Abstract
We study black holes in two and three dimensions that have spacelike curvature singularities behind horizons. The 2D solutions are obtained by dimensionally reducing certain 3D black holes, known as quantum BTZ solutions. Furthermore, we identify the corresponding dilaton potential and show how it can arise from a higher-dimensional theory. Finally, we show that the rotating BTZ black hole develops a singular inner horizon once quantum effects are properly accounted for, thereby solidifying strong cosmic censorship for all known cases.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on Orbifolds, Nucl. Phys. B 261 (1985) 678 [INSPIRE].
P.S. Aspinwall, B.R. Greene and D.R. Morrison, Multiple mirror manifolds and topology change in string theory, Phys. Lett. B 303 (1993) 249 [hep-th/9301043] [INSPIRE].
E. Witten, Phases of N=2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
A. Strominger, Massless black holes and conifolds in string theory, Nucl. Phys. B 451 (1995) 96 [hep-th/9504090] [INSPIRE].
G.T. Horowitz and A.R. Steif, Space-Time Singularities in String Theory, Phys. Rev. Lett. 64 (1990) 260 [INSPIRE].
G.T. Horowitz and A.R. Steif, Singular string solutions with nonsingular initial data, Phys. Lett. B 258 (1991) 91 [INSPIRE].
V.A. Belinsky, I.M. Khalatnikov and E.M. Lifshitz, Oscillatory approach to a singular point in the relativistic cosmology, Adv. Phys. 19 (1970) 525 [INSPIRE].
V. Belinski and M. Henneaux, The Cosmological Singularity, Cambridge University Press, Cambridge (2017) [https://doi.org/10.1017/9781107239333] [INSPIRE].
E. Witten, A Note On The Canonical Formalism for Gravity, arXiv:2212.08270 [INSPIRE].
A. Ori and E.E. Flanagan, How generic are null space-time singularities?, Phys. Rev. D 53 (1996) 1754 [gr-qc/9508066] [INSPIRE].
J. Luk, Weak null singularities in general relativity, J. Am. Math. Soc. 31 (2018) 1 [arXiv:1311.4970] [INSPIRE].
M. Dafermos and J. Luk, The interior of dynamical vacuum black holes I: The C0-stability of the Kerr Cauchy horizon, arXiv:1710.01722 [INSPIRE].
R. Emparan and M. Tomašević, Quantum backreaction on chronology horizons, JHEP 02 (2022) 182 [arXiv:2109.03611] [INSPIRE].
R. Bousso and A. Shahbazi-Moghaddam, Quantum singularities, Phys. Rev. D 107 (2023) 066002 [arXiv:2206.07001] [INSPIRE].
E. Witten, On string theory and black holes, Phys. Rev. D 44 (1991) 314 [INSPIRE].
T.G. Mertens and G.J. Turiaci, Solvable models of quantum black holes: a review on Jackiw-Teitelboim gravity, Living Rev. Rel. 26 (2023) 4 [arXiv:2210.10846] [INSPIRE].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
D.L. Jafferis, D.K. Kolchmeyer, B. Mukhametzhanov and J. Sonner, Jackiw-Teitelboim gravity with matter, generalized eigenstate thermalization hypothesis, and random matrices, Phys. Rev. D 108 (2023) 066015 [arXiv:2209.02131] [INSPIRE].
D. Grumiller, W. Kummer and D.V. Vassilevich, Dilaton gravity in two-dimensions, Phys. Rept. 369 (2002) 327 [hep-th/0204253] [INSPIRE].
D. Grumiller, R. Ruzziconi and C. Zwikel, Generalized dilaton gravity in 2d, SciPost Phys. 12 (2022) 032 [arXiv:2109.03266] [INSPIRE].
E. Witten, Matrix Models and Deformations of JT Gravity, Proc. Roy. Soc. Lond. A 476 (2020) 20200582 [arXiv:2006.13414] [INSPIRE].
H. Maxfield and G.J. Turiaci, The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral, JHEP 01 (2021) 118 [arXiv:2006.11317] [INSPIRE].
