The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
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.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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]
Citations
Cites
Lectures on Differential Geometry.
Vanstone, J. R., & Sternberg, S. (1966) · American Mathematical Monthly · doi:10.2307/2315376 · Cited by 1,207
Théories Relativistes de la Gravitation et de l'Électromagnétisme
Lichnerowicz, A., & Teichmann, T. (1955) · Physics Today · doi:10.1063/1.3061795 · Cited by 599
Singularities in Closed Universes
Geroch, R. (1966) · Physical Review Letters · doi:10.1103/physrevlett.17.445 · Cited by 114
Research works printed but not linked: 2
- Carter B., 1966, P hys, Lett., 21, 423
- 1965, P hys, Rev. Lett., 15, 689
Cited by
Sorted by citations
Particle creation by black holes
Hawking, S. W. (1975) · Communications In Mathematical Physics · doi:10.1007/bf02345020 · Cited by 13,106
Self-citationBreakdown of predictability in gravitational collapse
Hawking, S. W. (1976) · Physical Review D · doi:10.1103/physrevd.14.2460 · Cited by 2,554
Self-citationGlobal Structure of the Kerr Family of Gravitational Fields
Carter, B. (1968) · Physical Review · doi:10.1103/physrev.174.1559 · Cited by 2,294
The singularities of gravitational collapse and cosmology
Hawking, S. W., & Penrose, R. (1970) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1970.0021 · Cited by 2,100
Self-citationBlack holes in general relativity
Hawking, S. W. (1972) · Communications in Mathematical Physics · doi:10.1007/bf01877517 · Cited by 1,561
Self-citation
Metadata
- 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 › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
- Keywords
- cosmological singularity, causality, singularity theorems, spherical collapse, Cauchy surfaces
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
