Pith. sign in

REVIEW 1 minor 1 cited by

$C^0$-inextendibility of a class of warped-product black hole spacetimes

T0 review · 0 major / 1 minor · reviewed 2026-06-25 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A broad class of warped-product black hole spacetimes are future C^0-inextendible when their fibres are closed, connected, homogeneous and orientable.

desk verdict Adapts Sbierski's C^0-inextendibility argument to warped products under closed homogeneous fiber assumptions. read the letter →

arxiv 2606.25755 v1 pith:TDWCI2ST submitted 2026-06-24 math.DG gr-qc

Karim Mosani This is my paper · ORCID
classification math.DGgr-qc
keywords C0-inextendibilitywarped-productspacetimesblackholesingularitiesRiemannianfibreKretschmannscalarglobalhyperbolicity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper adapts an existing proof to establish that warped-product black hole spacetimes with a codimension-two fibre cannot be extended continuously into the future past their central singularities. The result applies to nonvacuum models and to geometries that lack spherical symmetry, provided the fibre meets the listed topological and symmetry conditions and the Kretschmann scalar diverges as the radial coordinate approaches zero. A reader would care because the claim shows that the singularities remain genuine barriers to continuous metric extensions in this enlarged family of spacetimes.

What carries the argument

Adaptation of Sbierski's proof technique to warped-product spacetimes whose metric is built from a static exterior region, a radial warping function r, and a codimension-two Riemannian fibre.

What would settle it

An explicit C^0 extension of the metric across the central region for one such spacetime that still obeys the fibre conditions would falsify the claim.

Watch

Extended reading notes

Core claim

Under the assumptions that the fibre is closed, connected, homogeneous and orientable, and that the spacetime admits a singularity at r approaching zero marked by diverging Kretschmann scalar, the spacetimes are future C^0-inextendible; the same conclusion holds for models containing more than one regular black hole horizon.

Load-bearing premise

The fibre must be closed, connected, homogeneous and orientable, and the Kretschmann scalar must diverge as r approaches zero.

Editorial extensions

If this is right

  • The inextendibility result applies directly to nonvacuum black hole models.
  • The result covers black hole geometries that lack spherical symmetry.
  • The same conclusion holds for spacetimes that contain more than one regular black hole horizon.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The homogeneity assumption on the fibre appears essential for blocking continuous extensions; relaxing it might allow extensions in some cases.
  • The same proof strategy could be tested on warped-product models whose fibres are not compact but still satisfy weaker symmetry conditions.
  • Numerical constructions of interior extensions for these metrics would need to violate at least one of the fibre assumptions to succeed.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 1 minor

Summary. The manuscript adapts Sbierski's proof of C^0-inextendibility of the maximal analytic Schwarzschild spacetime to a broad class of warped-product black hole spacetimes with a static exterior region. These spacetimes are globally hyperbolic, have a codimension-two Riemannian fibre and a radial coordinate (r) serving as the warping function of the fibre. They admit a spacetime singularity as r → 0 characterised by the divergence of the Kretschmann scalar. Under suitable assumptions, including that the fibre is closed (compact without boundary), connected, homogeneous, and orientable, the paper establishes future C^0-inextendibility for spacetimes in this class. The result further extends to spacetimes possessing more than one regular black hole horizon.

Significance. If the adaptation holds, the result would extend C^0-inextendibility beyond the vacuum spherically symmetric case to non-vacuum models and geometries with more general fibres, providing a tool for analyzing the strong cosmic censorship conjecture in a wider setting of black hole spacetimes.

minor comments (1)
  1. The abstract states the fibre assumptions and the Kretschmann divergence condition but does not specify the precise warped-product metric ansatz or the exact statement of the adapted theorem from Sbierski; adding these would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their summary of the manuscript and for recognizing the potential extension of C^0-inextendibility results beyond the vacuum spherically symmetric case. The recommendation of 'uncertain' is noted, but no specific major comments were provided in the report. We are prepared to address any concrete concerns regarding the adaptation of Sbierski's proof if they are raised.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity

full rationale

The paper's central result is obtained by adapting Sbierski's external C^0-inextendibility argument to a class of warped-product spacetimes once the fibre is assumed closed/connected/homogeneous/orientable and the Kretschmann scalar diverges at r=0. No equations or steps reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the derivation chain is self-contained against the cited external theorem and the explicitly listed geometric hypotheses.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The central claim rests on domain assumptions about the fibre geometry and the character of the singularity at r=0, plus the validity of adapting an external proof technique; no free parameters or invented entities are introduced in the abstract.

assumptions (3)
  • domain assumption The fibre is closed (compact without boundary), connected, homogeneous, and orientable.
    Listed explicitly as suitable assumptions under which the result holds.
  • domain assumption The spacetime admits a singularity as r → 0 characterised by the divergence of the Kretschmann scalar.
    Defines the class of spacetimes considered and the nature of the singularity.
  • domain assumption The spacetimes are globally hyperbolic with a codimension-two Riemannian fibre and radial coordinate r serving as the warping function.
    Describes the structural properties of the warped-product class.

how reviews work

0 comments
Cite this review

Pith. "Pith review of $C^0$-inextendibility of a class of warped-product black hole spacetimes." pith.science (2026). https://pith.science/paper/TDWCI2ST

@misc{pith2026260625755,
  author       = {Pith},
  title        = {Pith review of: $C^0$-inextendibility of a class of warped-product black hole spacetimes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TDWCI2ST}},
  note         = {Machine review of arXiv:2606.25755}
}
abstract

We adapt Sbierski's proof of $C^0$-inextendibility of the maximal analytic Schwarzschild spacetime to a broad class of warped-product black hole spacetimes with a static exterior region. These spacetimes are globally hyperbolic, have a codimension-two Riemannian fibre and a radial coordinate $(r)$, which serves as the warping function of the fibre. They admit a spacetime singularity as $r \to 0$, characterised by the divergence of the Kretschmann scalar. This class encompasses nonvacuum black hole models and geometries beyond spherical symmetry. Under suitable assumptions, including that the fibre is closed (compact without boundary), connected, homogeneous, and orientable, we establish future $C^0$-inextendibility for spacetimes in this class. The result further extends to spacetimes possessing more than one regular black hole horizon.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Warped Spacelike Singularities and the $C^0$-Inextendibility of Birmingham-Kottler Spacetimes

    gr-qc 2026-07 conditional novelty 7.0 of 10

    Every one-horizon Birmingham–Kottler spacetime with nonpositive cosmological constant and any closed Einstein fiber satisfying Ric=(n−2)kγ is C⁰-inextendible.

Reference graph

Works this paper leans on

266 extracted references · 155 canonical work pages · cited by 1 Pith paper

  1. [2]

    Globally non-causal space-times , journal =

    Clarke, C.J.S, de Felice, F. Globally non-causal space-times , journal =. 1982 , month =. doi:10.1088/0305-4470/15/8/020 , url =

    work page doi:10.1088/0305-4470/15/8/020 1982

  2. [3]

    Chronology protection in the Kerr metric

    Bini, Donato and de Felice, Fernando , date =. Chronology protection in the Kerr metric. General Relativity and Gravitation , number =. 2015 , bdsk-url-1 =. doi:10.1007/s10714-015-1973-6 , id =

    work page doi:10.1007/s10714-015-1973-6 2015

  3. [5]

    Sanzeni , date =

    G. Sanzeni , date =. Nonexistence of closed and bounded null geodesics in Kerr spacetimes. Letters in Mathematical Physics , number =. 2024 , bdsk-url-1 =. doi:10.1007/s11005-024-01875-z , id =

    work page doi:10.1007/s11005-024-01875-z 2024

  4. [6]

    Sanzeni , date =

    G. Sanzeni , date =. Nonexistence of closed timelike geodesics in Kerr spacetimes. doi:10.1063/5.0221959 , journal =

    work page doi:10.1063/5.0221959

  5. [7]

    Hawking, S. W. and Ellis, G. F. R. , year=. The Large Scale Structure of Space-Time , publisher=

  6. [8]