G.J. Turiaci, M. Usatyuk and W.W. Weng, 2D dilaton-gravity, deformations of the minimal string, and matrix models, Class. Quant. Grav. 38 (2021) 204001 [arXiv:2011.06038] [INSPIRE].
A. Blommaert, J. Kruthoff and S. Yao, An integrable road to a perturbative plateau, JHEP 04 (2023) 048 [arXiv:2208.13795] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The black hole singularity in AdS / CFT, JHEP 02 (2004) 014 [hep-th/0306170] [INSPIRE].
G. Festuccia and H. Liu, A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, Adv. Sci. Lett. 2 (2009) 221 [arXiv:0811.1033] [INSPIRE].
M. Dodelson, C. Iossa, R. Karlsson and A. Zhiboedov, A thermal product formula, arXiv:2304.12339 [INSPIRE].
G.T. Horowitz, H. Leung, L. Queimada and Y. Zhao, Boundary signature of singularity in the presence of a shock wave, arXiv:2310.03076 [INSPIRE].
V.P. Frolov, Vacuum polarization in a locally static multiply connected space-time and a time machine problem, Phys. Rev. D 43 (1991) 3878 [INSPIRE].
B.S. Kay, M.J. Radzikowski and R.M. Wald, Quantum field theory on space-times with a compactly generated Cauchy horizon, Commun. Math. Phys. 183 (1997) 533 [gr-qc/9603012] [INSPIRE].
S. Hollands, R.M. Wald and J. Zahn, Quantum instability of the Cauchy horizon in Reissner-Nordström-deSitter spacetime, Class. Quant. Grav. 37 (2020) 115009 [arXiv:1912.06047] [INSPIRE].
M. Simpson and R. Penrose, Internal instability in a Reissner-Nordstrom black hole, Int. J. Theor. Phys. 7 (1973) 183 [INSPIRE].
E. Poisson and W. Israel, Inner-horizon instability and mass inflation in black holes, Phys. Rev. Lett. 63 (1989) 1663 [INSPIRE].
A. Ori, Inner structure of a charged black hole: An exact mass-inflation solution, Phys. Rev. Lett. 67 (1991) 789 [INSPIRE].
P. Hintz and A. Vasy, The global non-linear stability of the Kerr-de Sitter family of black holes, arXiv:1606.04014 [10.4310/acta.2018.v220.n1.a1] [INSPIRE].
P. Hintz, Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes, arXiv:1612.04489 [https://doi.org/10.1007/s40818-018-0047-y] [INSPIRE].
O.J.C. Dias, H.S. Reall and J.E. Santos, Strong cosmic censorship: taking the rough with the smooth, JHEP 10 (2018) 001 [arXiv:1808.02895] [INSPIRE].
R. Luna et al., Strong cosmic censorship: The nonlinear story, Phys. Rev. D 99 (2019) 064014 [Addendum ibid. 103 (2021) 104043] [arXiv:1810.00886] [INSPIRE].
H.K. Kunduri, J. Lucietti and H.S. Reall, Near-horizon symmetries of extremal black holes, Class. Quant. Grav. 24 (2007) 4169 [arXiv:0705.4214] [INSPIRE].
H.K. Kunduri and J. Lucietti, Classification of near-horizon geometries of extremal black holes, Living Rev. Rel. 16 (2013) 8 [arXiv:1306.2517] [INSPIRE].
G. Holzegel and J. Smulevici, Decay properties of Klein-Gordon fields on Kerr-AdS spacetimes, Commun. Pure Appl. Math. 66 (2013) 1751 [arXiv:1110.6794] [INSPIRE].
S.A. Hartnoll, G.T. Horowitz, J. Kruthoff and J.E. Santos, Gravitational duals to the grand canonical ensemble abhor Cauchy horizons, JHEP 10 (2020) 102 [arXiv:2006.10056] [INSPIRE].
L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
P. Bueno, R. Emparan and Q. Llorens, Higher-curvature gravities from braneworlds and the holographic c-theorem, Phys. Rev. D 106 (2022) 044012 [arXiv:2204.13421] [INSPIRE].
