Abstract
We study the behavior of black hole singularities across the Hawking-Page phase transitions, uncovering possible connections between the physics inside and outside the horizon. We focus on the case of spacelike singularities in Einstein-scalar theory which are of the Kasner form. We find that the Kasner exponents are continuous and non-differentiable during the second order phase transitions, while discontinuous in the first order phase transitions. We give some arguments on the universality of this behavior. We also discuss possible observables in the dual field theory which encode the Kasner exponents.
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References
S.W. Hawking and R. Penrose, The Singularities of gravitational collapse and cosmology, Proc. Roy. Soc. Lond. A 314 (1970) 529.
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.a. Belinsky, I.m. Khalatnikov and E.m. Lifshitz, A General Solution of the Einstein Equations with a Time Singularity, Adv. Phys. 31 (1982) 639 [INSPIRE].
E. Kasner, Geometrical theorems on Einstein’s cosmological equations, Am. J. MAth. 43 (1921) 217.
V. Belinski and M. Henneaux, The Cosmological Singularity, Cambridge Univiversity Press, Cambridge Monogr. Math. Phys. , Cambridge U.K. (2017) [DOI] [INSPIRE].
A. Frenkel, S.A. Hartnoll, J. Kruthoff and Z.D. Shi, Holographic flows from CFT to the Kasner universe, JHEP 08 (2020) 003 [arXiv:2004.01192] [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].
S.A. Hartnoll, G.T. Horowitz, J. Kruthoff and J.E. Santos, Diving into a holographic superconductor, SciPost Phys. 10 (2021) 009 [arXiv:2008.12786] [INSPIRE].
R.-G. Cai, L. Li and R.-Q. Yang, No Inner-Horizon Theorem for Black Holes with Charged Scalar Hairs, JHEP 03 (2021) 263 [arXiv:2009.05520] [INSPIRE].
Y.-Q. Wang, Y. Song, Q. Xiang, S.-W. Wei, T. Zhu and Y.-X. Liu, Holographic flows with scalar self-interaction toward the Kasner universe, arXiv:2009.06277 [INSPIRE].
R.-Q. Yang, R.-G. Cai and L. Li, Constraining the number of horizons with energy conditions, arXiv:2104.03012 [INSPIRE].
S.A.H. Mansoori, L. Li, M. Rafiee and M. Baggioli, What’s inside a hairy black hole in massive gravity?, arXiv:2108.01471 [INSPIRE].
E. Shaghoulian and H. Wang, Timelike BKL singularities and chaos in AdS/CFT, Class. Quant. Grav. 33 (2016) 125020 [arXiv:1601.02599] [INSPIRE].
V.A. Belinski and I.M. Khalatnikov, Effect of Scalar and Vector Fields on the Nature of the Cosmological Singularity, Sov. Phys. JETP 36 (1973) 591 [INSPIRE].
T. Damour, M. Henneaux and H. Nicolai, Cosmological billiards, Class. Quant. Grav. 20 (2003) R145 [hep-th/0212256] [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, Excursions beyond the horizon: Black hole singularities in Yang-Mills theories. I, JHEP 04 (2006) 044 [hep-th/0506202] [INSPIRE].
M. Grinberg and J. Maldacena, Proper time to the black hole singularity from thermal one-point functions, JHEP 03 (2021) 131 [arXiv:2011.01004] [INSPIRE].
T. Hartman and J. Maldacena, Time Evolution of Entanglement Entropy from Black Hole Interiors, JHEP 05 (2013) 014 [arXiv:1303.1080] [INSPIRE].
L. Susskind, L. Thorlacius and J. Uglum, The Stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions, and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
M. Berkooz, A. Sever and A. Shomer, ‘Double trace’ deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].
T. Faulkner, G.T. Horowitz and M.M. Roberts, Holographic quantum criticality from multi-trace deformations, JHEP 04 (2011) 051 [arXiv:1008.1581] [INSPIRE].
I. Papadimitriou, Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT, JHEP 05 (2007) 075 [hep-th/0703152] [INSPIRE].
J.-H. She et al., Observing the origin of superconductivity in quantum critical metals, Phys. Rev. B 84 (2011) 144527 [arXiv:1105.5377] [INSPIRE].
N. Iqbal, H. Liu and M. Mezei, Quantum phase transitions in semilocal quantum liquids, Phys. Rev. D 91 (2015) 025024 [arXiv:1108.0425] [INSPIRE].
E. Mefford and G.T. Horowitz, Simple holographic insulator, Phys. Rev. D 90 (2014) 084042 [arXiv:1406.4188] [INSPIRE].
D.M. Hofman and N. Iqbal, Generalized global symmetries and holography, SciPost Phys. 4 (2018) 005 [arXiv:1707.08577] [INSPIRE].
S. Grozdanov and N. Poovuttikul, Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma, JHEP 04 (2019) 141 [arXiv:1707.04182] [INSPIRE].
R.A. Janik, J. Jankowski and H. Soltanpanahi, Real-Time dynamics and phase separation in a holographic first order phase transition, Phys. Rev. Lett. 119 (2017) 261601 [arXiv:1704.05387] [INSPIRE].
U. Gürsoy, E. Kiritsis, F. Nitti and L. Silva Pimenta, Exotic holographic RG flows at finite temperature, JHEP 10 (2018) 173 [arXiv:1805.01769] [INSPIRE].
Y. Bea and D. Mateos, Heating up Exotic RG Flows with Holography, JHEP 08 (2018) 034 [arXiv:1805.01806] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
L. Bellantuono, R.A. Janik, J. Jankowski and H. Soltanpanahi, Dynamics near a first order phase transition, JHEP 10 (2019) 146 [arXiv:1906.00061] [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93 (2021) 035002 [arXiv:2006.06872] [INSPIRE].
E. Caceres, A. Kundu, A.K. Patra and S. Shashi, Page Curves and Bath Deformations, arXiv:2107.00022 [INSPIRE].
M.J. Perry, No Future in Black Holes, arXiv:2106.03715 [INSPIRE].
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Liu, Y., Lyu, HD. & Raju, A. Black hole singularities across phase transitions. J. High Energ. Phys. 2021, 140 (2021). https://doi.org/10.1007/JHEP10(2021)140
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DOI: https://doi.org/10.1007/JHEP10(2021)140