[La conjecture de Censure Cosmique forte]
Dans le sillage des percées majeures de la relativité générale dans les années 1960, Roger Penrose a introduit la censure cosmique forte, une conjecture profonde concernant la nature déterministe de la théorie. La proposition de Penrose a depuis ouvert de nouvelles voies mathématiques d’une grande portée, révélant des liens avec des questions fondamentales sur les trous noirs et la nature des singularités gravitationnelles. Nous passons en revue les avancées récentes issues des techniques modernes de la théorie des équations aux dérivées partielles appliquées à la censure cosmique forte, en nous concentrant sur le contexte de l’effondrement gravitationnel qui a donné naissance à la conjecture.
In the wake of major breakthroughs in General Relativity during the 1960s, Roger Penrose introduced Strong Cosmic Censorship, a profound conjecture regarding the deterministic nature of the theory. Penrose’s proposal has since opened far-reaching new mathematical avenues, revealing connections to fundamental questions about black holes and the nature of gravitational singularities. We review recent advances arising from modern techniques in the theory of partial differential equations as applied to Strong Cosmic Censorship, maintaining a focus on the context of gravitational collapse that gave birth to the conjecture.
Accepté le :
Publié le :
Mots-clés : Relativité générale, Déterminisme de Laplace, Équations d’Einstein, Trous noirs
Maxime Van de Moortel 1
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@article{CRMECA_2025__353_G1_415_0, author = {Maxime Van de Moortel}, title = {The {Strong} {Cosmic} {Censorship} conjecture}, journal = {Comptes Rendus. M\'ecanique}, pages = {415--454}, publisher = {Acad\'emie des sciences, Paris}, volume = {353}, year = {2025}, doi = {10.5802/crmeca.271}, language = {en}, }
Maxime Van de Moortel. The Strong Cosmic Censorship conjecture. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 415-454. doi : 10.5802/crmeca.271. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.271/
[1] Some unsolved problems in classical general relativity, Seminar on Differential Geometry (Annals of Mathematics Studies), Volume 102, Princeton University Press, Princeton, NJ, 1982, pp. 631-668 | Zbl
[2] A Philosophical Essay on Probabilities, Dover Publications, Inc, New York, 1995
[3] Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes, The Clarendon Press, Oxford University Press, New York, 1995 | DOI
[4] Gravitational collapse: the role of general relativity, Nuovo Cimento, Volume 1 (1969), pp. 252-276 | DOI
[5] Singularities and time asymmetry, General Relativity: An Einstein Centenary Survey, Cambridge University Press, 1980, pp. 581-638
[6] The Large Scale Structure of Space-Time, Cambridge University Press, London-New York, 1973 | DOI
[7] Semi-Riemannian Geometry, Pure and Applied Mathematics, 103, Academic Press, Inc., [Harcourt Brace Jovanovich], New York, 1983
[8] The question of cosmic censorship, Black Holes and Relativistic Stars (Chicago, IL, 1996), University Chicago Press, Chicago, IL, 1998, pp. 103-122
[9] Gravitational collapse, Gravitational Radiation and Gravitational Collapse (C. DeWitt-Morette, ed.), Volume 64 of IAU Symposium, Springer, 1974, pp. 82-91
[10] The structure of spacetime, General Relativity: An Einstein Centenary Survey, Cambridge University Press, 1980, pp. 212-293
[11] On the global initial value problem and the issue of singularities, Class. Quantum Gravity, Volume 16 (1999) no. 12A, p. A23-A35 | DOI | Zbl
[12] Penrose’s 1965 singularity theorem: from geodesic incompleteness to cosmic censorship, Gen. Relativ. Gravit., Volume 54 (2022) no. 10, 115 | DOI | Zbl
[13] The global structure of spherically symmetric charged scalar field spacetimes, Commun. Math. Phys., Volume 323 (2013) no. 1, pp. 35-106 | DOI | Zbl
