From
https://www.nobelprize.org/prizes/physics/2020/advanced-information/
Schmidt’s discovery prompted Wheeler to reconsider the physics of gravitational collapse and he discussed this with Penrose, who began to think about the problem in late 1964.
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However, it was far from clear that this could happen in the real world and whether the assumption of spherical symmetry was a prerequisite for gravitational collapse.
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Penrose set out to analyse the situation without the assumption of spherical symmetry, assuming only that the collapsing matter had a positive energy density. To do this, he had to invent new mathematical methods and make use of topology. The key concept that Penrose introduced was that of a trapped surface.
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After realizing the power of the idea of trapped surfaces, Penrose proceeded to prove that once a trapped surface had formed, it is impossible, within the theory of general relativity and with a positive energy density, to prevent the collapse towards a singularity (Penrose 1965).
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Penrose’s result is heralded as the first post-Einsteinian result in general relativity. It proves that gravitational collapse cannot be stopped after the trapped surface is formed. One should note that its formation happens at a stage in the collapse when density of matter is not very high. (The supermassive black holes of Michell and Laplace have average densities no higher than those of the Sun or Earth.) A few years later Penrose, together with Stephen Hawking, went further to show that similar results also applied to cosmological singularities (Hawking 1965, Hawking & Penrose 1970). Under reasonable assumptions, a past singularity is inevitable in the Big Bang model. Penrose (1969) wrote a beautiful summary of many of these results.
Penrose, R., 1963, “Asymptotic properties of fields and space-times”,
Physical Review Letters, vol. 10, no. 2. pp. 66–68.
https://doi.org/10.1103/PhysRevLett.10.66
Penrose, R., 1965, “Gravitational collapse and space-time singularities”,
Physical Review Letters, vol. 14, no. 3. pp. 57–59, 1965.
https://doi.org/10.1103/PhysRevLett.14.57.
Penrose, R., 1969, “Gravitational collapse: the role of general relativity”,
Nuovo Cimento Rivista Serie, vol. 1. p. 252.
( reprinted as
Penrose, R. “Golden Oldie”: Gravitational Collapse: The Role of General Relativity.
General Relativity and Gravitation 34, 1141–1165 (2002).
https://doi.org/10.1023/A:1016578408204
)(Other references in the quoted document of possible interest:
Hawking, S. W., 1965, “Occurrence of singularities in open universes”,
Physical Review Letters, vol. 15, no. 17. pp. 689–690.
https://doi.org/10.1103/PhysRevLett.15.689.
Hawking, S. W., and Penrose, R., 1970, “The singularities of gravitational collapse and cosmology”,
Proceedings of the Royal Society of London Series A, vol. 314, no. 1519. pp. 529– 548.
https://doi.org/10.1098/rspa.1970.0021
Hawking, S. W., 1972, “Black holes in General Relativity”,
Communications in Mathematical Physics, vol. 25. pp. 152.
(
https://projecteuclid.org/euclid.cmp/1103857884 )
Hawking, S. W., 1975, “Particle creation by black holes”,
Communications in Mathematical Physics, vol. 43, no. 3. pp. 199–220.
https://doi.org/10.1007/BF02345020. (
https://projecteuclid.org/euclid.cmp/1103899181 )
)
Other references of possible interest:José M. M. Senovilla, David Garfinkle
"The 1965 Penrose singularity theorem"
https://arxiv.org/abs/1410.5226
https://iopscience.iop.org/issue/0264-9381/32/12
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