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
Flagged first, then by citations
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“Golden Oldie”: Gravitational Collapse: The Role of General Relativity
Penrose, R. (2002) · General Relativity and Gravitation · doi:10.1023/a:1016578408204 · Cited by 1,296
Gravitational Radiation from Colliding Black Holes
Hawking, S. W. (1971) · Physical Review Letters · doi:10.1103/physrevlett.26.1344 · Cited by 1,142
Self-citationGeroch, R. (1970) · Journal of Mathematical Physics · doi:10.1063/1.1665157 · Cited by 625
Teleparallel gravity: from theory to cosmology
Bahamonde, S., Dialektopoulos, K. F., Escamilla‐Rivera, C., Farrugia, G., Gakis, V., Hendry, M., Hohmann, M., Said, J. L., Mifsud, J., & Valentino, E. D. (2022) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac9cef · Cited by 668
Singularity Theorems and Their Consequences
Senovilla, J. M. M. (1998) · General Relativity and Gravitation · doi:10.1023/a:1018801101244 · Cited by 372
Mukhanov, V., & Brandenberger, R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.1969 · Cited by 260
The 1965 Penrose singularity theorem
Senovilla, J. M. M., & Garfinkle, D. (2015) · Classical and Quantum Gravity · doi:10.1088/0264-9381/32/12/124008 · Cited by 248
Topology change in classical and quantum gravity
Horowitz, G. T. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/4/007 · Cited by 240
Curiel, E. (2017) · Einstein Studies · doi:10.1007/978-1-4939-3210-8_3 · Cited by 226
Energy conditions in general relativity and quantum field theory
Kontou, E.-A., & Sanders, K. (2020) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab8fcf · Cited by 223
Is Black-Hole Evaporation Predictable?
Page, D. N. (1980) · Physical Review Letters · doi:10.1103/physrevlett.44.301 · Cited by 199
Numerical investigation of cosmological singularities
Berger, B. K., & Moncrief, V. (1993) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.48.4676 · Cited by 189
Open and closed universes, initial singularities, and inflation
Borde, A. (1994) · Physical Review D · doi:10.1103/physrevd.50.3692 · Cited by 175
Numerical Approaches to Spacetime Singularities
Berger, B. K. (2002) · Living Reviews in Relativity · doi:10.12942/lrr-2002-1 · Cited by 183
Shadow cast and deflection of light by charged rotating regular black holes
Kumar, R., Ghosh, S. G., & Wang, A. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.124024 · Cited by 166
Ashtekar, A., & Geroch, R. (1974) · Reports on Progress in Physics · doi:10.1088/0034-4885/37/10/001 · Cited by 156
Speck, J. (2012) · Selecta Mathematica · doi:10.1007/s00029-012-0090-6 · Cited by 136
Can the Universe create itself?
Gott, J. R., & Li, L.-X. (1998) · Physical Review D · doi:10.1103/physrevd.58.023501 · Cited by 127
Physical Processes in Naked Singularity Formation
Harada, T., Iguchi, H., & Nakao, K.-I. (2002) · Progress of Theoretical Physics · doi:10.1143/ptp.107.449 · Cited by 119
The Cauchy problem in general relativity
Ringström, H. (2013) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199680290.003.0002 · Cited by 143
Ansoldi, S. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0802.0330 · Cited by 118
On the instability of 3d null singularities
Lawrence, A. (2002) · Journal of High Energy Physics · doi:10.1088/1126-6708/2002/11/019 · Cited by 110
Present status of the Penrose inequality
Mars, M. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/19/193001 · Cited by 116
Test fields cannot destroy extremal black holes
Natário, J., Queimada, L., & Vicente, R. (2016) · Classical and Quantum Gravity · doi:10.1088/0264-9381/33/17/175002 · Cited by 109
Minguzzi, E. (2019) · Living Reviews in Relativity · doi:10.1007/s41114-019-0019-x · Cited by 132
Inner horizon instability and the unstable cores of regular black holes