[14] Spherically symmetric spacetimes with a trapped surface, Class. Quantum Gravity, Volume 22 (2005) no. 11, pp. 2221-2232 | DOI | Zbl
[15] Structure of space-time, Battelle Rencontres, 1968, pp. 121-235 | Zbl
[16] Internal instability in a Reissner–Nordström black hole, Int. J. Theor. Phys., Volume 7 (1973), pp. 183-197 | DOI
[17] Global aspects of the Cauchy problem in general relativity, Commun. Math. Phys., Volume 14 (1969), pp. 329-335 | DOI | Zbl
[18] Global properties of Gowdy spacetimes with T R topology, Ann. Phys., Volume 132 (1981) no. 1, pp. 87-107 | DOI
[19] Strong cosmic censorship in polarised Gowdy spacetimes, Class. Quantum Gravity, Volume 7 (1990) no. 10, pp. 1671-1680 | DOI | Zbl
[20] The Cauchy Problem in General Relativity, ESI Lectures in Mathematics and Physics, European Mathematical Society (EMS), Zürich, 2009 | DOI
[21] Black holes without spacelike singularities, Commun. Math. Phys., Volume 332 (2014) no. 2, pp. 729-757 | DOI | Zbl
[22] The interior of dynamical vacuum black holes I: The C-stability of the Kerr Cauchy horizon, preprint, 2017 (to appear in Ann. Math.) | arXiv
[23] Singularities in general relativity, ICM—International Congress of Mathematicians. Vol. 1. Sections 9–11, EMS Press, Berlin, 2023, pp. 4120-4141 (ISBN 978-3-98547-063-1; 978-3-98547-563-6; 978-3-98547-058-7) | DOI | Zbl
[24] The Formation of Black Holes in General Relativity, EMS Monographs in Mathematics, European Mathematical Society (EMS), Zürich, 2009 | DOI
[25] The interior of charged black holes and the problem of uniqueness in general relativity, Commun. Pure Appl. Math., Volume 58 (2005) no. 4, pp. 445-504 | DOI | Zbl
[26] Price’s law, mass inflation, and strong cosmic censorship, 7th Hungarian Relativity Workshop (RW 2003), 2004, pp. 79-90 | Zbl
[27] Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| M, Ann. Math. (2), Volume 183 (2016) no. 3, pp. 787-913 | DOI | Zbl
[28] Strong Cosmic Censorship in the presence of matter: the decisive effect of horizon oscillations on the black hole interior geometry, Anal. PDE, Volume 17 (2024) no. 5, pp. 1501-1592 | DOI | Zbl
[29] A Primer on Determinism, The Western Ontario Series in Philosophy of Science (WONS, volume 32), Springer, 1986 | DOI
[30] Penrose’s incompleteness theorem, Lond. Math. Soc. Newsl. (2021) no. 493, pp. 27-34 | Zbl
[31] General Relativity, University of Chicago Press, Chicago, IL, 1984 | DOI
[32] General Relativity and the Einstein Equations, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2009
[33] On the existence of a maximal Cauchy development for the Einstein equations: a dezornification, Ann. Henri Poincaré, Volume 17 (2016) no. 2, pp. 301-329 | DOI | Zbl
[34] The bounded L curvature conjecture, Invent. Math., Volume 202 (2015) no. 1, pp. 91-216 | DOI | Zbl
[35] Scattering of two impulsive gravitational plane waves, Nature, Volume 229 (1971), pp. 185-186 | DOI
[36] Local propagation of impulsive gravitational waves, Commun. Pure Appl. Math., Volume 68 (2015) no. 4, pp. 511-624 | DOI | Zbl
[37] Nonlinear interaction of impulsive gravitational waves for the vacuum Einstein equations, Camb. J. Math., Volume 5 (2017) no. 4, pp. 435-570 | DOI | Zbl
[38] Nonlinear interaction of three impulsive gravitational waves I: main result and the geometric estimates, preprint, 2021 | arXiv
[39] Nonlinear interaction of three impulsive gravitational waves II: the wave estimates, Ann. PDE, Volume 9 (2023) no. 1, 10 | Zbl
[40] Timelike completeness as an obstruction to C-extensions, Commun. Math. Phys., Volume 359 (2018) no. 3, pp. 937-949 | DOI | Zbl
[41] Gravitational collapse and space-time singularities, Phys. Rev. Lett., Volume 14 (1965), pp. 57-59 | DOI | Zbl
[42] Lectures on black holes and linear waves, Evolution Equations (Clay Mathematics Proceedings), Volume 17, American Mathematical Society, Providence, RI, 2013, pp. 97-205 | Zbl