    1983 , publisher=

    The Mathematical Theory of Black Holes , author=. 1983 , publisher=

    1983

  7. [9]

    Geometry of Black Holes , publisher =

    Chru. Geometry of Black Holes , publisher =. 2020 , url =

    2020

  8. [11]

    and Blue, P

    Andersson, L. and Blue, P. , title = "

Show all 266 references
  1. [12]

    2011 , publisher=

    Introduction to Black Hole Physics , author=. 2011 , publisher=

    2011

  2. [13]

    and Nemirovski, S

    Chernov, V. and Nemirovski, S. , title = ". doi:10.4310/jsg.2016.v14.n1.a6 , url =

    2016 doi

  3. [14]

    van Stockum, W. J. , year=. IX.—The gravitational gield of a distribution of particles rotating about an axis of symmetry. doi:10.1017/S0370164600013699 , journal=

    doi

  4. [15]

    Tipler, F. J. , journal =. Rotating cylinders and the possibility of global causality violation. 1974 , month =. doi:10.1103/PhysRevD.9.2203 , url =

    1974 doi

  5. [16]

    Steadman, B. R. , journal=. Letter: Causality Violation on van Stockum Geodesics

  6. [17]

    , journal =

    G\"odel, K. , journal =. An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation. 1949 , month =. doi:10.1103/RevModPhys.21.447 , url =

    1949 doi

  7. [18]

    , journal=

    Kundt, Von W. , journal=. Trägheitsbahnen in einem von Gödel angegebenen kosmologischen Modell. 1956 , volume=

    1956

  8. [19]

    On holonomy singularities in general relativity and the

    Jan Sbierski , journal=. On holonomy singularities in general relativity and the. 2021 , volume=

    2021

  9. [20]

    and Wright, J

    Chandrasekhar, S. and Wright, J. P. , journal=. The geodesics in G\"odel's universe. 1961 , volume=

    1961

  10. [21]

    Some Remarks on the C ^0 -(in)extendibility of Spacetimes

    Galloway, Gregory and Ling, Eric. Some Remarks on the C ^0 -(in)extendibility of Spacetimes. Annales Henri Poincare. 2017. doi:10.1007/s00023-017-0602-1

    2017 doi

  11. [22]

    , title = "

    Nolan, B.C. , title = ". 2020 , month =. doi:10.1088/1361-6382/ab74fa , url =

    2020 doi

  12. [23]

    Closed timelike curves produced by pairs of moving cosmic strings: exact solutions , author =. Phys. Rev. Lett. , volume =. 1991 , month =. doi:10.1103/PhysRevLett.66.1126 , url =

    1991 doi

  13. [24]

    On the asymptotic assumptions for Milne-like spacetimes , volume=

    Ling, Eric and Piubello, Annachiara , year=. On the asymptotic assumptions for Milne-like spacetimes , volume=. General Relativity and Gravitation , publisher=. doi:10.1007/s10714-023-03102-x , number=

    doi

  14. [25]

    and Pizzocchero, L

    Fermi, D. and Pizzocchero, L. , title =. 2018 , month =. doi:10.1088/1361-6382/aace6e , url =

    2018 doi

  15. [26]

    New light on time machines: against the chronology protection conjecture , author =. Phys. Rev. D , volume =. 1994 , month =. doi:10.1103/PhysRevD.50.R6037 , url =

    1994 doi

  16. [27]

    , title =

    Low, R.J. , title =. Classical and Quantum Gravity , abstract =. 1995 , month =. doi:10.1088/0264-9381/12/5/001 , url =

    1995 doi

  17. [28]

    Chronology protection conjecture , author =. Phys. Rev. D , volume =. 1992 , month =. doi:10.1103/PhysRevD.46.603 , url =

    1992 doi

  18. [30]

    Singular hypersurfaces and thin shells in general relativity

    Israel, W. Singular hypersurfaces and thin shells in general relativity. Nuovo Cim. B. 1966. doi:10.1007/BF02710419

    1966 doi

  19. [31]

    Dimensional dependence of naked singularity formation in spherical gravitational collapse

    Giambo, Roberto and Quintavalle, Sara. Dimensional dependence of naked singularity formation in spherical gravitational collapse. Class. Quant. Grav. 2008. doi:10.1088/0264-9381/25/14/145003. arXiv:0707.1608

    2008 doi arXiv

  20. [32]

    Naked singularities in self-similar spherical gravitational collapse , author =. Phys. Rev. Lett. , volume =. 1987 , month =. doi:10.1103/PhysRevLett.59.2137 , url =

    1987 doi

  21. [33]

    Naked Singularities in Self-Similar Spherical Gravitational Collapse

    Comment on "Naked Singularities in Self-Similar Spherical Gravitational Collapse" , author =. Phys. Rev. Lett. , volume =. 1988 , month =. doi:10.1103/PhysRevLett.60.241 , url =

    1988 doi

  22. [34]

    Dwivedi, I. H. and Joshi, P. S. On the occurrence of naked singularity in spherically symmetric gravitational collapse. Commun. Math. Phys. 1994. doi:10.1007/BF02099303. arXiv:gr-qc/9405049

    1994 doi arXiv

  23. [35]

    2005 , eprint=

    Higher Dimensional Generalizations of the Kerr Black Hole , author=. 2005 , eprint=

    2005

  24. [36]

    Naked singularities in higher dimensional gravitational collapse

    Banerjee, Asit and Debnath, Ujjal and Chakraborty, Subenoy. Naked singularities in higher dimensional gravitational collapse. Int. J. Mod. Phys. D. 2003. doi:10.1142/S021827180300375X. arXiv:gr-qc/0211099

    2003 doi arXiv

  25. [37]

    Gravitational radiation in an expanding universe

    Hawking, Stephen. Gravitational radiation in an expanding universe. J. Math. Phys. 1968. doi:10.1063/1.1664615

    1968 doi

  26. [38]

    and Szekeres, Peter

    Scott, Susan M. and Szekeres, Peter. The Abstract boundary: A new approach to singularities of manifolds. J. Geom. Phys. 1994. doi:10.1016/0393-0440(94)90032-9. arXiv:gr-qc/9405063

    1994 doi arXiv

  27. [39]

    and Saraykar, Ravindra V

    Joshi, Pankaj S. and Saraykar, Ravindra V. Shell-crossings in Gravitational Collapse. Int. J. Mod. Phys. D. 2013. doi:10.1142/S0218271813500272. arXiv:1205.3263

    2013 doi arXiv

  28. [40]

    What is a shell crossing singularity?

    Szekeres, Peter and Lun, Anthony. What is a shell crossing singularity?. J. Austral. Math. Soc. B. 1999. doi:10.1017/S0334270000011140

    1999 doi

  29. [41]

    Relativistic Equations for Adiabatic, Spherically Symmetric Gravitational Collapse , author =. Phys. Rev. , volume =. 1964 , month =. doi:10.1103/PhysRev.136.B571 , url =

    1964 doi

  30. [42]

    and Deser, Stanley and Misner, Charles W

    Arnowitt, Richard L. and Deser, Stanley and Misner, Charles W. The Dynamics of general relativity. Gen. Rel. Grav. 2008. doi:10.1007/s10714-008-0661-1. arXiv:gr-qc/0405109

    2008 doi arXiv

  31. [43]

    Quasilocal gravitational energy , author =. Phys. Rev. D , volume =. 1994 , month =. doi:10.1103/PhysRevD.49.831 , url =

    1994 doi

  32. [44]

    Asymptotic flatness and Hawking quasilocal mass

    Faraoni, Valerio and Giusti, Andrea and Bean, Tyler F. Asymptotic flatness and Hawking quasilocal mass. Phys. Rev. D. 2021. doi:10.1103/PhysRevD.103.044026. arXiv:2010.00069

    2021 doi

  33. [45]

    Joshi, P. S. and Dwivedi, I. H. The Structure of Naked Singularity in Self-Similar Gravitational Collapse. Commun. Math. Phys. 1992. doi:10.1007/BF02102631

    1992 doi

  34. [46]