R. Emparan et al., Black holes in dS3, JHEP 11 (2022) 073 [arXiv:2207.03302] [INSPIRE].
R. Emparan, A.M. Frassino and B. Way, Quantum BTZ black hole, JHEP 11 (2020) 137 [arXiv:2007.15999] [INSPIRE].
R. Emparan and M. Tomašević, Strong cosmic censorship in the BTZ black hole, JHEP 06 (2020) 038 [arXiv:2002.02083] [INSPIRE].
R. Emparan, G.T. Horowitz and R.C. Myers, Exact description of black holes on branes. 2. Comparison with BTZ black holes and black strings, JHEP 01 (2000) 021 [hep-th/9912135] [INSPIRE].
R. Emparan, A. Fabbri and N. Kaloper, Quantum black holes as holograms in AdS brane worlds, JHEP 08 (2002) 043 [hep-th/0206155] [INSPIRE].
R. Emparan and M. Tomašević, Holography of time machines, JHEP 03 (2022) 212 [arXiv:2107.14200] [INSPIRE].
M. Tomašević, On the Inaccessibility of Time Machines, Universe 9 (2023) 159 [INSPIRE].
A.M. Frassino, J.F. Pedraza, A. Svesko and M.R. Visser, Higher-Dimensional Origin of Extended Black Hole Thermodynamics, Phys. Rev. Lett. 130 (2023) 161501 [arXiv:2212.14055] [INSPIRE].
R. Emparan, A.M. Frassino, M. Sasieta and M. Tomašević, Holographic complexity of quantum black holes, JHEP 02 (2022) 204 [arXiv:2112.04860] [INSPIRE].
E. Panella and A. Svesko, Quantum Kerr-de Sitter black holes in three dimensions, JHEP 06 (2023) 127 [arXiv:2303.08845] [INSPIRE].
C. Martinez and J. Zanelli, Conformally dressed black hole in (2+1)-dimensions, Phys. Rev. D 54 (1996) 3830 [gr-qc/9604021] [INSPIRE].
A. Cisterna, F. Diaz, R.B. Mann and J. Oliva, Exploring accelerating hairy black holes in 2+1 dimensions: the asymptotically locally anti-de Sitter class and its holography, JHEP 11 (2023) 073 [arXiv:2309.05559] [INSPIRE].
N. Engelhardt and G.T. Horowitz, Holographic Consequences of a No Transmission Principle, Phys. Rev. D 93 (2016) 026005 [arXiv:1509.07509] [INSPIRE].
N.D. Birrell and P.C.W. Davies, On falling through a black hole into another universe, Nature 272 (1978) 35 [INSPIRE].
P. Shrivastava, Quantum aspects of charged black holes in de-Sitter space, arXiv:2009.03261 [INSPIRE].
S. Hollands, C. Klein and J. Zahn, Quantum stress tensor at the Cauchy horizon of the Reissner-Nordström-de Sitter spacetime, Phys. Rev. D 102 (2020) 085004 [arXiv:2006.10991] [INSPIRE].
S. Bhattacharjee, S. Sarkar and A. Bhattacharyya, Scalar perturbations of black holes in Jackiw-Teitelboim gravity, Phys. Rev. D 103 (2021) 024008 [arXiv:2011.08179] [INSPIRE].
U. Moitra, Strong Cosmic Censorship in Two Dimensions, Phys. Rev. D 103 (2021) L081502 [arXiv:2011.03499] [INSPIRE].
K. Papadodimas, S. Raju and P. Shrivastava, A simple quantum test for smooth horizons, JHEP 12 (2020) 003 [arXiv:1910.02992] [INSPIRE].
O.J.C. Dias, H.S. Reall and J.E. Santos, The BTZ black hole violates strong cosmic censorship, JHEP 12 (2019) 097 [arXiv:1906.08265] [INSPIRE].
A. Ghosh, H. Maxfield and G.J. Turiaci, A universal Schwarzian sector in two-dimensional conformal field theories, JHEP 05 (2020) 104 [arXiv:1912.07654] [INSPIRE].
L.V. Iliesiu and G.J. Turiaci, The statistical mechanics of near-extremal black holes, JHEP 05 (2021) 145 [arXiv:2003.02860] [INSPIRE].