[43] Roger Penrose – Facts – 2020, 2024 https://www.nobelprize.org/prizes/physics/2020/penrose/facts/ (NobelPrize.org. Nobel Prize Outreach AB 2024)
[44] The Global Nonlinear Stability of the Minkowski Space, Princeton Mathematical Series, 41, Princeton University Press, Princeton, NJ, 1993
[45] The global stability of Minkowski space-time in harmonic gauge, Ann. Math. (2), Volume 171 (2010) no. 3, pp. 1401-1477 | DOI | Zbl
[46] Gravitation, W. H. Freeman and Co., San Francisco, CA, 1973
[47] The C-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian geometry, J. Differ. Geom., Volume 108 (2018) no. 2, pp. 319-378 | DOI | Zbl
[48] Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett., Volume 11 (1963), pp. 237-238 | DOI | Zbl
[49] On continued gravitational contraction, Phys. Rev. (2), Volume 56 (1939) no. 5, pp. 455-459 | DOI | Zbl
[50] Violation of cosmic censorship in the gravitational collapse of a dust cloud, Commun. Math. Phys., Volume 93 (1984) no. 2, pp. 171-195 | DOI
[51] Examples of naked singularity formation in the gravitational collapse of a scalar field, Ann. Math. (2), Volume 140 (1994) no. 3, pp. 607-653 | DOI | Zbl
[52] Bounded variation solutions of the spherically symmetric Einstein-scalar field equations, Commun. Pure Appl. Math., Volume 46 (1993) no. 8, pp. 1131-1220 | DOI | Zbl
[53] The instability of naked singularities in the gravitational collapse of a scalar field, Ann. Math. (2), Volume 149 (1999) no. 1, pp. 183-217 | DOI | Zbl
[54] Naked singularities for the Einstein vacuum equations: the exterior solution, Ann. Math. (2), Volume 198 (2023) no. 1, pp. 231-391 | DOI | Zbl
[55] Universality and scaling in gravitational collapse of a massless scalar field, Phys. Rev. Lett., Volume 70 (1993), pp. 9-12 | DOI
[56] Understanding critical collapse of a scalar field, Phys. Rev. D, Volume 55 (1997), pp. 695-713 | DOI
[57] On crossing the Cauchy horizon of a Reissner–Nordström black-hole, Proc. R. Soc. Lond. A, Volume 384 (1982) no. 1787, pp. 301-315 | DOI | Zbl
[58] Time-translation invariance of scattering maps and blue-shift instabilities on Kerr black hole spacetimes, Commun. Math. Phys., Volume 350 (2017) no. 3, pp. 985-1016 | DOI | Zbl
[59] Instability of black hole inner horizons, Proc. R. Soc. Lond. Ser. A, Volume 358 (1978) no. 1695, pp. 499-517 | DOI
[60] Characterisation of the energy of Gaussian beams on Lorentzian manifolds: with applications to black hole spacetimes, Anal. PDE, Volume 8 (2015) no. 6, pp. 1379-1420 | DOI | Zbl
[61] Proof of linear instability of the Reissner–Nordström Cauchy horizon under scalar perturbations, Duke Math. J., Volume 166 (2017) no. 3, pp. 437-493 | DOI | Zbl
[62] Instability results for the wave equation in the interior of Kerr black holes, J. Funct. Anal., Volume 271 (2016) no. 7, pp. 1948-1995 | DOI | Zbl
[63] Precise late-time asymptotics of scalar field in the interior of a subextreme Kerr black hole and its application in strong cosmic censorship conjecture, Trans. Amer. Math. Soc., Volume 376 (2023) no. 11, pp. 7815-7856 | Zbl
[64] A scattering theory approach to Cauchy horizon instability and applications to mass inflation, Ann. Henri Poincaré, Volume 24 (2023) no. 2, pp. 363-411 | DOI | Zbl
[65] Instability of the Kerr Cauchy horizon under linearised gravitational perturbations, Ann. PDE, Volume 9 (2023) no. 1, 7 | DOI | Zbl
[66] The formation of black holes and singularities in spherically symmetric gravitational collapse, Commun. Pure Appl. Math., Volume 44 (1991) no. 3, pp. 339-373 | DOI | Zbl
[67] Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations, Ann. Math. (2), Volume 158 (2003) no. 3, pp. 875-928 | DOI | Zbl
[68] Stability and instability of the sub-extremal Reissner–Nordström black hole interior for the Einstein–Maxwell–Klein–Gordon equations in spherical symmetry, Commun. Math. Phys., Volume 360 (2018) no. 1, pp. 103-168 | DOI | Zbl