    Spherical gravitational collapse in N dimensions , author =. Phys. Rev. D , volume =. 2007 , month =. doi:10.1103/PhysRevD.76.084026 , url =

    2007 doi

  35. [47]

    Generalized Chaplygin gas, accelerated expansion, and dark-energy-matter unification , author =. Phys. Rev. D , volume =. 2002 , month =. doi:10.1103/PhysRevD.66.043507 , url =

    2002 doi

  36. [48]

    Communications in Mathematical Physics , volume =

    On Witten's proof of the positive energy theorem , author =. Communications in Mathematical Physics , volume =. 1982 , month =. doi:10.1007/BF01208569 , url =

    1982 doi

  37. [49]

    Classical and Quantum Gravity , abstract =

    Demetrios Christodoulou , title =. Classical and Quantum Gravity , abstract =. 1999 , month =. doi:10.1088/0264-9381/16/12A/302 , url =

    1999 doi

  38. [50]

    2009 , publisher=

    General Relativity and the Einstein Equations , author=. 2009 , publisher=

    2009

  39. [51]

    Time functions in numerical relativity: Marginally bound dust collapse , author =. Phys. Rev. D , volume =. 1979 , month =. doi:10.1103/PhysRevD.19.2239 , url =

    1979 doi

  40. [52]

    Curvature singularities: The Good, the bad, and the naked

    Gubser, Steven S. Curvature singularities: The Good, the bad, and the naked. Adv. Theor. Math. Phys. 2000. doi:10.4310/ATMP.2000.v4.n3.a6. arXiv:hep-th/0002160

    2000 doi arXiv

  41. [53]

    The Large N limit of superconformal field theories and supergravity

    Maldacena, Juan Martin. The Large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 1998. doi:10.4310/ATMP.1998.v2.n2.a1. arXiv:hep-th/9711200

    1998 doi arXiv

  42. [54]

    New mathematical framework for spherical gravitational collapse

    Giambo, Roberto and Giannoni, Fabio and Magli, Giulio and Piccione, Paolo. New mathematical framework for spherical gravitational collapse. Class. Quant. Grav. 2003. doi:10.1088/0264-9381/20/6/102. arXiv:gr-qc/0212082

    2003 doi arXiv

  43. [55]

    Spacetime junctions and the collapse to black holes in higher dimensions

    Mena, Filipe C. Spacetime junctions and the collapse to black holes in higher dimensions. Adv. Math. Phys. 2012. doi:10.1155/2012/638726

    2012 doi

  44. [57]

    Dynamical extensions for shell-crossing singularities , volume=

    Nolan, Brien C , year=. Dynamical extensions for shell-crossing singularities , volume=. Classical and Quantum Gravity , publisher=. doi:10.1088/0264-9381/20/4/302 , number=

    doi

  45. [58]

    Strong Cosmic Censorship

    On Uniqueness in the Large of Solutions of Einstein's Equations ("Strong Cosmic Censorship") , author=. 1991 , address=

    1991

  46. [60]

    Is cosmic censorship restored in higher dimensions? , author =. Phys. Rev. D , volume =. 2015 , month =. doi:10.1103/PhysRevD.92.024041 , url =

    2015 doi

  47. [61]

    Towards a theory of spacetime theories , pages=

    A primer on energy conditions , author=. Towards a theory of spacetime theories , pages=. 2017 , publisher=

    2017

  48. [62]

    A Simple Proof of the Positive Energy Theorem

    Witten, Edward. A Simple Proof of the Positive Energy Theorem. Commun. Math. Phys. 1981. doi:10.1007/BF01208277

    1981 doi

  49. [63]

    Positivity of the Total Mass of a General Space-Time

    Schoen, Richard and Yau, Shing-Tung. Positivity of the Total Mass of a General Space-Time. Phys. Rev. Lett. 1979. doi:10.1103/PhysRevLett.43.1457

    1979 doi

  50. [64]

    2007 , publisher=

    Gravitational collapse and spacetime singularities , author=. 2007 , publisher=

    2007

  51. [65]

    Hawking, S. W. and Penrose, R. The Singularities of gravitational collapse and cosmology. Proc. Roy. Soc. Lond. A. 1970. doi:10.1098/rspa.1970.0021

    1970 doi

  52. [66]

    2020 , publisher=

    Geometry of black holes , author=. 2020 , publisher=

    2020

  53. [67]

    Future null singularity due to gravitational collapse , author =. Phys. Rev. D , volume =. 2024 , month =. doi:10.1103/PhysRevD.109.064019 , url =

    2024 doi

  54. [68]

    Lorentzian causality theory

    Minguzzi, E. Lorentzian causality theory. Living Rev. Rel. 2019. doi:10.1007/s41114-019-0019-x

    2019 doi

  55. [69]

    Energy conditions in arbitrary dimensions

    Maeda, Hideki and Martinez, Cristian. Energy conditions in arbitrary dimensions. PTEP. 2020. doi:10.1093/ptep/ptaa009. arXiv:1810.02487

    2020 doi

  56. [70]

    Basics of Apparent horizons in black hole physics , volume=

    Altas, E and Tekin, B , year=. Basics of Apparent horizons in black hole physics , volume=. Journal of Physics: Conference Series , publisher=. doi:10.1088/1742-6596/2191/1/012002 , number=

    doi

  57. [71]

    Geroch and E

    R. Geroch and E. H. Kronheimer and R. Penrose , journal =. Ideal Points in Space-Time , urldate =

  58. [72]

    Ellis, G. F. R. and Schmidt, B. G. Singular space-times. Gen. Rel. Grav. 1977. doi:10.1007/BF00759240

    1977 doi

  59. [73]

    Singularities in conformally flat spacetimes

    Tipler, Frank J. Singularities in conformally flat spacetimes. Phys. Lett. A. 1977. doi:10.1016/0375-9601(77)90508-4

    1977 doi

  60. [74]

    Journal of Geometry and Physics , year = 1985, month = jan, volume =

    Conditions for the occurence of strong curvature singularities. Journal of Geometry and Physics , year = 1985, month = jan, volume =. doi:10.1016/0393-0440(85)90012-9 , adsurl =

    1985 doi

  61. [75]

    2023 , publisher=

    The large scale structure of space-time , author=. 2023 , publisher=

    2023

  62. [76]

    Penrose’s 1965 singularity theorem: from geodesic incompleteness to cosmic censorship , volume=

    Landsman, Klaas , year=. Penrose’s 1965 singularity theorem: from geodesic incompleteness to cosmic censorship , volume=. General Relativity and Gravitation , publisher=. doi:10.1007/s10714-022-02973-w , number=

    1965 doi

  63. [77]

    Kerr, R. P. Do Black Holes have Singularities?. 2023. arXiv:2312.00841

    2023

  64. [78]

    Confrontation of Cosmological Theories with Observational Data , year = 1974, editor =

    Singularities in cosmology. Confrontation of Cosmological Theories with Observational Data , year = 1974, editor =

    1974

  65. [79]

    Gravitational collapse: The role of general relativity

    Penrose, R. Gravitational collapse: The role of general relativity. Riv. Nuovo Cim. 1969. doi:10.1023/A:1016578408204

    1969 doi

  66. [80]

    and Geroch, Robert P

    Choquet-Bruhat, Y. and Geroch, Robert P. Global aspects of the Cauchy problem in general relativity. Commun. Math. Phys. 1969. doi:10.1007/BF01645389

    1969 doi

  67. [81]

    Acta Mathematica , keywords =

    Th \'e or \`e me d'existence pour certains syst \`e mes d' \'e quations aux d \'e riv \'e es partielles non lin \'e aires. Acta Mathematica , keywords =. doi:10.1007/BF02392131 , adsurl =

    doi

  68. [82]

    om, Hans , title =

    Ringstr\"om, Hans , title = ". Class. Quant. Grav. 2015. doi:10.1088/0264-9381/32/12/124003

    2015 doi

  69. [83]

    On the Existence of a Maximal Cauchy Development for the Einstein Equations: a Dezornification