Carballo-Rubio, R., Filippo, F. D., Liberati, S., Pacilio, C., & Visser, M. (2021) · Journal of High Energy Physics · doi:10.1007/jhep05(2021)132 · Cited by 105
Singularities in nonsimply connected space–times
Gannon, D. (1975) · Journal of Mathematical Physics · doi:10.1063/1.522498 · Cited by 103
Wang, Q., Zhu, Z. G., & Unruh, W. G. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.103504 · Cited by 106
Bouncing cosmological solutions from $$f(\mathsf{R,T})$$ f ( R , T ) gravity
Shabani, H., & Ziaie, A. H. (2018) · The European Physical Journal C · doi:10.1140/epjc/s10052-018-5886-x · Cited by 95
On the global isometric embedding of pseudo-Riemannian manifolds
Clarke, C. J. (1970) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1970.0015 · Cited by 95
Present Status of the Penrose InequalityPreprint
Mars, M., & Ciencias, F. D. (2009) · Cited by 116
Gravitational perfect fluid collapse in f(R) gravity
Sharif, M., & Kausar, H. R. (2010) · Astrophysics and Space Science · doi:10.1007/s10509-010-0426-7 · Cited by 80
D-dimensional Bardeen–AdS black holes in Einstein–Gauss–Bonnet theory
Kumar, A., Singh, D. V., & Ghosh, S. G. (2019) · The European Physical Journal C · doi:10.1140/epjc/s10052-019-6773-9 · Cited by 81
Exploring New Physics Frontiers Through Numerical Relativity
Cardoso, V., Gualtieri, L., Herdeiro, C., & Sperhake, U. (2015) · Living Reviews in Relativity · doi:10.1007/lrr-2015-1 · Cited by 98
Inside black holes with synchronized hair
Brihaye, Y., Herdeiro, C., & Radu, E. (2016) · Physics Letters B · doi:10.1016/j.physletb.2016.06.078 · Cited by 71
Do massive compact objects without event horizon exist in infinite derivative gravity?
Koshelev, A. S., & Mazumdar, A. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.084069 · Cited by 71
The Penrose-Hawking Singularity Theorems: History and Implications
Earman, J. (1999) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4612-0639-2_7 · Cited by 67
Lorentzian wormholes in higher-derivative gravity and the weak energy condition
Ghoroku, K., & Soma, T. (1992) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.46.1507 · Cited by 65
Role of Rastall gravity in constructing new spherically symmetric stellar solutions
Naseer, T. (2024) · Physics of the Dark Universe · doi:10.1016/j.dark.2024.101663 · Cited by 58
Jang, P. S. (1979) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.20.834 · Cited by 58
String field theory in curved spacetime and the resolution of spacelike singularities
Lawrence, A., & Martinec, E. J. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/1/007 · Cited by 57
Stable and generic properties in general relativity
Hawking, S. W. (1971) · General Relativity and Gravitation · doi:10.1007/bf00759218 · Cited by 55
Self-citationRodnianski, I., & Speck, J. (2018) · Selecta Mathematica · doi:10.1007/s00029-018-0437-8 · Cited by 54
More on the initial singularity problem in gravity’s rainbow cosmology
Khodadi, M., Nozari, K., & Sepangi, H. R. (2016) · General Relativity and Gravitation · doi:10.1007/s10714-016-2160-0 · Cited by 55
Smoothing and extending cosmic time functions
Seifert, H. J. (1977) · General Relativity and Gravitation · doi:10.1007/bf00759586 · Cited by 54
From geometry to numerics: interdisciplinary aspects in mathematical and numerical relativity
Jaramillo, J. L., Kroon, J. A. V., & Gourgoulhon, É. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/9/093001 · Cited by 53
On the structure and applications of the Bondi–Metzner–Sachs group
Alessio, F., & Esposito, G. V. M. (2017) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887818300027 · Cited by 51
GRAVITATIONAL PERFECT FLUID COLLAPSE WITH COSMOLOGICAL CONSTANT
Sharif, M., & Ahmad, Z. (2007) · Modern Physics Letters A · doi:10.1142/s0217732307021834 · Cited by 51
Nonpolynomial Lagrangian approach to regular black holes