[69] Exponentially growing finite energy solutions for the Klein–Gordon equation on sub-extremal Kerr spacetimes, Commun. Math. Phys., Volume 329 (2014) no. 3, pp. 859-891 | DOI | Zbl
[70] The asymptotics of massive fields on stationary spherically symmetric black holes for all angular momenta, preprint, 2023 | arXiv
[71] Stationary axisymmetric black holes with matter, Commun. Anal. Geom., Volume 29 (2021) no. 1, pp. 19-76 | DOI | Zbl
[72] Time-periodic Einstein–Klein–Gordon bifurcations of Kerr, Commun. Math. Phys., Volume 356 (2017) no. 3, pp. 1155-1250 | DOI | Zbl
[73] Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data I. The interior of the black hole region, Ann. Math. (2), Volume 190 (2019) no. 1, pp. 1-111 | DOI | Zbl
[74] A proof of Price’s law for the collapse of a self-gravitating scalar field, Invent. Math., Volume 162 (2005) no. 2, pp. 381-457 | DOI | Zbl
[75] Late-time evolution of charged gravitational collapse and decay of charged scalar hair. II, Phys. Rev. D (3), Volume 58 (1998) no. 2, 024018 | DOI
[76] Mass inflation in dynamical gravitational collapse of a charged scalar field, Phys. Rev. Lett., Volume 81 (1998), pp. 1554-1557 | DOI
[77] Kerr stability for small angular momentum, Pure Appl. Math. Q., Volume 19 (2023) no. 3, pp. 791-1678 | DOI | Zbl
[78] Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes, preprint, 2022 (to appear in Pure Appl. Math. Quarter.) | arXiv | DOI | Zbl
[79] Internal structure of black holes, Phys. Rev. D (3), Volume 41 (1990) no. 6, pp. 1796-1809 | DOI
[80] Inner-horizon instability and mass inflation in black holes, Phys. Rev. Lett., Volume 63 (1989) no. 16, pp. 1663-1666 | DOI
[81] Inner structure of a charged black hole: an exact mass-inflation solution, Phys. Rev. Lett., Volume 67 (1991) no. 7, pp. 789-792 | DOI | Zbl
[82] Evolution of the interior of a charged black hole, Phys. Lett. A, Volume 83 (1981) no. 3, pp. 110-112 | DOI
[83] Mass inflation and the C-inextendibility of spherically symmetric charged scalar field dynamical black holes, Commun. Math. Phys., Volume 382 (2021) no. 2, pp. 1263-1341 | DOI | Zbl
[84] Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data II: the exterior of the black hole region, Ann. PDE, Volume 5 (2019) no. 1, 6 | DOI | Zbl
[85] Weak null singularities in general relativity, J. Amer. Math. Soc., Volume 31 (2018) no. 1, pp. 1-63 | DOI | Zbl
[86] Violent nonlinear collapse in the interior of charged hairy black holes, Arch. Ration. Mech. Anal., Volume 248 (2024), 89 | Zbl
[87] The breakdown of weak null singularities inside black holes, Duke Math. J., Volume 172 (2023) no. 15, pp. 2957-3012 | DOI | Zbl
[88] On holonomy singularities in general relativity and the -inextendibility of spacetimes, Duke Math. J., Volume 171 (2022) no. 14, pp. 2881-2942 | DOI | Zbl
[89] Kasner bounces and fluctuating collapse inside hairy black holes with charged matter, Ann. PDE, Volume 11 (2025), 3 | DOI
[90] Asymptotically Anti-de-Sitter hairy black holes, preprint, 2024 | arXiv
[91] Geometrical theorems on Einstein’s cosmological equations, Amer. J. Math., Volume 43 (1921), pp. 217-221 | DOI | Zbl
[92] Stable big bang formation for Einstein’s equations: the complete sub-critical regime, J. Amer. Math. Soc., Volume 36 (2023) no. 3, pp. 827-916 | DOI | Zbl
[93] Oscillatory approach to a singular point in relativistic cosmology, Sov. Phys. Uspekhi, Volume 13 (1971) no. 6, p. 745 | DOI
[94] A general solution of the Einstein equations with a time singularity, Adv. Phys., Volume 31 (1982) no. 6, pp. 639-667 | DOI
[95] The coexistence of null and spacelike singularities inside spherically symmetric black holes (in preparation)
[96] Topological censorship from the initial data point of view, J. Differ. Geom., Volume 95 (2013) no. 3, pp. 389-405 | DOI | Zbl
