The occurrence of singularities in cosmology. ɪɪɪ. Causality and singularities
Abstract
The questions about singularities that remain to be answered are discussed. It is shown, without any assumption about causality, that there are fully general solutions which evolve from a non-singular state to an inevitable singularity. An observationally testable condition is given which would imply the existence of a singularity if a reasonable assumption about causality were made. This condition would also be satisfied in an approximately spherical collapsing star and so would enable one to prove the occurrence of a singularity in such circumstances without assuming that space-time admits a Cauchy surface. If the assumption about causality held, the singularity could not be of the Misner type but would presumably involve infinite curvature. This would probably indicate that the Einstein theory broke down but only in very strong fields.
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High curvatures occur in collapsing stars and at the beginning of the present universe, and are hidden from us by an event horizon.
“From the classical singularity theorems [3-6], one would expect such high curvatures to occur in collapsing stars and, in the past, at the beginning of the present espe se e oone o on oet e ne o e e osones of high curvature to be hidden from us by an event horizon [7].”
From Particle creation by black holes (1975) · cites this paper as [4]
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- Authors
- Hawking, S. W.
- Affiliations
- University of Cambridge (GB)
- Corresponding author
- Hawking, Stephen William
- Venue
- Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1967-08-30
- Volume
- 300
- Issue
- 1461
- Pages
- 187-201
- ISSN
- 0080-4630 (ISSN-L)
- 2053-9169
- OpenAlex
- W2075536196
- Cited by
- 360
- References
- 3
- Citations by year
- 2026: 11 · 2025: 37 · 2024: 16 · 2023: 41 · 2022: 15 · 2021: 11 · 2020: 10 · 2019: 16 · 2018: 16 · 2017: 17 · 2016: 10 · 2015: 13 · 2014: 11 · 2013: 6 · 2012: 9
- FWCI
- 5.97
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Proceedings of the Royal Society of London A Mathematical and Physical Sciences (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- cosmological singularity, causality, singularity theorems, spherical collapse, Cauchy surfaces
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