Abstract
Using extended island formula we compute entanglement entropy of Hawking radiation for black hole solutions of certain gravitational models containing higher derivative terms. To be concrete we consider two different four dimensional models to compute entropy for both asymptotically flat and AdS black holes. One observes that the resultant entropy follows the Page curve, thanks to the contribution of the island, despite the fact that the corresponding gravitational models might be non-unitary.
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].
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
D.N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].
D.N. Page, Time Dependence of Hawking Radiation Entropy, JCAP 09 (2013) 028 [arXiv:1301.4995] [INSPIRE].
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09 (2020) 002 [arXiv:1905.08255] [INSPIRE].
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, JHEP 12 (2019) 063 [arXiv:1905.08762] [INSPIRE].
A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, JHEP 03 (2020) 149 [arXiv:1908.10996] [INSPIRE].
A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon, arXiv:1910.11077 [INSPIRE].
R. Bousso and M. Tomašević, Unitarity From a Smooth Horizon?, Phys. Rev. D 102 (2020) 106019 [arXiv:1911.06305] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
N. Engelhardt and A.C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [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].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, arXiv:1911.11977 [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05 (2020) 013 [arXiv:1911.12333] [INSPIRE].
T.J. Hollowood and S.P. Kumar, Islands and Page Curves for Evaporating Black Holes in JT Gravity, JHEP 08 (2020) 094 [arXiv:2004.14944] [INSPIRE].
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, A simple model of quantum holography talks at KITP, 7 April and 27 May 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev.
C.G. Callan Jr., S.B. Giddings, J.A. Harvey and A. Strominger, Evanescent black holes, Phys. Rev. D 45 (1992) 1005 [hep-th/9111056] [INSPIRE].
F.F. Gautason, L. Schneiderbauer, W. Sybesma and L. Thorlacius, Page Curve for an Evaporating Black Hole, JHEP 05 (2020) 091 [arXiv:2004.00598] [INSPIRE].
T. Anegawa and N. Iizuka, Notes on islands in asymptotically flat 2d dilaton black holes, JHEP 07 (2020) 036 [arXiv:2004.01601] [INSPIRE].
T. Hartman, E. Shaghoulian and A. Strominger, Islands in Asymptotically Flat 2D Gravity, JHEP 07 (2020) 022 [arXiv:2004.13857] [INSPIRE].
A. Almheiri, R. Mahajan and J.E. Santos, Entanglement islands in higher dimensions, SciPost Phys. 9 (2020) 001 [arXiv:1911.09666] [INSPIRE].
K. Hashimoto, N. Iizuka and Y. Matsuo, Islands in Schwarzschild black holes, JHEP 06 (2020) 085 [arXiv:2004.05863] [INSPIRE].
C. Krishnan, V. Patil and J. Pereira, Page Curve and the Information Paradox in Flat Space, arXiv:2005.02993 [INSPIRE].
X. Dong, Holographic Entanglement Entropy for General Higher Derivative Gravity, JHEP 01 (2014) 044 [arXiv:1310.5713] [INSPIRE].
D.V. Fursaev, A. Patrushev and S.N. Solodukhin, Distributional Geometry of Squashed Cones, Phys. Rev. D 88 (2013) 044054 [arXiv:1306.4000] [INSPIRE].
S.N. Solodukhin, Entanglement entropy, conformal invariance and extrinsic geometry, Phys. Lett. B 665 (2008) 305 [arXiv:0802.3117] [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, arXiv:2006.06872 [INSPIRE].
P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory, J. Stat. Mech. 0911 (2009) P11001 [arXiv:0905.2069] [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
H. Lü and C.N. Pope, Critical Gravity in Four Dimensions, Phys. Rev. Lett. 106 (2011) 181302 [arXiv:1101.1971] [INSPIRE].
M. Alishahiha and R. Fareghbal, D-Dimensional Log Gravity, Phys. Rev. D 83 (2011) 084052 [arXiv:1101.5891] [INSPIRE].
L. Susskind and J. Lindesay, An introduction to black holes, information and the string theory revolution, World Scientific Publishing Co. (2005).
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: 2005.08715
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
Alishahiha, M., Astaneh, A.F. & Naseh, A. Island in the presence of higher derivative terms. J. High Energ. Phys. 2021, 35 (2021). https://doi.org/10.1007/JHEP02(2021)035
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2021)035