[97] Trapped surface formation for spherically symmetric Einstein–Maxwell-charged scalar field system with double null foliation, Ann. Henri Poincare, Volume 23 (2022) no. 9, pp. 3159-3190 | DOI | Zbl
[98] A fully anisotropic mechanism for formation of trapped surfaces in vacuum, Invent. Math., Volume 198 (2014) no. 1, pp. 1-26 | DOI | Zbl
[99] On the formation of trapped surfaces, Acta Math., Volume 208 (2012) no. 2, pp. 211-333 | DOI | Zbl
[100] Trapped surfaces in vacuum arising dynamically from mild incoming radiation, Adv. Theor. Math. Phys., Volume 21 (2017) no. 1, pp. 1-120 | DOI | Zbl
[101] The formation of trapped surfaces in spherically-symmetric Einstein–Euler spacetimes with bounded variation, J. Math. Pures Appl. (9), Volume 102 (2014) no. 6, pp. 1164-1217 | DOI | Zbl
[102] Curvature blow-up and mass inflation in spherically symmetric collapse to a Schwarzschild black hole, Arch. Ration. Mech. Anal., Volume 247 (2023) no. 3, 51 | DOI | Zbl
[103] Polynomial blow-up upper bounds for the Einstein-scalar field system under spherical symmetry, Commun. Math. Phys., Volume 376 (2020) no. 2, pp. 1671-1704 | DOI | Zbl
[104] Kasner-like description of spacelike singularities in spherically symmetric spacetimes with scalar matter, Ann. PDE, Volume 11 (2025), 5 | DOI
[105] A proof of weak cosmic censorship conjecture for the spherically symmetric Einstein–Maxwell–Charged scalar field system, preprint, 2024 | arXiv
[106] Gravitational collapse to extremal black holes and the third law of black hole thermodynamics, J. Eur. Math. Soc. (2025) (Online first) | DOI
[107] Asymptotically Kasner-like singularities, Amer. J. Math., Volume 145 (2023) no. 4, pp. 1183-1272 | DOI | Zbl
[108] The Bianchi IX attractor, Ann. Henri Poincaré, Volume 2 (2001) no. 3, pp. 405-500 | DOI | Zbl
[109] Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations, Phys. Rev. D (3), Volume 5 (1972), pp. 2419-2438 | DOI
[110] Phase space analysis on some black hole manifolds, J. Funct. Anal., Volume 256 (2009) no. 1, pp. 1-90 | DOI | Zbl
[111] The red-shift effect and radiation decay on black hole spacetimes, Commun. Pure Appl. Math., Volume 62 (2009) no. 7, pp. 859-919 | DOI | Zbl
[112] Stability for linearized gravity on the Kerr spacetime, preprint, 2019 | arXiv
[113] Local decay of waves on asymptotically flat stationary space-times, Amer. J. Math., Volume 130 (2008) no. 3, pp. 571-634
[114] Hidden symmetries and decay for the wave equation on the Kerr spacetime, Ann. Math. (2), Volume 182 (2015) no. 3, pp. 787-853 | DOI | Zbl
[115] On pointwise decay of linear waves on a schwarzschild black hole background, Commun. Math. Phys., Volume 309 (2012), pp. 51-86 | DOI | Zbl
[116] A proof of Price’s Law on Schwarzschild black hole manifolds for all angular momenta, Adv. Math., Volume 226 (2011) no. 1, pp. 484-540 | DOI | Zbl
[117] Price’s law on nonstationary space-times, Adv. Math., Volume 230 (2012) no. 3, pp. 995-1028 | DOI | Zbl
[118] A sharp version of Price’s law for wave decay on asymptotically flat spacetimes, Commun. Math. Phys., Volume 389 (2022), pp. 491-542 | DOI | Zbl
[119] Late-time asymptotics for the wave equation on spherically symmetric, stationary spacetimes, Adv. Math., Volume 323 (2018), pp. 529-621 | DOI | Zbl
[120] Price’s Law and precise late-time asymptotics for subextremal reissner–nordström black holes, Ann. Henri Poincare, Volume 24 (2023) no. 9, pp. 3215-3287 | DOI | Zbl
[121] Perturbations of a rotating black hole. 1. Fundamental equations for gravitational electromagnetic and neutrino field perturbations, Astrophys. J., Volume 185 (1973), pp. 635-647 | DOI
[122] Boundedness and decay for the Teukolsky equation on Kerr in the full subextremal range |a| M: frequency space analysis, preprint, 2020 | arXiv
[123] Boundedness and decay for the Teukolsky equation on Kerr in the full subextremal range |a| M: physical space analysis, preprint, 2023 | arXiv