    Sbierski, Jan. On the Existence of a Maximal Cauchy Development for the Einstein Equations: a Dezornification. Annales Henri Poincare. 2016. doi:10.1007/s00023-015-0401-5. arXiv:1309.7591

    2016 doi arXiv

  70. [84]

    The Ninth Marcel Grossmann Meeting , year = 2002, editor =

    The Global Initial Value Problem in General Relativity. The Ninth Marcel Grossmann Meeting , year = 2002, editor =. doi:10.1142/9789812777386_0004 , adsurl =

    2002 doi

  71. [85]

    Hawking, S. W. , title =. Communications in Mathematical Physics , volume =. 1972 , doi =

    1972

  72. [86]

    Strengths of singularities in spherical symmetry

    Nolan, Brien C. Strengths of singularities in spherical symmetry. Phys. Rev. D. 1999. doi:10.1103/PhysRevD.60.024014. arXiv:gr-qc/9902021

    1999 doi arXiv

  73. [87]

    Remark on the strength of singularities with a C0 metric

    Ori, Amos. Remark on the strength of singularities with a C0 metric. 1999. arXiv:gr-qc/9902055

    1999 arXiv

  74. [88]

    Strength of curvature singularities

    Ori, Amos. Strength of curvature singularities. Phys. Rev. D. 2000. doi:10.1103/PhysRevD.61.064016

    2000 doi

  75. [90]

    The Central singularity in spherical collapse

    Nolan, Brien C. The Central singularity in spherical collapse. Phys. Rev. D. 2000. doi:10.1103/PhysRevD.62.044015. arXiv:gr-qc/0001026

    2000 doi arXiv

  76. [91]

    1993 , publisher=

    The analysis of space-time singularities , author=. 1993 , publisher=

    1993

  77. [92]

    Large Mass Hierarchy from a Small Extra Dimension , volume=

    Randall, Lisa and Sundrum, Raman , year=. Large Mass Hierarchy from a Small Extra Dimension , volume=. Physical Review Letters , publisher=. doi:10.1103/physrevlett.83.3370 , number=

    doi

  78. [93]

    2020 , publisher=

    Measure, integration & real analysis , author=. 2020 , publisher=

    2020

  79. [94]

    2022 , publisher=

    A Mathematical Introduction to General Relativity , author=. 2022 , publisher=

    2022

  80. [95]

    On Continued Gravitational Contraction , author =. Phys. Rev. , volume =. 1939 , month =. doi:10.1103/PhysRev.56.455 , url =

    1939 doi

  81. [96]

    2008 , publisher=

    Foundations of mechanics , author=. 2008 , publisher=

    2008

  82. [97]

    Cosmic censorship in higher dimensions , author =. Phys. Rev. D , volume =. 2004 , month =. doi:10.1103/PhysRevD.69.104002 , url =

    2004 doi

  83. [98]

    Cosmic censorship in higher dimensions. II. , author =. Phys. Rev. D , volume =. 2005 , month =. doi:10.1103/PhysRevD.72.024006 , url =

    2005 doi

  84. [99]

    Quantum Evaporation of a Naked Singularity , author =. Phys. Rev. Lett. , volume =. 2006 , month =. doi:10.1103/PhysRevLett.96.031302 , url =

    2006 doi

  85. [100]

    Naked singularities and quantum gravity , author =. Phys. Rev. D , volume =. 2001 , month =. doi:10.1103/PhysRevD.64.041501 , url =

    2001 doi

  86. [101]

    Black Holes in Higher Dimensions

    Emparan, Roberto and Reall, Harvey S. Black Holes in Higher Dimensions. Living Rev. Rel. 2008. doi:10.12942/lrr-2008-6. arXiv:0801.3471

    2008 doi arXiv

  87. [102]

    and Malafarina, Daniele and Narayan, Ramesh

    Joshi, Pankaj S. and Malafarina, Daniele and Narayan, Ramesh. Equilibrium configurations from gravitational collapse. Class. Quant. Grav. 2011. doi:10.1088/0264-9381/28/23/235018. arXiv:1106.5438

    2011 doi arXiv

  88. [103]

    2024 , eprint=

    Regular black hole from regular initial data , author=. 2024 , eprint=

    2024

  89. [104]

    Collapse and bounce of null fluids , author =. Phys. Rev. D , volume =. 2017 , month =. doi:10.1103/PhysRevD.95.124033 , url =

    2017 doi

  90. [105]

    Lectures on black holes and linear waves

    Dafermos, Mihalis and Rodnianski, Igor. Lectures on black holes and linear waves. Clay Math. Proc. 2013. arXiv:0811.0354

    2013 arXiv

  91. [106]

    Spacetime Singularities

    Joshi, Pankaj S. Spacetime Singularities. Springer Handbook of Spacetime. 2014. doi:10.1007/978-3-642-41992-8_20. arXiv:1311.0449

    2014 doi arXiv

  92. [107]

    Packing extra mass in compact stellar structures: An interplay between Kalb-Ramond field and extra dimensions

    Chakraborty, Sumanta and Sengupta, Soumitra. Packing extra mass in compact stellar structures: An interplay between Kalb-Ramond field and extra dimensions. JCAP. 2018. doi:10.1088/1475-7516/2018/05/032. arXiv:1708.08315

    2018 doi arXiv

  93. [108]

    and Perlmutter, Eric

    Alday, Luis F. and Perlmutter, Eric. Growing Extra Dimensions in AdS/CFT. JHEP. 2019. doi:10.1007/JHEP08(2019)084. arXiv:1906.01477

    2019 doi

  94. [109]

    and Mei, Jianwei and Pope, C

    Lu, H. and Mei, Jianwei and Pope, C. N. Kerr/CFT Correspondence in Diverse Dimensions. JHEP. 2009. doi:10.1088/1126-6708/2009/04/054. arXiv:0811.2225

    2009 doi arXiv

  95. [110]

    and Pedraza, Juan F

    Frassino, Antonia M. and Pedraza, Juan F. and Svesko, Andrew and Visser, Manus R. Higher-Dimensional Origin of Extended Black Hole Thermodynamics. Phys. Rev. Lett. 2023. doi:10.1103/PhysRevLett.130.161501. arXiv:2212.14055

    2023 doi

  96. [111]

    and Kokabi, K

    Pourhassan, B. and Kokabi, K. and Rangyan, S. Thermodynamics of higher dimensional black holes with higher order thermal fluctuations. Gen. Rel. Grav. 2017. doi:10.1007/s10714-017-2315-7. arXiv:1710.06299

    2017 doi arXiv

  97. [112]

    Wald entropy in Kaluza-Klein black holes

    Gomez-Fayren, Carmen and Meessen, Patrick and Ortin, Tomas and Zatti, Matteo. Wald entropy in Kaluza-Klein black holes. JHEP. 2023. doi:10.1007/JHEP08(2023)039. arXiv:2305.01742

    2023 doi

  98. [113]

    Stability and phase transition of rotating Kaluza Klein black holes

    Hendi, Seyed Hossein and Hajkhalili, Somayeh and Jamil, Mubasher and Momennia, Mehrab. Stability and phase transition of rotating Kaluza Klein black holes. Eur. Phys. J. C. 2021. doi:10.1140/epjc/s10052-021-09836-9. arXiv:2111.10117

    2021 doi

  99. [114]

    Entropy-current for dynamical black holes in Chern-Simons theories of gravity

    Deo, Ishan and Dhivakar, Prateksh and Kundu, Nilay. Entropy-current for dynamical black holes in Chern-Simons theories of gravity. JHEP. 2023. doi:10.1007/JHEP11(2023)114. arXiv:2306.12491

    2023 doi

  100. [115]

    Violation of cosmic censorship in the gravitational collapse of a dust cloud

    Christodoulou, Demetrios. Violation of cosmic censorship in the gravitational collapse of a dust cloud. Commun. Math. Phys. 1984. doi:10.1007/BF01223743

    1984 doi

  101. [116]

    C^0 -inextendibility of the Kasner spacetime

    Miethke, Benedikt. C^0 -inextendibility of the Kasner spacetime. 2024. doi:10.25365/thesis.76304. arXiv:2408.05257