D. Christodoulou, The Formation of Black Holes in General Relativity, in the proceedings of the 12th Marcel Grossmann Meeting on General Relativity, (2008), p. 24–34 [https://doi.org/10.1142/9789814374552_0002] [arXiv:0805.3880] [INSPIRE].
M.J. Radzikowski, Micro-local approach to the Hadamard condition in quantum field theory on curved space-time, Commun. Math. Phys. 179 (1996) 529 [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
A. Achucarro and M.E. Ortiz, Relating black holes in two-dimensions and three-dimensions, Phys. Rev. D 48 (1993) 3600 [hep-th/9304068] [INSPIRE].
H. Geng et al., Jackiw-Teitelboim Gravity from the Karch-Randall Braneworld, Phys. Rev. Lett. 129 (2022) 231601 [arXiv:2206.04695] [INSPIRE].
H. Geng, Aspects of AdS2 quantum gravity and the Karch-Randall braneworld, JHEP 09 (2022) 024 [arXiv:2206.11277] [INSPIRE].
S.E. Aguilar-Gutierrez, A.K. Patra and J.F. Pedraza, Entangled universes in dS wedge holography, JHEP 10 (2023) 156 [arXiv:2308.05666] [INSPIRE].
A. Svesko, E. Verheijden, E.P. Verlinde and M.R. Visser, Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity, JHEP 08 (2022) 075 [arXiv:2203.00700] [INSPIRE].
I. Rakić, M. Rangamani and G.J. Turiaci, Near-extremal Kerr and its entropy, in proceedings of ExU-YITP Workshop on Holography, Gravity and Quantum Information (QIMG 2023), YITP, Kyoto, Japan, 14 September 2023, https://www2.yukawa.kyoto-u.ac.jp/~qimg2023/presentation_files/Rangamani_Mukund_09_14_.pdf.
J.M. Bardeen and G.T. Horowitz, The extreme Kerr throat geometry: A vacuum analog of AdS2 × S2, Phys. Rev. D 60 (1999) 104030 [hep-th/9905099] [INSPIRE].
D. Kapec, A. Sheta, A. Strominger and C. Toldo, Logarithmic Corrections to Kerr Thermodynamics, arXiv:2310.00848 [INSPIRE].
W. Abou Hamdan, N. Čeplak, M. Kolanowski and M. Tomašević, Spontaneous superradiance of near-extremal black holes, in progress.
G.T. Horowitz, M. Kolanowski, G.N. Remmen and J.E. Santos, Extremal Kerr Black Holes as Amplifiers of New Physics, Phys. Rev. Lett. 131 (2023) 091402 [arXiv:2303.07358] [INSPIRE].
R. Brito, V. Cardoso and P. Pani, Superradiance: New Frontiers in Black Hole Physics, Lect. Notes Phys. 906 (2015) 1 [arXiv:1501.06570] [INSPIRE].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
N. Čeplak, R. Emparan, A. Puhm and M. Tomašević, The correspondence between rotating black holes and fundamental strings, JHEP 11 (2023) 226 [arXiv:2307.03573] [INSPIRE].
N. Graham and K.D. Olum, Achronal averaged null energy condition, Phys. Rev. D 76 (2007) 064001 [arXiv:0705.3193] [INSPIRE].
R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS / CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].
S.M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Cambridge University Press (2019) [https://doi.org/10.1017/9781108770385] [INSPIRE].
Acknowledgments
We thank Jan Boruch, Roberto Emparan, and Wayne Weng for their very useful comments on the draft of this paper. We thank Weam Abou Hamdan, Robie Hennigar, Stefan Hollands, Luca Iliesiu, Adam Levine, Sean McBride, Suvrat Raju, Mukund Rangamani, Harvey Reall, Mikel Sanchez Garitaonandia, Arvin Shahbazi-Moghaddam, Misha Usatyuk, and Jochen Zahn for useful discussions. MT is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 852386). The work of MK was supported in part by NSF Grant PHY-2107939.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2310.06014
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kolanowski, M., Tomašević, M. Singularities in 2D and 3D quantum black holes. J. High Energ. Phys. 2023, 102 (2023). https://doi.org/10.1007/JHEP12(2023)102
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2023)102