Abstract
We examine the averaged null energy condition (ANEC) for strongly coupled fields, along the event horizon of an evaporating black hole by using the AdS/CFT duality. First, we consider a holographic model of a 3-dimensional evaporating black hole with a perturbed 4-dimensional black droplet geometry as the bulk dual, and investigate how negative energy flux going into the boundary black hole horizon appears. We show that the ingoing negative energy flux always appears at the boundary black hole horizon when the horizon area decreases. Second, we test the ANEC in a holographic model whose boundary geometry is a 4-dimensional asymptotically flat spacetime, describing the formation and subsequent evaporation of a spherically symmetric black hole. By applying the “bulk-no-shortcut principle”, we show that the ANEC is always satisfied when the local null energy is averaged with a weight function along the incomplete null geodesic on the event horizon from beginning of the formation to the final instant of the black hole evaporation. Our results indicate that the total ingoing negative energy flux is compensated by a large amount of positive energy flux in the early stage of the black hole formation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
P.C.W. Davies, S.A. Fulling and W.G. Unruh, Energy Momentum Tensor Near an Evaporating Black Hole, Phys. Rev. D 13 (1976) 2720 [INSPIRE].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
P. Figueras, J. Lucietti and T. Wiseman, Ricci solitons, Ricci flow, and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua, Class. Quant. Grav. 28 (2011) 215018 [arXiv:1104.4489] [INSPIRE].
J.E. Santos and B. Way, Black Funnels, JHEP 12 (2012) 060 [arXiv:1208.6291] [INSPIRE].
S. Fischetti and J.E. Santos, Rotating Black Droplet, JHEP 07 (2013) 156 [arXiv:1304.1156] [INSPIRE].
P. Figueras and S. Tunyasuvunakool, CFTs in rotating black hole backgrounds, Class. Quant. Grav. 30 (2013) 125015 [arXiv:1304.1162] [INSPIRE].
E. Mefford, Entanglement Entropy in Jammed CFTs, JHEP 09 (2017) 006 [arXiv:1605.09369] [INSPIRE].
V.E. Hubeny, D. Marolf and M. Rangamani, Hawking radiation in large N strongly-coupled field theories, Class. Quant. Grav. 27 (2010) 095015 [arXiv:0908.2270] [INSPIRE].
S. Fischetti and D. Marolf, Flowing Funnels: Heat sources for field theories and the AdS3 dual of CFT2 Hawking radiation, Class. Quant. Grav. 29 (2012) 105004 [arXiv:1202.5069] [INSPIRE].
S. Fischetti, D. Marolf and J.E. Santos, AdS flowing black funnels: Stationary AdS black holes with non-Killing horizons and heat transport in the dual CFT, Class. Quant. Grav. 30 (2013) 075001 [arXiv:1212.4820] [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
A.C. Wall, A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices, Phys. Rev. D 85 (2012) 104049 [Erratum ibid. 87 (2013) 069904] [arXiv:1105.3445] [INSPIRE].
W. Bunting, Z. Fu and D. Marolf, A coarse-grained generalized second law for holographic conformal field theories, Class. Quant. Grav. 33 (2016) 055008 [arXiv:1509.00074] [INSPIRE].
V.E. Hubeny, D. Marolf and M. Rangamani, Hawking radiation from AdS black holes, Class. Quant. Grav. 27 (2010) 095018 [arXiv:0911.4144] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
N. Iizuka, A. Ishibashi and K. Maeda, Conformally invariant averaged null energy condition from AdS/CFT, JHEP 03 (2020) 161 [arXiv:1911.02654] [INSPIRE].
N. Iizuka, A. Ishibashi and K. Maeda, The averaged null energy conditions in even dimensional curved spacetimes from AdS/CFT duality, JHEP 10 (2020) 106 [arXiv:2008.07942] [INSPIRE].
S. Gao and R.M. Wald, Theorems on gravitational time delay and related issues, Class. Quant. Grav. 17 (2000) 4999 [gr-qc/0007021] [INSPIRE].
S. de Haro, K. Skenderis and S.N. Solodukhin, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
H. Kodama and A. Ishibashi, A Master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions, Prog. Theor. Phys. 110 (2003) 701 [hep-th/0305147] [INSPIRE].
M. Mars and J.M.M. Senovilla, Axial symmetry and conformal Killing vectors, Class. Quant. Grav. 10 (1993) 1633 [gr-qc/0201045] [INSPIRE].
W.A. Hiscock, Models of Evaporating Black Holes. Part I, Phys. Rev. D 23 (1981) 2813 [INSPIRE].
R.M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, The University of Chicago Press, Chicago IL U.S.A. (1994).
W.R. Kelly and A.C. Wall, Holographic proof of the averaged null energy condition, Phys. Rev. D 90 (2014) 106003 [Erratum ibid. 91 (2015) 069902] [arXiv:1408.3566] [INSPIRE].
F. Rosso, Global aspects of conformal symmetry and the ANEC in dS and AdS, JHEP 03 (2020) 186 [arXiv:1912.08897] [INSPIRE].
N. Haddad, Black Strings Ending on Horizons, Class. Quant. Grav. 29 (2012) 245001 [arXiv:1207.2305] [INSPIRE].
A. Ishibashi, K. Maeda and E. Mefford, Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole, Phys. Rev. D 96 (2017) 024005 [arXiv:1703.09743] [INSPIRE].
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: 2111.05151
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
Ishibashi, A., Maeda, K. The averaged null energy condition on holographic evaporating black holes. J. High Energ. Phys. 2022, 104 (2022). https://doi.org/10.1007/JHEP03(2022)104
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2022)104