    2024 doi

  102. [117]

    Newman, Richard P. A. C. Strengths of naked singularities in Tolman-Bondi space-times. Class. Quant. Grav. 1986. doi:10.1088/0264-9381/3/4/007

    1986 doi

  103. [118]

    Quasi-Local Energy-Momentum and Angular Momentum in General Relativity

    Szabados, L\'aszl\'o B. Quasi-Local Energy-Momentum and Angular Momentum in General Relativity. Living Rev. Rel. 2009. doi:10.12942/lrr-2009-4

    2009 doi

  104. [120]

    The Singularity Theorems of General Relativity and Their Low Regularity Extensions , volume=

    Steinbauer, Roland , year=. The Singularity Theorems of General Relativity and Their Low Regularity Extensions , volume=. Jahresbericht der Deutschen Mathematiker-Vereinigung , publisher=. doi:10.1365/s13291-022-00263-7 , number=

    doi

  105. [121]

    LETTER: Generalized Vaidya Solutions , volume=

    Wang, Anzhong and Wu, Yumei , year=. LETTER: Generalized Vaidya Solutions , volume=. General Relativity and Gravitation , publisher=. doi:10.1023/a:1018819521971 , number=

    doi

  106. [122]

    Vaidya, P. C. The External Field of a Radiating Star in Relativity. Gen. Rel. Grav. 1999. doi:10.1023/A:1018871522880

    1999 doi

  107. [123]

    Monthly Notices of the Royal Astronomical Society , volume =

    Pretel, J M Z and da Silva, M F A , title = ". Monthly Notices of the Royal Astronomical Society , volume =. 2020 , month =. doi:10.1093/mnras/staa1493 , url =

    2020 doi

  108. [124]

    Communications in Theoretical Physics , abstract =

    Zahid Ahmad and Hassan Shah and Suhail Khan , title =. Communications in Theoretical Physics , abstract =. 2018 , month =. doi:10.1088/0253-6102/70/2/185 , url =

    2018 doi

  109. [125]

    Gravitational collapse of an isentropic perfect fluid with a linear equation of state

    Goswami, Rituparno and Joshi, Pankaj S. Gravitational collapse of an isentropic perfect fluid with a linear equation of state. Class. Quant. Grav. 2004. doi:10.1088/0264-9381/21/15/002. arXiv:gr-qc/0406052

    2004 doi arXiv

  110. [126]

    The Global structure of spherically symmetric charged scalar field spacetimes

    Kommemi, Jonathan. The Global structure of spherically symmetric charged scalar field spacetimes. Commun. Math. Phys. 2013. doi:10.1007/s00220-013-1759-1. arXiv:1107.0949

    2013 doi arXiv

  111. [127]

    Black hole regions containing no trapped surfaces

    Dotti, Gustavo. Black hole regions containing no trapped surfaces. Class. Quant. Grav. 2024. doi:10.1088/1361-6382/ad0fb9. arXiv:2308.13950

    2024 doi

  112. [128]

    Breakdown of predictability in gravitational collapse , author =. Phys. Rev. D , volume =. 1976 , month =. doi:10.1103/PhysRevD.14.2460 , url =

    1976 doi

  113. [129]

    61", number=

    An interpretation of the Kerr metric in general relativity , author=. Mathematical Proceedings of the Cambridge Philosophical Society , volume="61", number="2", pages="531–534", year="1965", doi="10.1017/S0305004100004096", publisher=

    1965 doi

  114. [130]

    , journal =

    Carter, B. , journal =. Complete analytic extension of the symmetry axis of Kerr's solution of Einstein's equations. 1966 , month =. doi:10.1103/PhysRev.141.1242 , url =

    1966 doi

  115. [131]

    Equatorial geodesic motion in the gravitational field of a rotating source

    de Felice, F. Equatorial geodesic motion in the gravitational field of a rotating source. Nuovo Cim. B. 1968. doi:10.1007/BF02710207

    1968 doi

  116. [132]

    and de Felice, Fernando and Muchotrzeb, B

    Calvani, M. and de Felice, Fernando and Muchotrzeb, B. and Salmistraro, F. Time machine and geodesic motion in Kerr metric. Gen. Rel. Grav. 1978. doi:10.1007/BF00760150

    1978 doi

  117. [133]

    and Calvani, M.,

    de Felice, F. and Calvani, M.,. Causality violation in the Kerr metric. Gen. Rel. Grav. 1979. doi:10.1007/BF00759491

    1979 doi

  118. [134]

    , title = "

    Penrose, R. , title = ". Annals of the New York Academy of Sciences , volume =

  119. [135]

    Kerr, R. P. , journal =. Gravitational field of a spinning mass as an example of algebraically special metrics. 1963 , month =. doi:10.1103/PhysRevLett.11.237 , url =

    1963 doi

  120. [136]

    Journal of Mathematical Physics , year = 1967, month = feb, volume =

    Maximal analytic extension of the Kerr metric. Journal of Mathematical Physics , year = 1967, month = feb, volume =

    1967

  121. [137]

    , series=

    O'Neill, B. , series=. The geometry of Kerr black holes. 1995 , publisher= "

    1995

  122. [138]

    Global structure of the Kerr family of gravitational fields

    Carter, B , journal =. Global structure of the Kerr family of gravitational fields. 1968 , month =. doi:10.1103/PhysRev.174.1559 , url =

    1968 doi

  123. [139]

    1999 , publisher=

    Lectures on Differential geometry , author=. 1999 , publisher=

    1999

  124. [140]

    , description =

    O'Neill, B. , description =. Semi-Riemannian geometry with applications to relativity, 103, Volume 103 (Pure and Applied Mathematics) , year =

  125. [141]

    A twist in the geometry of rotating black holes: seeking the cause of acausality , journal =

    Andr. A twist in the geometry of rotating black holes: seeking the cause of acausality , journal =. 2008 , month =. doi:10.1007/s10714-007-0577-1 , url =

    2008 doi

  126. [142]

    Space-time diagrammatics , journal =

    Chru. Space-time diagrammatics , journal =. 2012 , month =. doi:10.1103/physrevd.86.124041 , url =

    2012 doi

  127. [143]

    and Penrose,R

    Walker,M. and Penrose,R. On quadratic first integrals of the geodesic equations for type \ 22\ spacetimes. Commun. Math. Phys. 1970. doi:10.1007/BF01649445

    1970 doi

  128. [144]

    Low,R. J. , title =. Journal of Mathematical Physics , volume =. 1989 , doi =

    1989

  129. [145]

    , title = "

    Teo,E. , title = ". General Relativity and Gravitation , volume =

  130. [146]

    and Lupsasca,A

    Gralla,S.E. and Lupsasca,A. , title = ". doi:10.1103/physrevd.101.044032 , url =

    doi

  131. [147]

    2026 , eprint=

    The Hawking Singularity Theorem for H\"older Continuous Metrics with L^p -Bounded Curvature , author=. 2026 , eprint=

    2026

  132. [148]

    and Lupsasca,A

    Kapec,D. and Lupsasca,A. , title =. doi:10.1088/1361-6382/ab519e , url =

    doi

  133. [149]

    Gradshteyn, I. S. and Ryzhik, I. M. , biburl =

  134. [150]

    and Askey, Richard and Roy, Ranjan , year=

    Andrews, George E. and Askey, Richard and Roy, Ranjan , year=. Special Functions , DOI=

  135. [151]

    Zwillinger, D. , isbn=. CRC Standard Mathematical Tables and Formulae. 2012 , publisher=

    2012

  136. [152]

    Structure of the singular ring in Kerr-like metrics , author =. Phys. Rev. D , volume =. 2020 , month =. doi:10.1103/PhysRevD.101.104048 , url =

    2020 doi

  137. [153]

    Bound Geodesics in the Kerr Metric , author =. Phys. Rev. D , volume =. 1972 , month =. doi:10.1103/PhysRevD.5.814 , url =

    1972 doi

  138. [154]

    Twistor quantization and curved space-time

    Penrose, R. Twistor quantization and curved space-time. Int. J. Theor. Phys. 1968. doi:10.1007/BF00668831

