Abstract
The holographic entanglement entropy is studied numerically in (4+1)-dimensional spherically symmetric Gauss-Bonnet AdS black hole spacetime with compact boundary. On the bulk side the black hole spacetime undergoes a van der Waals-like phase transition in the extended phase space, which is reviewed with emphasis on the behavior on the temperature-entropy plane. On the boundary, we calculated the regularized HEE of a disk region of different sizes. We find strong numerical evidence for the failure of equal area law for isobaric curves on the temperature-HEE plane and for the correctness of first law of entanglement entropy, and briefly give an explanation for why the latter may serve as a reason for the former, i.e. the failure of equal area law on the temperature-HEE plane.
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-De Sitter Space, Commun. Math. Phys. 87 (1983) 577.
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [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].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Holography, thermodynamics and fluctuations of charged AdS black holes, Phys. Rev. D 60 (1999) 104026 [hep-th/9904197] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav. 26 (2009) 195011 [arXiv:0904.2765] [INSPIRE].
D. Kubiznak and R.B. Mann, P-V criticality of charged AdS black holes, JHEP 07 (2012) 033 [arXiv:1205.0559] [INSPIRE].
M. Cvetič, G.W. Gibbons, D. Kubiznak and C.N. Pope, Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume, Phys. Rev. D 84 (2011) 024037 [arXiv:1012.2888] [INSPIRE].
M.B.J. Poshteh, B. Mirza and Z. Sherkatghanad, Phase transition, critical behavior and critical exponents of Myers-Perry black holes, Phys. Rev. D 88 (2013) 024005 [arXiv:1306.4516] [INSPIRE].
N. Altamirano, D. Kubiznak and R.B. Mann, Reentrant phase transitions in rotating anti-de Sitter black holes, Phys. Rev. D 88 (2013) 101502 [arXiv:1306.5756] [INSPIRE].
N. Altamirano, D. Kubiznak, R.B. Mann and Z. Sherkatghanad, Thermodynamics of rotating black holes and black rings: phase transitions and thermodynamic volume, Galaxies 2 (2014) 89 [arXiv:1401.2586] [INSPIRE].
S.-W. Wei and Y.-X. Liu, Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes, Phys. Rev. D 87 (2013) 044014 [arXiv:1209.1707] [INSPIRE].
R.-G. Cai, L.-M. Cao, L. Li and R.-Q. Yang, P-V criticality in the extended phase space of Gauss-Bonnet black holes in AdS space, JHEP 09 (2013) 005 [arXiv:1306.6233] [INSPIRE].
D.-C. Zou, Y. Liu and B. Wang, Critical behavior of charged Gauss-Bonnet AdS black holes in the grand canonical ensemble, Phys. Rev. D 90 (2014) 044063 [arXiv:1404.5194] [INSPIRE].
S. Gunasekaran, R.B. Mann and D. Kubiznak, Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization, JHEP 11 (2012) 110 [arXiv:1208.6251] [INSPIRE].
D.-C. Zou, S.-J. Zhang and B. Wang, Critical behavior of Born-Infeld AdS black holes in the extended phase space thermodynamics, Phys. Rev. D 89 (2014) 044002 [arXiv:1311.7299] [INSPIRE].
C.V. Johnson, Thermodynamic Volumes for AdS-Taub-NUT and AdS-Taub-Bolt, Class. Quant. Grav. 31 (2014) 235003 [arXiv:1405.5941] [INSPIRE].
C.V. Johnson, The Extended Thermodynamic Phase Structure of Taub-NUT and Taub-Bolt, Class. Quant. Grav. 31 (2014) 225005 [arXiv:1406.4533] [INSPIRE].
W. Xu, H. Xu and L. Zhao, Gauss-Bonnet coupling constant as a free thermodynamical variable and the associated criticality, Eur. Phys. J. C 74 (2014) 2970 [arXiv:1311.3053] [INSPIRE].
H. Xu, W. Xu and L. Zhao, Extended phase space thermodynamics for third order Lovelock black holes in diverse dimensions, Eur. Phys. J. C 74 (2014) 3074 [arXiv:1405.4143] [INSPIRE].
W. Xu and L. Zhao, Critical phenomena of static charged AdS black holes in conformal gravity, Phys. Lett. B 736 (2014) 214 [arXiv:1405.7665] [INSPIRE].
A.M. Frassino, D. Kubiznak, R.B. Mann and F. Simovic, Multiple Reentrant Phase Transitions and Triple Points in Lovelock Thermodynamics, JHEP 09 (2014) 080 [arXiv:1406.7015] [INSPIRE].
B.P. Dolan, A. Kostouki, D. Kubiznak and R.B. Mann, Isolated critical point from Lovelock gravity, Class. Quant. Grav. 31 (2014) 242001 [arXiv:1407.4783] [INSPIRE].
C.O. Lee, The extended thermodynamic properties of Taub-NUT/Bolt-AdS spaces, Phys. Lett. B 738 (2014) 294 [arXiv:1408.2073] [INSPIRE].
A. Rajagopal, D. Kubizňák and R.B. Mann, Van der Waals black hole, Phys. Lett. B 737 (2014) 277 [arXiv:1408.1105] [INSPIRE].