[124] Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: The case |a|M, Ann. PDE, Volume 5 (2019) no. 1, 2 | DOI | Zbl
[125] Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole II: Linearized gravity, Commun. Math. Phys., Volume 377 (2020) no. 3, pp. 2489-2551 | DOI | Zbl
[126] Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior, J. Hyperbolic Differ. Equ., Volume 12 (2015) no. 4, pp. 689-743 | DOI | Zbl
[127] Optimal decay for solutions of the Teukolsky equation on the Kerr metric for the full subextremal range |a| M, preprint, 2023 | arXiv
[128] Almost Price’s law in Schwarzschild and decay estimates in Kerr for Maxwell field, J. Differ. Equ., Volume 339 (2022), pp. 1-89 | DOI | Zbl
[129] Sharp decay for Teukolsky equation in Kerr spacetimes, Commun. Math. Phys., Volume 401 (2023), pp. 333-434 | DOI | Zbl
[130] Sharp decay estimates for massless Dirac fields on a Schwarzschild background, J. Funct. Anal., Volume 282 (2022) no. 6, 109375 | Zbl
[131] The spin 1 Teukolsky equations and the Maxwell system on Schwarzschild, Ann. Henri Poincaré, Volume 20 (2019) no. 4, pp. 1263-1323 | DOI | Zbl
[132] Local energy decay for Maxwell fields part I: Spherically symmetric black-hole backgrounds, Int. Math. Res. Not., Volume 2015 (2015) no. 11, pp. 3298-3342 | Zbl
[133] Pointwise decay for the Maxwell field on black hole space-times, Adv. Math., Volume 316 (2017), pp. 53-93 | DOI | Zbl
[134] Decay of the Maxwell field on the Schwarzschild manifold, J. Hyperbolic Differ. Equ., Volume 5 (2008) no. 4, pp. 807-856 | DOI | Zbl
[135] The linear stability of Reissner–Nordström spacetime: the full subextremal range |Q| M, Commun. Math. Phys., Volume 380 (2020) no. 3, pp. 1313-1360 | DOI | Zbl
[136] Decay of weakly charged solutions for the spherically symmetric Maxwell-charged-scalar-field equations on a Reissner–Nordström exterior space-time, Ann. Sci. Éc. Norm. Supér. (4), Volume 55 (2022) no. 2, pp. 283-404 | DOI | Zbl
[137] Late-time tails for scale-invariant wave equations with a potential and the near-horizon geometry of null infinity, preprint, 2024 | arXiv
[138] Klein–Gordon equation and rotating black holes, Phys. Rev. D, Volume 22 (1980), pp. 2323-2326 | DOI
[139] Instabilities of massive scalar perturbations of a rotating black hole, Ann. Phys., Volume 118 (1979) no. 1, pp. 139-155 | DOI
[140] Superradiance—New Frontiers in Black Hole Physics, Lecture Notes in Physics, 971, Springer, 2020 | DOI
[141] Plausible scenario for a generic violation of the weak cosmic censorship conjecture in asymptotically flat four dimensions, Phys. Rev. D, Volume 101 (2020) no. 4, 041502(R) | DOI
[142] Scalar hairy black holes in four dimensions are unstable, Phys. Rev. Lett., Volume 120 (2018), 171101 | DOI
[143] Polynomial time decay for solutions of the Klein–Gordon equation on a subextremal Reissner–Nordström black hole, preprint, 2024 | arXiv
[144] Late time tail of waves on dynamic asymptotically flat spacetimes of odd space dimensions, preprint, 2024 | arXiv
[145] A general formalism for the stability of Kerr, preprint, 2020 | arXiv
[146] Construction of GCM spheres in perturbations of Kerr, Ann. PDE, Volume 8 (2022) no. 2, 17 | Zbl
[147] Effective results on uniformization and intrinsic GCM spheres in perturbations of Kerr, Ann. PDE, Volume 8 (2022) no. 2, 18 | Zbl
[148] Construction of GCM hypersurfaces in perturbations of Kerr, Ann. PDE, Volume 9 (2023) no. 1, 11 | DOI | Zbl
[149] The non-linear stability of the Schwarzschild family of black holes, preprint, 2021 | arXiv
[150] Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holes, preprint, 2022 | arXiv
[151] Global Nonlinear Stability of Schwarzschild Spacetime Under Polarized Perturbations, Annals of Mathematics Studies, 210, Princeton University Press, Princeton, NJ, 2020 | DOI
[152] Linear stability of slowly rotating Kerr black holes, Invent. Math., Volume 223 (2021) no. 3, pp. 1227-1406 | DOI | Zbl