    1968 doi

  139. [155]

    Techniques of Differential Topology in Relativity

    Penrose, R. Techniques of Differential Topology in Relativity. 1972 , publisher=

    1972

  140. [156]

    and Nemirovski, S

    Chernov, V. and Nemirovski, S. , year =. Legendrian Links, Causality, and the. Geometric and Functional Analysis , doi =

  141. [157]

    and Nemirovski, S

    Chernov, V. and Nemirovski, S. Non-negative Legendrian isotopy in ST^*M. Geom.Topol. , number =. 2010 , doi =

    2010

  142. [158]

    and Suhr, S

    Hedicke, J. and Suhr, S. Conformally Embedded Spacetimes and the Space of Null Geodesics. Communications in Mathematical Physics , number =. 2020 , bdsk-url-1 =. doi:10.1007/s00220-019-03499-0 , isbn =

    2020 doi

  143. [159]

    1996 , publisher=

    Global Lorentzian Geometry , author=. 1996 , publisher=

    1996

  144. [160]

    Sitzungsberichte der K

    \"U ber das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der K

  145. [161]

    First M87 Event Horizon Telescope Results

    Event Horizon Telescope Collaboration, Akiyama, K., Alberdi, A., et al. First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole. 2019 , month =. doi:10.3847/2041-8213/ab0ec7 , url =

    2019 doi

  146. [162]

    2021 , month =

    Thomas Bronzwaer and Heino Falcke , title =. 2021 , month =. doi:10.3847/1538-4357/ac1738 , url =

    2021 doi

  147. [163]

    Foundations of General Relativity: From Einstein to Black Holes , urldate =

    Landsman,K. Foundations of General Relativity: From Einstein to Black Holes , urldate =

  148. [164]

    Observation of Gravitational Waves from a Binary Black Hole Merger , author = ". Phys. Rev. Lett. , volume =. 2016 , month =. doi:10.1103/PhysRevLett.116.061102 , url =

    2016 doi

  149. [165]

    2001 , note =

    The space of null geodesics , journal = ". 2001 , note =. doi:https://doi.org/10.1016/S0362-546X(01)00421-7 , url =

    2001 doi

  150. [166]

    Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1

    Victor Guillemin , publisher =. Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121) , urldate =

  151. [167]

    A Counterexample to Guillemin’s Zollfrei Conjecture

    Suhr, S. A Counterexample to Guillemin’s Zollfrei Conjecture. 2013 , month =. doi:10.1142/s1793525313500143 , url =

    2013 doi

  152. [168]

    Nuovo Cimento Rivista Serie , year = 1969, month = jan, volume =

    Gravitational Collapse: the Role of General Relativity. Nuovo Cimento Rivista Serie , year = 1969, month = jan, volume =

    1969

  153. [169]

    Commun.Math

    Violation of cosmic censorship in the gravitational collapse of a dust cloud. Commun.Math. Phys. , year = 1984, volume =

    1984

  154. [170]

    Annals of Mathematics , year = 1999, volume =

    The Instability of Naked Singularities in the Gravitational Collapse of a Scalar Field. Annals of Mathematics , year = 1999, volume =

    1999

  155. [171]

    Joshi, P. S. and Dwivedi, I. H. , year=. Naked singularities in spherically symmetric inhomogeneous Tolman-Bondi dust cloud collapse , volume=. Physical Review D , publisher=. doi:10.1103/physrevd.47.5357 , number=

    doi

  156. [172]

    Mosani, Karim and Dey, Dipanjan and Joshi, Pankaj S. , year=. Strong curvature naked singularities in spherically symmetric perfect fluid collapse , volume=. Physical Review D , publisher=. doi:10.1103/physrevd.101.044052 , number=

    doi

  157. [173]

    Joshi, P. S. Global aspects in gravitation and cosmology. 1993. doi:https://global.oup.com/academic/product/global-aspects-in-gravitation-and-cosmology-9780198500797?cc=us&lang=en&

    1993

  158. [174]

    Proceedings of the Royal Society of London

    Ideal. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences , author =. doi:https://doi.org/10.1098/rspa.1972.0062 , abstract =

    1972 doi

  159. [175]

    Sbierski , title =

    J. Sbierski , title =. Journal of Differential Geometry , volume =

  160. [176]

    On the proof of the

    Sbierski, Jan , journal =. On the proof of the. 2018 , doi =

    2018

  161. [177]

    1996 , isbn =

    Matt Visser , title =. 1996 , isbn =

    1996

  162. [178]

    Metric measure spaces with Riemannian Ricci curvature bounded from below , volume=

    Ambrosio, Luigi and Gigli, Nicola and Savaré, Giuseppe , year=. Metric measure spaces with Riemannian Ricci curvature bounded from below , volume=. Duke Mathematical Journal , publisher=. doi:10.1215/00127094-2681605 , number=

    doi

  163. [179]

    2025 , eprint=

    A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes , author=. 2025 , eprint=

    2025

  164. [180]

    Borde and A

    A. Borde and A. H. Guth and A. Vilenkin , title =. Physical Review Letters , volume =. 2003 , doi =

    2003

  165. [181]

    2024 , eprint=

    Causal convergence conditions through variable timelike Ricci curvature bounds , author=. 2024 , eprint=

    2024

  166. [182]

    and Minguzzi, E

    Bykov, A. and Minguzzi, E. and Suhr, S. , TITLE =. Lett. Math. Phys. , FJOURNAL =. 2025 , NUMBER =

    2025

  167. [183]

    Burago and Y

    D. Burago and Y. Burago and S. Ivanov , title =

  168. [184]

    Burgos and J

    S. Burgos and J. L. Flores and J. Herrera , title =. Classical and Quantum Gravity , volume =. 2023 , doi =

    2023

  169. [185]

    Calisti and M

    M. Calisti and M. Graf and E. Hafemann and M. Kunzinger and R. Steinbauer , title =. 2501.18450 , archivePrefix =

  170. [186]

    The Penrose property with a cosmological constant , volume=

    Cameron, Peter , year=. The Penrose property with a cosmological constant , volume=. Classical and Quantum Gravity , publisher=. doi:10.1088/1361-6382/ac66b7 , number=

    doi

  171. [187]

    Cavalletti and A

    F. Cavalletti and A. Mondino , title =. Cambridge Journal of Mathematics , volume =. 2024 , doi=

    2024

  172. [188]

    Cavalletti and D

    F. Cavalletti and D. Manini and A. Mondino , title =. 2506.04934 , archivePrefix =

    arXiv

  173. [189]

    Journal of Physics: Conference Series , year =

    Carla Cederbaum and Karim Mosani , title =. Journal of Physics: Conference Series , year =

  174. [190]

    On Lorentzian causality with continuous metrics , volume=

    Chruściel, Piotr T and Grant, James D E , year=. On Lorentzian causality with continuous metrics , volume=. Classical and Quantum Gravity , publisher=. doi:10.1088/0264-9381/29/14/145001 , number=

    doi

  175. [191]

    J. L. Flores and J. Herrera and M. S. On the final definition of the causal boundary and its relation with the conformal boundary , journal =. 2011 , doi=

    2011

  176. [192]

    Galloway and E

    G. Galloway and E. Ling , title =. Annales Henri Poincaré , volume =. 2017 , doi=

    2017

  177. [193]

    Galloway and E

    G. Galloway and E. Ling and J. Sbierski , title = ". Communications in Mathematical Physics , volume =. 2018 , doi=

    2018

  178. [194]

    G. J. Galloway , title =. Classical and Quantum Gravity , volume =. 1995 , doi =

    1995

  179. [195]

    Maximizers in Lipschitz spacetimes are either timelike or null , volume=

    Graf, Melanie and Ling, Eric , year=. Maximizers in Lipschitz spacetimes are either timelike or null , volume=. Classical and Quantum Gravity , publisher=. doi:10.1088/1361-6382/aab259 , number=

    doi

  180. [196]