Colléaux, A., Chinaglia, S., & Zerbini, S. (2018) · International Journal of Modern Physics D · doi:10.1142/s0218271818300021 · Cited by 60
Strong energy condition in R+R2 gravity
Kung, J. H. (1996) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.53.3017 · Cited by 51
AN INTRODUCTION TO QUANTUM GRAVITY
DeWitt, B. S., & Esposito, G. V. M. (2008) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887808002679 · Cited by 59
Quantization of general relativity
Brill, D. R., & Gowdy, R. H. (1970) · Reports on Progress in Physics · doi:10.1088/0034-4885/33/2/301 · Cited by 50
Black Holes and Gravitational Theory
Penrose, R. (1972) · Nature · doi:10.1038/236377a0 · Cited by 47
Rodnianski, I., & Speck, J. (2017) · Annals of Mathematics · doi:10.4007/annals.2018.187.1.2 · Cited by 46
On the propagation across the big bounce in an open quantum FLRW cosmology
Battista, E., & Steinacker, H. C. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10874-0 · Cited by 51
Topology of nonlinearly charged black hole chemistry via massive gravity
Zhang, M., Chen, H., HASSANABADI, H., Long, Z., & Yang, H. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-11933-w · Cited by 51
On singular semi-Riemannian manifolds
Stoica, O. C. (2014) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887814500418 · Cited by 45
Exploring New Physics Frontiers Through Numerical RelativityPreprint
Cardoso, V., Gualtieri, L., Herdeiro, C., & Sperhake, U. (2015) · Cited by 55
Cosmic Censorship for Gowdy Spacetimes
Ringström, H. (2010) · Living Reviews in Relativity · doi:10.12942/lrr-2010-2 · Cited by 44
Coley, A. A., & Ellis, G. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab49b6 · Cited by 42
Quantum evolution of black hole initial data sets: Foundations
Alesci, E., Bahrami, S., & Pranzetti, D. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.046014 · Cited by 43
Shadow and greybody bounding of a regular scale-dependent black hole solution
Övgün, A., Pantig, R. C., & Rincón, Á. (2024) · Annals of Physics · doi:10.1016/j.aop.2024.169625 · Cited by 41
Cosmological perturbations and stability of nonsingular cosmologies with limiting curvature
Yoshida, D., Quintin, J., Yamaguchi, M., & Brandenberger, R. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.043502 · Cited by 41
Gravitational Radiation from a Naked Singularity: Odd-Parity Perturbation
Iguchi, H., Harada, T., & Nakao, K.-I. (1999) · Progress of Theoretical Physics · doi:10.1143/ptp.101.1235 · Cited by 41
Cuscuton gravity as a classically stable limiting curvature theory
Quintin, J., & Yoshida, D. (2020) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2020/02/016 · Cited by 40
Penrose’s singularity theorem in a Finsler spacetime*
Aazami, A. B., & Javaloyes, M. Á. (2015) · Classical and Quantum Gravity · doi:10.1088/0264-9381/33/2/025003 · Cited by 40
Yang, Y. (2022) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac840b · Cited by 41
Iguchi, H., Nakao, K.-I., & Harada, T. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.57.7262 · Cited by 38
The Hawking–Penrose Singularity Theorem for C 1,1-Lorentzian Metrics
Graf, M., Grant, J. D. E., Kunzinger, M., & Steinbauer, R. (2017) · Communications in Mathematical Physics · doi:10.1007/s00220-017-3047-y · Cited by 36
Gravitational Radiation from a Naked Singularity. II: Even-Parity Perturbation
Iguchi, H., Harada, T., & Nakao, K.-I. (2000) · Progress of Theoretical Physics · doi:10.1143/ptp.103.53 · Cited by 36
A Philosophy for Big-Bang Cosmology
McCrea, W. H. (1970) · Nature · doi:10.1038/228021a0 · Cited by 35
Letter: State of Matter for Effective Yang-Mills Fields and Energy Conditions
Zhang, Y. (2002) · General Relativity and Gravitation · doi:10.1023/a:1021195720598 · Cited by 35
Correction to Lagrangian for bouncing cosmologies in f(Q) gravity
Gadbail, G. N., Kolhatkar, A., Mandal, S., & Sahoo, P. K. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-11798-z · Cited by 35
