Abstract
We argue that the proper time from the event horizon to the black hole singularity can be extracted from the thermal expectation values of certain operators outside the horizon. This works for fields which couple to higher-curvature terms, so that they can decay into two gravitons. To extract this proper time, it is necessary to vary the mass of the field.
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R.C. Myers, T. Sierens and W. Witczak-Krempa, A Holographic Model for Quantum Critical Responses, JHEP 05 (2016) 073 [Addendum ibid. 09 (2016) 066] [arXiv:1602.05599] [INSPIRE].
P. Kraus and A. Maloney, A cardy formula for three-point coefficients or how the black hole got its spots, JHEP 05 (2017) 160 [arXiv:1608.03284] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [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].
C. Cordova, J. Maldacena and G.J. Turiaci, Bounds on OPE Coefficients from Interference Effects in the Conformal Collider, JHEP 11 (2017) 032 [arXiv:1710.03199] [INSPIRE].
D. Meltzer and E. Perlmutter, Beyond a = c: gravitational couplings to matter and the stress tensor OPE, JHEP 07 (2018) 157 [arXiv:1712.04861] [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFTd/AdSd+1 correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
L. Iliesiu, M. Koloğlu, R. Mahajan, E. Perlmutter and D. Simmons-Duffin, The Conformal Bootstrap at Finite Temperature, JHEP 10 (2018) 070 [arXiv:1802.10266] [INSPIRE].
Y. Gobeil, A. Maloney, G.S. Ng and J.-q. Wu, Thermal Conformal Blocks, SciPost Phys. 7 (2019) 015 [arXiv:1802.10537] [INSPIRE].
S. Mizera and A. Pokraka, From Infinity to Four Dimensions: Higher Residue Pairings and Feynman Integrals, JHEP 02 (2020) 159 [arXiv:1910.11852] [INSPIRE].
S. El-Showk and K. Papadodimas, Emergent Spacetime and Holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [INSPIRE].
M. Kulaxizi, G.S. Ng and A. Parnachev, Black Holes, Heavy States, Phase Shift and Anomalous Dimensions, SciPost Phys. 6 (2019) 065 [arXiv:1812.03120] [INSPIRE].
A.L. Fitzpatrick and K.-W. Huang, Universal Lowest-Twist in CFTs from Holography, JHEP 08 (2019) 138 [arXiv:1903.05306] [INSPIRE].
Y.-Z. Li, Heavy-light Bootstrap from Lorentzian Inversion Formula, JHEP 07 (2020) 046 [arXiv:1910.06357] [INSPIRE].
A.L. Fitzpatrick, K.-W. Huang, D. Meltzer, E. Perlmutter and D. Simmons-Duffin, Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs, JHEP 11 (2020) 060 [arXiv:2007.07382] [INSPIRE].
M. Dodelson and H. Ooguri, Singularities of thermal correlators at strong coupling, arXiv:2010.09734 [INSPIRE].
E. Witten, Analytic Continuation Of Chern-Simons Theory, AMS/IP Stud. Adv. Math. 50 (2011) 347 [arXiv:1001.2933] [INSPIRE].
T. Bargheer, J.A. Minahan and R. Pereira, Computing Three-Point Functions for Short Operators, JHEP 03 (2014) 096 [arXiv:1311.7461] [INSPIRE].
E. D’Hoker, D.Z. Freedman and L. Rastelli, AdS/CFT four point functions: How to succeed at z integrals without really trying, Nucl. Phys. B 562 (1999) 395 [hep-th/9905049] [INSPIRE].
P. Kraus, H. Ooguri and S. Shenker, Inside the horizon with AdS/CFT, Phys. Rev. D 67 (2003) 124022 [hep-th/0212277] [INSPIRE].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
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ArXiv ePrint: 2011.01004
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Grinberg, M., Maldacena, J. Proper time to the black hole singularity from thermal one-point functions. J. High Energ. Phys. 2021, 131 (2021). https://doi.org/10.1007/JHEP03(2021)131
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DOI: https://doi.org/10.1007/JHEP03(2021)131