    Graf, Melanie and Grant, James D. E. and Kunzinger, Michael and Steinbauer, Roland , year=. The Hawking–Penrose Singularity Theorem for. Communications in Mathematical Physics , publisher=. doi:10.1007/s00220-017-3047-y , number=

    doi

  181. [197]

    Graf and M

    M. Graf and M. van den Beld-Serrano , title =. 2025 , doi=

    2025

  182. [198]

    J. D. E. Grant and M. Kunzinger and C. S. Inextendibility of spacetimes and Lorentzian length spaces , journal =. 2019 , doi=

    2019

  183. [199]

    J. B. Griffiths and Ji. Exact Space-Times in Einstein's General Relativity , series =

  184. [200]

    Harris , title =

    S. Harris , title =. Classical and Quantum Gravity , volume =. 2000 , doi=

    2000

  185. [201]

    L. A. Hau and A. J. Cabrera Pacheco and D. A. Solis , title =. Classical and Quantum Gravity , volume =. 2020 , doi=

    2020

  186. [202]

    Calculus of Variations and Partial Differential Equations , volume =

    Jérôme Bertrand and Marjolaine Puel , title =. Calculus of Variations and Partial Differential Equations , volume =. 2013 , DOI=

    2013

  187. [203]

    and Frisch, U

    Brenier, Y. and Frisch, U. and Hénon, M. and Loeper, G. and Matarrese, S. and Mohayaee, R. and Sobolevskiĭ, A. , title =. Monthly Notices of the Royal Astronomical Society , volume =. 2003 , month =

    2003

  188. [204]

    L. A. Hau and S. Burgos and D. A. Solis , title =. General Relativity and Gravitation , volume =. 2022 , doi=

    2022

  189. [205]

    Gigli , year =

    N. Gigli , year =. On the differential structure of metric measure spaces and applications , publisher =

  190. [206]

    Causality for Nonlocal Phenomena , volume=

    Eckstein, Michał and Miller, Tomasz , year=. Causality for Nonlocal Phenomena , volume=. Annales Henri Poincaré , publisher=. doi:10.1007/s00023-017-0566-1 , number=

    doi

  191. [207]

    2022 , doi =

    Karim Mosani , title =. 2022 , doi =

    2022

  192. [208]

    The C^0 -inextendibility of some spatially flat FLRW spacetimes

    Ling, Eric. The C^0 -inextendibility of some spatially flat FLRW spacetimes. Gen. Rel. Grav. 2026. doi:10.1007/s10714-026-03555-w

    2026 doi

  193. [209]

    Physical Review Letters , volume =

    Roger Penrose , title =. Physical Review Letters , volume =. 1965 , doi =

    1965

  194. [210]

    Hawking , title =

    Stephen W. Hawking , title =. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences , volume =. 1966 , doi =

    1966

  195. [211]

    S. W. Hawking and G. F. R. Ellis , title =

  196. [212]

    S. W. Hawking and A. R. King and P. J. McCarthy , title =. Journal of Mathematical Physics , volume =. 1976 , doi =

    1976

  197. [213]

    Hedicke , title =

    J. Hedicke , title =. Journal of Topology and Analysis , volume =. 2024 , doi=

    2024

  198. [214]

    E. H. Kronheimer and R. Penrose , title =. Proceedings of the Cambridge Philosophical Society , volume =. 1967 , doi=

    1967

  199. [215]

    Kunzinger and R

    M. Kunzinger and R. Steinbauer and J. A. Vickers and M. Stojkovic , title =. General Relativity and Gravitation , volume =. 2014 , doi=

    2014

  200. [216]

    The Penrose singularity theorem in regularity C 1,1 , volume=

    Kunzinger, Michael and Steinbauer, Roland and Vickers, James A , year=. The Penrose singularity theorem in regularity C 1,1 , volume=. Classical and Quantum Gravity , publisher=. doi:10.1088/0264-9381/32/15/155010 , number=

    doi

  201. [217]

    Kunzinger and C

    M. Kunzinger and C. S. Lorentzian length spaces , journal =. 2018 , doi=

    2018

  202. [218]

    C. Barrab. Singular Null Hypersurfaces in General Relativity: Light-Like Signals from Violent Astrophysical Events , publisher =

  203. [219]

    Ricci curvature for metric-measure spaces via optimal transport , journal =

    John Lott and C. Ricci curvature for metric-measure spaces via optimal transport , journal =. 2009 , doi =

    2009

  204. [220]

    , TITLE =

    Minguzzi, E. , TITLE =. Monatsh. Math. , FJOURNAL =. 2015 , NUMBER =

    2015

  205. [221]

    2025 , eprint=

    Conformal transformations of metric spaces and Lorentzian pre-length spaces , author=. 2025 , eprint=

    2025

  206. [222]

    2020 , journal=

    Displacement convexity of Boltzmann's entropy characterizes the strong energy condition from general relativity , author=. 2020 , journal=

    2020

  207. [223]

    and Suhr, S

    Minguzzi, E. and Suhr, S. , year=. Some regularity results for Lorentz–Finsler spaces , volume=. Annals of Global Analysis and Geometry , publisher=. doi:10.1007/s10455-019-09681-w , number=

    doi

  208. [224]

    and Suhr, S

    Minguzzi, E. and Suhr, S. , TITLE =. Lett. Math. Phys. , FJOURNAL =. 2024 , PAGES =

    2024

  209. [225]

    Lorentzian

    Andrea Mondino and Clemens Sämann , year=. Lorentzian

  210. [226]

    An optimal transport formulation of the Einstein equations of general relativity , volume=

    Mondino, Andrea and Suhr, Stefan , year=. An optimal transport formulation of the Einstein equations of general relativity , volume=. Journal of the European Mathematical Society , publisher=. doi:10.4171/jems/1188 , number=

    doi

  211. [227]

    2025 , eprint=

    Gromov-Hausdorff metrics and dimensions of Lorentzian length spaces , author=. 2025 , eprint=

    2025

  212. [228]

    New Frontiers in Gravitational Collapse and Spacetime Singularities , pages =

    Dipanjan Dey and Karim Mosani , title =. New Frontiers in Gravitational Collapse and Spacetime Singularities , pages =. 2024 , doi =

    2024

  213. [229]

    Mosani, Karim and Dey, Dipanjan and Joshi, Pankaj S. , year=. Global visibility of a strong curvature singularity in nonmarginally bound dust collapse , volume=. Physical Review D , publisher=. doi:10.1103/physrevd.102.044037 , number=

    doi

  214. [230]

    Globally visible singularity in an astrophysical setup , volume=

    Mosani, Karim and Dey, Dipanjan and Joshi, Pankaj S , year=. Globally visible singularity in an astrophysical setup , volume=. Monthly Notices of the Royal Astronomical Society , publisher=. doi:10.1093/mnras/stab1186 , number=

    doi

  215. [231]

    and Mosani, Karim and Vertogradov, Vitalii , year=

    Dey, Dipanjan and Joshi, Pankaj S. and Mosani, Karim and Vertogradov, Vitalii , year=. Causal structure of singularity in non-spherical gravitational collapse , volume=. The European Physical Journal C , publisher=. doi:10.1140/epjc/s10052-022-10401-1 , number=

    doi

  216. [232]

    On the visibility of singularities in general relativity and modified gravity theories , volume=

    Mosani, Karim and Dey, Dipanjan and Joshi, Pankaj S and Samanta, Gauranga C and Menon, Harikrishnan and Patel, Vaishnavi D , year=. On the visibility of singularities in general relativity and modified gravity theories , volume=. Classical and Quantum Gravity , publisher=. doi...

    doi

  217. [233]

    Mosani, Karim and Dey, Dipanjan and Bhattacharya, Kaushik and Joshi, Pankaj S. , year=. Singularity resolution in gravitational collapse , volume=. Physical Review D , publisher=. doi:10.1103/physrevd.105.064048 , number=

    doi

  218. [234]

    2023 , eprint=

    Gravitational collapse of scalar and vector fields , author=. 2023 , eprint=

    2023

  219. [235]

    2025 , eprint=

    Regular black hole from regular initial data , author=. 2025 , eprint=

    2025

  220. [236]

