860: 4858: 4855: 4853: 4850: 4848: 4845: 4843: 4840: 4838: 4835: 4833: 4830: 4828: 4825: 4823: 4822:XTE J1118+480 4820: 4818: 4817:XTE J1650-500 4815: 4813: 4810: 4809: 4807: 4803: 4797: 4794: 4792: 4789: 4787: 4784: 4782: 4779: 4777: 4774: 4772: 4769: 4767: 4764: 4762: 4759: 4757: 4754: 4752: 4749: 4747: 4744: 4742: 4739: 4737: 4734: 4732: 4729: 4727: 4724: 4722: 4719: 4717: 4714: 4710: 4707: 4705: 4702: 4701: 4700: 4697: 4695: 4692: 4690: 4687: 4685: 4682: 4680: 4677: 4675: 4672: 4670: 4667: 4665: 4662: 4661: 4659: 4655: 4649: 4646: 4644: 4641: 4639: 4636: 4634: 4631: 4629: 4626: 4625: 4623: 4621: 4617: 4611: 4608: 4606: 4603: 4602: 4600: 4596: 4590: 4587: 4585: 4582: 4580: 4577: 4575: 4572: 4570: 4567: 4565: 4562: 4560: 4557: 4555: 4552: 4550: 4547: 4545: 4542: 4541: 4539: 4535: 4529: 4526: 4524: 4521: 4519: 4516: 4514: 4511: 4508: 4504: 4503:Schwarzschild 4501: 4500: 4498: 4494: 4488: 4485: 4483: 4480: 4478: 4475: 4473: 4470: 4468: 4465: 4463: 4460: 4458: 4455: 4453: 4450: 4449: 4447: 4443: 4437: 4434: 4432: 4429: 4425: 4422: 4421: 4420: 4417: 4415: 4412: 4410: 4407: 4405: 4402: 4400: 4397: 4395: 4392: 4388: 4385: 4384: 4383: 4380: 4378: 4375: 4373: 4370: 4366: 4363: 4361: 4358: 4357: 4356: 4353: 4351: 4348: 4346: 4345:Photon sphere 4343: 4341: 4340:Event horizon 4338: 4334: 4331: 4329: 4326: 4325: 4324: 4321: 4319: 4316: 4315: 4313: 4309: 4303: 4300: 4298: 4295: 4293: 4290: 4288: 4285: 4283: 4280: 4278: 4275: 4273: 4270: 4266: 4265:Related links 4263: 4261: 4258: 4256: 4253: 4252: 4251: 4248: 4244: 4243:Related links 4241: 4240: 4239: 4236: 4234: 4231: 4227: 4226:Related links 4224: 4223: 4222: 4219: 4217: 4214: 4212: 4209: 4208: 4206: 4202: 4194: 4191: 4189: 4186: 4184: 4181: 4179: 4176: 4174: 4171: 4169: 4166: 4164: 4161: 4160: 4159: 4156: 4154: 4151: 4147: 4144: 4143: 4142: 4139: 4134: 4132: 4129: 4127: 4124: 4123: 4122: 4119: 4118: 4116: 4112: 4107: 4097: 4094: 4092: 4089: 4087: 4084: 4082: 4079: 4077: 4074: 4072: 4069: 4067: 4064: 4062: 4059: 4057: 4054: 4052: 4051:Schwarzschild 4049: 4047: 4044: 4043: 4041: 4037: 4031: 4028: 4027: 4024: 4020: 4013: 4008: 4006: 4001: 3999: 3994: 3993: 3990: 3978: 3970: 3968: 3960: 3959: 3956: 3950: 3947: 3945: 3942: 3940: 3937: 3935: 3932: 3931: 3929: 3925: 3919: 3916: 3914: 3911: 3909: 3906: 3904: 3901: 3900: 3898: 3896:investigation 3892: 3886: 3883: 3881: 3880:Centaurus X-3 3878: 3876: 3873: 3872: 3870: 3866: 3860: 3857: 3855: 3852: 3850: 3847: 3845: 3844:Pulsar planet 3842: 3840: 3837: 3833: 3832:Related links 3830: 3829: 3828: 3825: 3821: 3820:Related links 3818: 3817: 3816: 3813: 3811: 3808: 3806: 3803: 3801: 3798: 3796: 3793: 3791: 3788: 3784: 3783:Related links 3781: 3779: 3776: 3775: 3774: 3771: 3767: 3764: 3762: 3759: 3758: 3757: 3754: 3752: 3749: 3747: 3744: 3743: 3741: 3737: 3731: 3728: 3726: 3723: 3721: 3718: 3716: 3713: 3711: 3708: 3706: 3703: 3701: 3698: 3696: 3693: 3691: 3688: 3686: 3683: 3681: 3678: 3676: 3673: 3671: 3668: 3666: 3663: 3661: 3658: 3654: 3651: 3650: 3649: 3646: 3645: 3643: 3639: 3633: 3630: 3628: 3625: 3623: 3620: 3618: 3615: 3611: 3608: 3606: 3605:X-ray burster 3603: 3601: 3598: 3597: 3596: 3593: 3591: 3588: 3587: 3585: 3581: 3575: 3572: 3567: 3565: 3562: 3560: 3557: 3556: 3555: 3552: 3551: 3549: 3545: 3539: 3536: 3534: 3531: 3530: 3528: 3524: 3520: 3513: 3508: 3506: 3501: 3499: 3494: 3493: 3490: 3479: 3475: 3471: 3467: 3463: 3459: 3454: 3449: 3445: 3441: 3434: 3426: 3422: 3417: 3412: 3408: 3404: 3399: 3394: 3390: 3386: 3382: 3375: 3367: 3363: 3359: 3355: 3351: 3347: 3343: 3339: 3334: 3329: 3325: 3321: 3314: 3306: 3302: 3297: 3292: 3288: 3284: 3279: 3274: 3270: 3266: 3262: 3255: 3247: 3243: 3238: 3233: 3229: 3225: 3220: 3215: 3212:: L104–L108. 3211: 3207: 3203: 3196: 3188: 3184: 3179: 3174: 3170: 3166: 3161: 3156: 3152: 3148: 3144: 3137: 3128: 3123: 3119: 3115: 3110: 3105: 3101: 3097: 3093: 3086: 3078: 3074: 3070: 3066: 3062: 3058: 3054: 3050: 3045: 3040: 3036: 3032: 3031: 3023: 3015: 3014: 3009: 3002: 2994: 2990: 2986: 2982: 2978: 2974: 2970: 2966: 2961: 2956: 2952: 2948: 2944: 2943:Dingus, B. 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Index

mass
neutron stars
Chandrasekhar limit
white dwarf
black hole
solar masses
M
GW170817
merging neutron stars
Lev Landau
Pauli exclusion principle
fermionic
rest mass
quantum wavelength
Planck units
reduced Planck constant
speed of light
gravitational constant
pressure
virial theorem
proton mass
white dwarf
Chandrasekhar limit
neutron stars
J. Robert Oppenheimer
George Volkoff
Richard Chace Tolman
neutrons
degenerate
Fermi gas

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