Through the Big Bang in inflationary cosmology
Mercati, F. (2019) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2019/10/025 · Cited by 34
Uses of complex metrics in cosmology
Jonas, C., Lehners, J.-L., & Quintin, J. (2022) · Journal of High Energy Physics · doi:10.1007/jhep08(2022)284 · Cited by 43
Semiclassical dynamics of horizons in spherically symmetric collapse
Tavakoli, Y., Marto, J., & Dapor, A. (2014) · International Journal of Modern Physics D · doi:10.1142/s0218271814500618 · Cited by 36
Stable Big Bang formation for Einstein’s equations: The complete sub-critical regime
Fournodavlos, G., Rodnianski, I., & Speck, J. (2023) · Journal of the American Mathematical Society · doi:10.1090/jams/1015 · Cited by 31
Exact nonsingular black holes and thermodynamics
Singh, D. V., Ghosh, S. G., & Maharaj, S. D. (2022) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2022.115854 · Cited by 35
Black holes in higher dimensional gravity theory with corrections quadratic in curvature
Frolov, V. P., & Shapiro, I. L. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.044034 · Cited by 31
Naked singularity formation in $${f({\mathcal R})}$$ gravity
Ziaie, A. H., Atazadeh, K., & Rasouli, S. M. M. (2011) · General Relativity and Gravitation · doi:10.1007/s10714-011-1216-4 · Cited by 33
Big bang singularity resolution in quantum cosmology
Thébault, K. P. Y. (2023) · Classical and Quantum Gravity · doi:10.1088/1361-6382/acb752 · Cited by 37
Maximal extensions and singularities in inflationary spacetimes
Yoshida, D., & Quintin, J. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aacf4b · Cited by 29
Origins and development of the Cauchy problem in general relativity
Ringström, H. (2015) · Classical and Quantum Gravity · doi:10.1088/0264-9381/32/12/124003 · Cited by 29
Thermodynamic consequences of well-known regular black holes under modified first law
Jawad, A., & Khawer, A. (2018) · The European Physical Journal C · doi:10.1140/epjc/s10052-018-6305-z · Cited by 28
The Big Bang and its Dark-Matter Content: Whence, Whither, and Wherefore
Penrose, R. (2018) · Foundations of Physics · doi:10.1007/s10701-018-0162-3 · Cited by 26
Nonsingular black holes as dark matter
Davies, P. C. W., Easson, D. A., & Levin, P. B. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.103512 · Cited by 26
Speck, J. (2018) · Communications in Mathematical Physics · doi:10.1007/s00220-018-3272-z · Cited by 26
How Different Connections in Flat FLRW Geometry Impact Energy Conditions in f(Q)$f(Q)$ Theory?
Subramaniam, G., De, A., Loo, T., & Goh, Y. K. (2023) · Fortschritte der Physik · doi:10.1002/prop.202300038 · Cited by 26
High-speed cylindrical collapse of two perfect fluids
Sharif, M., & Ahmad, Z. (2007) · General Relativity and Gravitation · doi:10.1007/s10714-007-0440-4 · Cited by 26
PLANE SYMMETRIC GRAVITATIONAL COLLAPSE
Sharif, M., & Ahmad, Z. (2008) · International Journal of Modern Physics A · doi:10.1142/s0217751x0803797x · Cited by 26
Boundary of the future of a surface
Akers, C., Raphael Bousso, A., Halpern, I. F., & Remmen, G. N. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.024018 · Cited by 26
General Relativity Needs No Interpretation
Curiel, E. (2009) · Philosophy of Science · doi:10.1086/599277 · Cited by 25
Cyclic cosmology in modified gravity
Pavlović, P., & Sossich, M. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.103519 · Cited by 25
Nonsingular bounces catalyzed by dark energy
Bramberger, S. F., & Lehners, J.-L. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.123523 · Cited by 25
Beyond the Friedmann—Lemaître—Robertson—Walker Big Bang Singularity
Stoica, C. (2012) · Communications in Theoretical Physics · doi:10.1088/0253-6102/58/4/28 · Cited by 24
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