    2024 , eprint=

    Future-null singularity due to gravitational collapse , author=. 2024 , eprint=

    2024

  221. [237]

    Tipler naked singularities in N dimensions , volume=

    Solanki, Kharanshu N and Mosani, Karim and Deshpande, Omkar and Joshi, Pankaj S , year=. Tipler naked singularities in N dimensions , volume=. Classical and Quantum Gravity , publisher=. doi:10.1088/1361-6382/ad6115 , number=

    doi

  222. [238]

    Geodesic causality in Kerr spacetimes with |a| ≥ M , volume=

    Sanzeni, Giulio and Mosani, Karim , year=. Geodesic causality in Kerr spacetimes with |a| ≥ M , volume=. doi:10.1016/j.geomphys.2025.105589 , journal=

    2025 doi

  223. [239]

    Mosani, Karim and Saemann, Clemens , title =

  224. [240]

    Mosani, Karim and Saemann, Clemens and Solanki, Kharanshu , title =

  225. [241]

    R. J. McCann , title =. Communications in Mathematical Physics , volume =. 2024 , doi=

    2024

  226. [242]

    Minguzzi , title =

    E. Minguzzi , title =. Reviews in Mathematical Physics , volume =. 2019 , doi=

    2019

  227. [243]

    Mondino and S

    A. Mondino and S. Suhr , title =. Journal of the European Mathematical Society , volume =. 2022 , doi=

    2022

  228. [244]

    Penrose , title =

    R. Penrose , title =. Physical Review Letters , volume =. 1963 , doi =

    1963

  229. [245]

    Podolsky and R

    J. Podolsky and R. Steinbauer , title =. General Relativity and Gravitation , volume =. 2022 , doi=

    2022

  230. [246]

    Saemann , title =

    C. Saemann , title =. Annales Henri Poincar. 2016 , doi=

    2016

  231. [247]

    2025 , eprint=

    The C^0 -inextendibility of a class of FLRW spacetimes , author=. 2025 , eprint=

    2025

  232. [248]

    Acta Mathematica , volume =

    Karl-Theodor Sturm , title =. Acta Mathematica , volume =. 2006 , doi =

    2006

  233. [249]

    Jahresber

    Steinbauer, Roland , TITLE =. Jahresber. Dtsch. Math.-Ver. , FJOURNAL =. 2023 , PAGES =

    2023

  234. [250]

    Münster J

    Stefan Suhr , title =. Münster J. Math. , volume =. 2018 , doi =

    2018

  235. [251]

    Surya , title =

    S. Surya , title =. Living Reviews in Relativity , volume =. 2019 , doi=

    2019

  236. [252]

    R. M. Wald , title =. doi:10.7208/chicago/9780226870373.001.0001 , year =

    doi

  237. [253]

    Gravitational collapse with non-vanishing tangential pressure

    Malafarina, Daniele and Joshi, Pankaj S. Gravitational collapse with non-vanishing tangential pressure. Int. J. Mod. Phys. D. 2011. doi:10.1142/S0218271811018901. arXiv:1009.2169

    2011 doi arXiv

  238. [254]

    A Regular C^0 singularity is not necessarily weak

    Nolan, Brien C. A Regular C^0 singularity is not necessarily weak. 1999. arXiv:gr-qc/9902020

    1999 arXiv

  239. [255]

    Inventiones mathematicae , year =

    Jan Sbierski , title =. Inventiones mathematicae , year =

  240. [256]

    Hawking’s singularity theorem for

    Kunzinger, Michael and Steinbauer, Roland and Stojković, Milena and Vickers, James A , year=. Hawking’s singularity theorem for. Classical and Quantum Gravity , publisher=. doi:10.1088/0264-9381/32/7/075012 , number=

    doi

  241. [257]

    A note on the Gannon–Lee theorem , volume=

    Schinnerl, Benedict and Steinbauer, Roland , year=. A note on the Gannon–Lee theorem , volume=. Letters in Mathematical Physics , publisher=. doi:10.1007/s11005-021-01481-3 , number=

    doi

  242. [258]

    The Hawking–Penrose Singularity Theorem for

    Kunzinger, Michael and Ohanyan, Argam and Schinnerl, Benedict and Steinbauer, Roland , year=. The Hawking–Penrose Singularity Theorem for. Communications in Mathematical Physics , publisher=. doi:10.1007/s00220-022-04335-8 , number=

    doi

  243. [259]

    Senovilla, J. M. M. , year=. Singularity Theorems and Their Consequences , volume=. doi:10.1023/a:1018801101244 , journal=

    doi

  244. [260]

    A critical appraisal of the singularity theorems , JOURNAL =

    Senovilla, Jos\'. A critical appraisal of the singularity theorems , JOURNAL =. 2022 , NUMBER =

    2022

  245. [261]

    and Traschen, Jennie H

    Geroch, Robert P. and Traschen, Jennie H. Strings and Other Distributional Sources in General Relativity. Conf. Proc. C. 1986. doi:10.1103/PhysRevD.36.1017

    1986 doi

  246. [262]

    Strong Cosmic Censorship

    Piotr T. Chru. On Uniqueness in the Large of Solutions of Einstein's Equations ("Strong Cosmic Censorship") , series =. 1991 , publisher =

    1991

  247. [263]

    2009 , publisher =

    Demetrios Christodoulou , title =. 2009 , publisher =. doi:10.4171/068 , isbn =

    2009 doi

  248. [264]

    The interior of dynamical vacuum black holes I: The

    Dafermos, Mihalis and Luk, Jonathan , year=. The interior of dynamical vacuum black holes I: The. Annals of Mathematics , publisher=. doi:10.4007/annals.2025.202.2.1 , number=

    2025 doi

  249. [265]

    Comptes Rendus

    Van de Moortel, Maxime , title =. Comptes Rendus. M. 2025 , volume =

    2025

  250. [266]

    Joshi , title =

    Pankaj S. Joshi , title =. 1996 , isbn =

    1996

  251. [267]

    2011 , eprint=

    Constraints on the topology of higher dimensional black holes , author=. 2011 , eprint=

    2011

  252. [268]

    Topological black holes in anti-de Sitter space , volume=

    Birmingham, Danny , year=. Topological black holes in anti-de Sitter space , volume=. Classical and Quantum Gravity , publisher=. doi:10.1088/0264-9381/16/4/009 , number=

    doi

  253. [269]

    Galloway, G. J. and Schleich, K. and Witt, D. M. and Woolgar, E. , year=. Topological censorship and higher genus black holes , volume=. Physical Review D , publisher=. doi:10.1103/physrevd.60.104039 , number=

    doi

  254. [270]

    Scalar fields, energy conditions and traversable wormholes , volume=

    Barceló, Carlos and Visser, Matt , year=. Scalar fields, energy conditions and traversable wormholes , volume=. Classical and Quantum Gravity , publisher=. doi:10.1088/0264-9381/17/18/318 , number=

    doi

  255. [271]

    On the topology and area of higher-dimensional black holes , volume=

    Cai, Mingliang and Galloway, Gregory J , year=. On the topology and area of higher-dimensional black holes , volume=. Classical and Quantum Gravity , publisher=. doi:10.1088/0264-9381/18/14/308 , number=

    doi

  256. [272]

    and Lucietti, James , year=

    Kunduri, Hari K. and Lucietti, James , year=. Classification of Near-Horizon Geometries of Extremal Black Holes , volume=. Living Reviews in Relativity , publisher=. doi:10.12942/lrr-2013-8 , number=

    2013 doi

  257. [273]

    and Schoen, Richard , year=

    Galloway, Gregory J. and Schoen, Richard , year=. A Generalization of Hawking’s Black Hole Topology Theorem to Higher Dimensions , volume=. Communications in Mathematical Physics , publisher=. doi:10.1007/s00220-006-0019-z , number=

    doi

  258. [274]

    , title =

    Galloway, Gregory J. , title =. Communications in Analysis and Geometry , volume =. 2008 , doi =

    2008

Pith tools

Reviewed June 25, 2026 · model on record in the stance chip above.