A.M. Frassino, R.B. Mann and J.R. Mureika, Lower-Dimensional Black Hole Chemistry, Phys. Rev. D 92 (2015) 124069 [arXiv:1509.05481] [INSPIRE].
C.O. Lee, The extended thermodynamic properties of a topological Taub-NUT/Bolt-AdS spaces, Phys. Lett. B 753 (2016) 470 [arXiv:1510.06217] [INSPIRE].
C.V. Johnson, Large-N Phase Transitions, Finite Volume and Entanglement Entropy, JHEP 03 (2014) 047 [arXiv:1306.4955] [INSPIRE].
P.H. Nguyen, An equal area law for holographic entanglement entropy of the AdS-RN black hole, JHEP 12 (2015) 139 [arXiv:1508.01955] [INSPIRE].
E. Caceres, P.H. Nguyen and J.F. Pedraza, Holographic entanglement entropy and the extended phase structure of STU black holes, JHEP 09 (2015) 184 [arXiv:1507.06069] [INSPIRE].
X.-X. Zeng, H. Zhang and L.-F. Li, Phase transition of holographic entanglement entropy in massive gravity, Phys. Lett. B 756 (2016) 170 [arXiv:1511.00383] [INSPIRE].
X.-X. Zeng and L.-F. Li, Van der Waals phase transition in the framework of holography, arXiv:1512.08855 [INSPIRE].
A. Dey, S. Mahapatra and T. Sarkar, Thermodynamics and Entanglement Entropy with Weyl Corrections, Phys. Rev. D 94 (2016) 026006 [arXiv:1512.07117] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
X. Dong, Holographic Entanglement Entropy for General Higher Derivative Gravity, JHEP 01 (2014) 044 [arXiv:1310.5713] [INSPIRE].
R.-X. Miao and W.-z. Guo, Holographic Entanglement Entropy for the Most General Higher Derivative Gravity, JHEP 08 (2015) 031 [arXiv:1411.5579] [INSPIRE].
L.-Y. Hung, R.C. Myers and M. Smolkin, On Holographic Entanglement Entropy and Higher Curvature Gravity, JHEP 04 (2011) 025 [arXiv:1101.5813] [INSPIRE].
R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133] [INSPIRE].
H. Xu and Z.-M. Xu, Maxwell’s equal area law for Lovelock Thermodynamics, arXiv:1510.06557 [INSPIRE].
X. Zeng and W. Liu, Holographic thermalization in Gauss-Bonnet gravity, Phys. Lett. B 726 (2013) 481 [arXiv:1305.4841] [INSPIRE].
D.G. Boulware and S. Deser, String Generated Gravity Models, Phys. Rev. Lett. 55 (1985) 2656 [INSPIRE].
D.L. Wiltshire, Spherically Symmetric Solutions of Einstein-Maxwell Theory With a Gauss-Bonnet Term, Phys. Lett. B 169 (1986) 36 [INSPIRE].
M. Cvetič, S. Nojiri and S.D. Odintsov, Black hole thermodynamics and negative entropy in de Sitter and anti-de Sitter Einstein-Gauss-Bonnet gravity, Nucl. Phys. B 628 (2002) 295 [hep-th/0112045] [INSPIRE].
G. Kofinas and R. Olea, Vacuum energy in Einstein-Gauss-Bonnet AdS gravity, Phys. Rev. D 74 (2006) 084035 [hep-th/0606253] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Mass and Free Energy of Lovelock Black Holes, Class. Quant. Grav. 28 (2011) 195022 [arXiv:1106.2764] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys. A 42 (2009) 504007 [arXiv:0905.2562] [INSPIRE].
L. Amico, R. Fazio, A. Osterloh and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80 (2008) 517 [quant-ph/0703044] [INSPIRE].
V. Vedra, The role of relative entropy in quantum information theory, Rev. Mod. Phys. 74 (2002) 197 [quant-ph/0102094].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
T. Jacobson and R.C. Myers, Black hole entropy and higher curvature interactions, Phys. Rev. Lett. 70 (1993) 3684 [hep-th/9305016] [INSPIRE].
J. Bhattacharya, M. Nozaki, T. Takayanagi and T. Ugajin, Thermodynamical Property of Entanglement Entropy for Excited States, Phys. Rev. Lett. 110 (2013) 091602 [arXiv:1212.1164] [INSPIRE].
W.-z. Guo, S. He and J. Tao, Note on Entanglement Temperature for Low Thermal Excited States in Higher Derivative Gravity, JHEP 08 (2013) 050 [arXiv:1305.2682] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
S. He, L.-F. Li and X.-X. Zeng, Holographic Van der Waals-like phase transition in the Gauss-Bonnet gravity, arXiv:1608.04208 [INSPIRE].
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Sun, Y., Xu, H. & Zhao, L. Thermodynamics and holographic entanglement entropy for spherical black holes in 5D Gauss-Bonnet gravity. J. High Energ. Phys. 2016, 60 (2016). https://doi.org/10.1007/JHEP09(2016)060
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DOI: https://doi.org/10.1007/JHEP09(2016)060