[153] Extremal black hole formation as a critical phenomenon, preprint, 2024 | arXiv
[154] The interior of dynamical extremal black holes in spherical symmetry, Pure Appl. Anal., Volume 1 (2019) no. 2, pp. 263-326 | DOI | Zbl
[155] Linear waves in the interior of extremal black holes I, Commun. Math. Phys., Volume 353 (2017) no. 2, pp. 717-770 | DOI | Zbl
[156] Linear waves in the interior of extremal black holes II, Ann. Henri Poincaré, Volume 18 (2017) no. 12, pp. 4005-4081 | DOI | Zbl
[157] Charged scalar fields on black hole space-times, PhD thesis, University of Cambridge (2019)
[158] The occurrence of singularities in cosmology. III. Causality and singularities, Proc. R. Soc. Lond. A, Volume 300 (1967), pp. 187-201 | DOI | Zbl
[159] Symmetries of cosmological Cauchy horizons with non-closed orbits, Commun. Math. Phys., Volume 374 (2020) no. 1, pp. 145-186 | DOI | Zbl
[160] Extension of Killing vector fields beyond compact Cauchy horizons, Adv. Math., Volume 391 (2021), 107953 | Zbl
[161] On the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon, Commun. Math. Phys., Volume 204 (1999) no. 3, pp. 691-707 | DOI | Zbl
[162] Vacuum spacetimes with two-parameter spacelike isometry groups and compact invariant hypersurfaces: topologies and boundary conditions, Ann. Phys., Volume 83 (1974), pp. 203-241 | DOI | Zbl
[163] On space-times with U(1) U(1) symmetric compact Cauchy surfaces, Ann. Phys., Volume 202 (1990) no. 1, pp. 100-150 | DOI | Zbl
[164] Cosmic censorship for gowdy spacetimes, Living Rev. Rel., Volume 13 (2010), 2 | DOI
[165] Strong cosmic censorship in T-Gowdy spacetimes, Ann. Math. (2), Volume 170 (2009) no. 3, pp. 1181-1240 | DOI | Zbl
[166] Existence of an asymptotic velocity and implications for the asymptotic behavior in the direction of the singularity in T-Gowdy, Commun. Pure Appl. Math., Volume 59 (2006) no. 7, pp. 977-1041 | DOI
[167] Inextendibility of expanding cosmological models with symmetry, Class. Quantum Gravity, Volume 22 (2005) no. 23, p. L143-L147 | DOI | Zbl
[168] An extension principle for the Einstein–Vlasov system in spherical symmetry, Ann. Henri Poincaré, Volume 6 (2005) no. 6, pp. 1137-1155 | DOI | Zbl
[169] Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter, Commun. Pure Appl. Math., Volume 69 (2016) no. 5, pp. 815-908 | DOI | Zbl
[170] Strong cosmic censorship for T-symmetric spacetimes with cosmological constant and matter, Ann. Henri Poincaré, Volume 9 (2008) no. 8, pp. 1425-1453 | DOI | Zbl
[171] Mixmaster universe, Phys. Rev. Lett., Volume 22 (1969), pp. 1071-1074 | DOI | Zbl
[172] Formation of quiescent big bang singularities, preprint, 2023 | arXiv
[173] Black holes in higher-dimensional space-times, Ann. Phys., Volume 172 (1986) no. 2, pp. 304-347 | DOI | Zbl
[174] Uniform boundedness for solutions to the Teukolsky equation on Schwarzschild from conservation laws of linearised gravity, Commun. Math. Phys., Volume 405 (2024) no. 6, 138 | Zbl
[175] Coercivity properties of the canonical energy in double null gauge on the 4-dimensional Schwarzschild exterior, Class. Quant. Grav., Volume 40 (2023) no. 22, 225013 | Zbl
[176] Localized energy estimates for wave equations on (1 + 4)-dimensional Myers-Perry space-times, SIAM J. Math. Anal., Volume 47 (2015) no. 3, pp. 1933-1957 | DOI | Zbl
[177] Linear stability of higher dimensional Schwarzschild spacetimes: decay of master quantities, Ann. PDE, Volume 6 (2020) no. 2, 7 | Zbl
[178] Decay of linear waves on higher-dimensional Schwarzschild black holes, Anal. PDE, Volume 6 (2013) no. 3, pp. 515-600 | DOI | Zbl
[179] Black rings, Class. Quantum Gravity, Volume 23 (2006) no. 20, p. R169-R197 | DOI | Zbl
[180] Black strings and p-branes are unstable, Phys. Rev. Lett., Volume 70 (1993), pp. 2837-2840 | DOI | Zbl
[181] The Gregory–Laflamme instability of the Schwarzschild black string exterior, J. Math. Phys., Volume 62 (2021) no. 3, 032502 | Zbl
