×

The entropy of a hole in spacetime. (English) Zbl 1342.83226

Summary: We compute the gravitational entropy of ‘spherical Rindler space’, a time-dependent, spherically symmetric generalization of ordinary Rindler space, defined with reference to a family of observers traveling along non-parallel, accelerated trajectories. All these observers are causally disconnected from a spherical region \(H\) (a ‘hole’) located at the origin of Minkowski space. The entropy evaluates to \(S=\mathcal A/4G\), where \(\mathcal A\) is the area of the spherical acceleration horizon, which coincides with the boundary of \(H\). We propose that \(S\) is the entropy of entanglement between quantum gravitational degrees of freedom supporting the interior and the exterior of the sphere \(H\).

MSC:

83C75 Space-time singularities, cosmic censorship, etc.
83C45 Quantization of the gravitational field

References:

[1] S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96 (2006) 181602 [hep-th/0603001] [INSPIRE]. · Zbl 1228.83110 · doi:10.1103/PhysRevLett.96.181602
[2] V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP07 (2007) 062 [arXiv:0705.0016] [INSPIRE]. · doi:10.1088/1126-6708/2007/07/062
[3] M. Van Raamsdonk, Comments on quantum gravity and entanglement, arXiv:0907.2939 [INSPIRE]. · Zbl 1359.81171
[4] M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav.42 (2010) 2323 [arXiv:1005.3035] [INSPIRE]. · Zbl 1200.83052 · doi:10.1007/s10714-010-1034-0
[5] B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, Rindler Quantum Gravity, Class. Quant. Grav.29 (2012) 235025 [arXiv:1206.1323] [INSPIRE]. · Zbl 1258.83029 · doi:10.1088/0264-9381/29/23/235025
[6] S.L. Braunstein, S. Pirandola and K. Zyczkowski, Entangled black holes as ciphers of hidden information, Phys. Rev. Lett.110 (2013) 101301 [arXiv:0907.1190] [INSPIRE]. · doi:10.1103/PhysRevLett.110.101301
[7] A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP02 (2013) 062 [arXiv:1207.3123] [INSPIRE]. · Zbl 1342.83121 · doi:10.1007/JHEP02(2013)062
[8] V. Balasubramanian, M.B. McDermott and M. Van Raamsdonk, Momentum-space entanglement and renormalization in quantum field theory, Phys. Rev.D 86 (2012) 045014 [arXiv:1108.3568] [INSPIRE].
[9] A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP08 (2013) 090 [arXiv:1304.4926] [INSPIRE]. · Zbl 1342.83185 · doi:10.1007/JHEP08(2013)090
[10] R. Laflamme, Entropy of a Rindler wedge, Phys. Lett.B 196 (1987) 449.
[11] J.D. Bekenstein, Black holes and entropy, Phys. Rev.D 7 (1973) 2333 [INSPIRE]. · Zbl 1369.83037
[12] J.M. Bardeen, B. Carter and S. Hawking, The Four laws of black hole mechanics, Commun. Math. Phys.31 (1973) 161 [INSPIRE]. · Zbl 1125.83309 · doi:10.1007/BF01645742
[13] G. Gibbons and S. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev.D 15 (1977) 2752 [INSPIRE].
[14] S.W. Hawking, The path-integral approach to quantum gravity, Chapter 15 in General Relativity: An Einstein Centenary Survey, eds. S.W. Hawking and W. Israel, Cambridge U.K. (1979).
[15] R. Kallosh, T. Ortín and A.W. Peet, Entropy and action of dilaton black holes, Phys. Rev.D 47 (1993) 5400 [hep-th/9211015] [INSPIRE].
[16] L. Susskind, Some speculations about black hole entropy in string theory, hep-th/9309145 [INSPIRE]. · Zbl 0963.83024
[17] V. Iyer and R.M. Wald, A Comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes, Phys. Rev.D 52 (1995) 4430 [gr-qc/9503052] [INSPIRE].
[18] V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev.D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
[19] K. Parattu, B.R. Majhi and T. Padmanabhan, The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm, Phys. Rev.D 87 (2013) 124011 [arXiv:1303.1535] [INSPIRE].
[20] S.F. Ross, Black hole thermodynamics, hep-th/0502195 [INSPIRE]. · Zbl 1186.83095
[21] D.V. Fursaev and S.N. Solodukhin, On the description of the Riemannian geometry in the presence of conical defects, Phys. Rev.D 52 (1995) 2133 [hep-th/9501127] [INSPIRE].
[22] M. Bañados, C. Teitelboim and J. Zanelli, Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem, Phys. Rev. Lett.72 (1994) 957 [gr-qc/9309026] [INSPIRE]. · Zbl 0973.83531 · doi:10.1103/PhysRevLett.72.957
[23] D.V. Fursaev, A. Patrushev and S.N. Solodukhin, Distributional Geometry of Squashed Cones, arXiv:1306.4000 [INSPIRE].
[24] A.J. Bray and M.A. Moore, Replica-Symmetry Breaking in Spin-Glass Theories, Phys. Rev. Lett.41 (1978) 1068. · doi:10.1103/PhysRevLett.41.1068
[25] T. Castellani and A. Cavagna, Spin-glass theory for pedestrians, J. Stat. Mech. (2005) P05012 [cond-mat/0505032] [INSPIRE]. · Zbl 1456.82490
[26] B. Swingle, Entanglement Renormalization and Holography, Phys. Rev.D 86 (2012) 065007 [arXiv:0905.1317] [INSPIRE].
[27] B. Swingle, Constructing holographic spacetimes using entanglement renormalization, arXiv:1209.3304 [INSPIRE].
[28] E. Bianchi and R.C. Myers, On the Architecture of Spacetime Geometry, arXiv:1212.5183 [INSPIRE]. · Zbl 1303.83010
[29] R.C. Myers, R. Pourhasan and M. Smolkin, On Spacetime Entanglement, JHEP06 (2013) 013 [arXiv:1304.2030] [INSPIRE]. · Zbl 1342.83197 · doi:10.1007/JHEP06(2013)013
[30] D.V. Fursaev, Entanglement entropy in quantum gravity and the Plateau groblem, Phys. Rev.D 77 (2008) 124002 [arXiv:0711.1221] [INSPIRE].
[31] H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP05 (2011) 036 [arXiv:1102.0440] [INSPIRE]. · Zbl 1296.81073 · doi:10.1007/JHEP05(2011)036
[32] D.V. Fursaev, Proof of the holographic formula for entanglement entropy, JHEP09 (2006) 018 [hep-th/0606184] [INSPIRE]. · doi:10.1088/1126-6708/2006/09/018
[33] M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev.D 82 (2010) 126010 [arXiv:1006.0047] [INSPIRE].
[34] D. Fursaev, Entanglement Renyi Entropies in Conformal Field Theories and Holography, JHEP05 (2012) 080 [arXiv:1201.1702] [INSPIRE]. · Zbl 1348.81389 · doi:10.1007/JHEP05(2012)080
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.