[182] The stable trapping phenomenon for black strings and black rings and its obstructions on the decay of linear waves, Anal. PDE, Volume 14 (2021) no. 8, pp. 2427-2496 | DOI | Zbl
[183] Linear stability of the slowly-rotating Kerr-de Sitter family, preprint, 2022 | arXiv
[184] Morawetz estimates without relative degeneration and exponential decay on Schwarzschild–de Sitter spacetimes, Ann. Henri Poincaré, Volume 24 (2023) no. 9, pp. 3113-3152 | DOI | Zbl
[185] Quasi-normal modes and exponential energy decay for the Kerr–de Sitter black hole, Commun. Math. Phys., Volume 306 (2011) no. 1, pp. 119-163 | DOI | Zbl
[186] Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov), Invent. Math., Volume 194 (2013) no. 2, pp. 381-513 | DOI | Zbl
[187] Global analysis of quasilinear wave equations on asymptotically Kerr–de Sitter spaces, Int. Math. Res. Not., Volume 2016 (2016) no. 17, pp. 5355-5426 | DOI | Zbl
[188] Quasilinear wave equations on Schwarzschild–de Sitter, Commun. Partial Differ. Equ., Volume 49 (2024) no. 1-2, pp. 38-87 | DOI | Zbl
[189] Semilinear wave equations on asymptotically de Sitter, Kerr–de Sitter and Minkowski spacetimes, Anal. PDE, Volume 8 (2015) no. 8, pp. 1807-1890 | DOI | Zbl
[190] The global non-linear stability of the Kerr–de Sitter family of black holes, Acta Math., Volume 220 (2018) no. 1, pp. 1-206 | DOI | Zbl
[191] Nonlinear stability of the slowly-rotating Kerr-de Sitter family, preprint, 2021 | arXiv
[192] Analysis of linear waves near the Cauchy horizon of cosmological black holes, J. Math. Phys., Volume 58 (2017) no. 8, 081509 | DOI | Zbl
[193] Quasinormal modes and strong cosmic censorship, Phys. Rev. Lett., Volume 120 (2018), 031103 | DOI
[194] Glimpses of violation of strong cosmic censorship in rotating black holes, Phys. Rev. D, Volume 106 (2022), 044060 | DOI
[195] Strong cosmic censorship in de Sitter space, Phys. Rev. D, Volume 97 (2018), 104060 | DOI
[196] Strong cosmic censorship for the spherically symmetric Einstein–Maxwell–Charged–Klein–Gordon system with positive : stability of the Cauchy horizon and H Extensions, Ann. Henri Poincaré (2024) (to appear)
[197] On the global uniqueness for the Einstein–Maxwell–Scalar field system with a cosmological constant: Part 3. Mass inflation and extendibility of the solutions, Ann. PDE, Volume 3 (2017), 8 | DOI
[198] On the occurrence of mass inflation for the Einstein–Maxwell-Scalar field system with a cosmological constant and an exponential price law, Commun. Math. Phys., Volume 361 (2018) no. 1, pp. 289-341 | DOI
[199] Quasimodes and a lower bound on the uniform energy decay rate for Kerr-AdS spacetimes, Anal. PDE, Volume 7 (2014) no. 5, pp. 1057-1090 | DOI | Zbl
[200] Quasinormal modes for Schwarzschild-AdS black holes: exponential convergence to the real axis, Commun. Math. Phys., Volume 330 (2014) no. 2, pp. 771-799 | DOI | Zbl
[201] Exponentially-growing Mode Instability on Reissner–Nordström-Anti-de-Sitter black holes, preprint, 2024 | arXiv
[202] Holographic superconductors, J. High Energy Phys., Volume 2008 (2008) no. 12, 015 | Zbl
[203] Hairy black holes and the endpoint of AdS charged superradiance, J. High Energy Phys. (2017) no. 2, 128 | Zbl
[204] Uniform boundedness and continuity at the Cauchy horizon for linear waves on Reissner–Nordström-AdS black holes, Commun. Math. Phys., Volume 376 (2020) no. 1, pp. 145-200 | DOI | Zbl
[205] Blowup of the local energy of linear waves at the Reissner–Nordström-AdS Cauchy horizon, Class. Quantum Gravity, Volume 38 (2021) no. 21, 214001 | DOI | Zbl
[206] Diophantine approximation as cosmic censor for Kerr-AdS black holes, Invent. Math., Volume 227 (2022) no. 3, pp. 1169-1321 | DOI | Zbl
[207] Non-linear instability of slowly rotating Kerr-AdS black holes, preprint, 2023 | arXiv
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