Abstract
We study charged black holes in D dimensional AdS space, in the presence of four derivative Weyl correction. We obtain the black hole solution perturbatively up to first as well as second order in the Weyl coupling, and show that first law of black hole thermodynamics is satisfied in all dimensions. We study its thermodynamic phase transition and then calculate the quasinormal frequencies of the massless scalar field perturbation. We find that, here too, the quasinormal frequencies capture the essence of black hole phase transition. Few subtleties near the second order critical point are discussed.
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References
S.W. Hawking and D.N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [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].
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].
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].
T.K. Dey, S. Mukherji, S. Mukhopadhyay and S. Sarkar, Phase transitions in higher derivative gravity, JHEP 04 (2007) 014 [hep-th/0609038] [INSPIRE].
T.K. Dey, S. Mukherji, S. Mukhopadhyay and S. Sarkar, Phase transitions in higher derivative gravity and gauge theory: R-charged black holes, JHEP 09 (2007) 026 [arXiv:0706.3996] [INSPIRE].
S. Fernando, Thermodynamics of Born-Infeld-anti-de Sitter black holes in the grand canonical ensemble, Phys. Rev. D 74 (2006) 104032 [hep-th/0608040] [INSPIRE].
A. Sahay, T. Sarkar and G. Sengupta, Thermodynamic geometry and phase transitions in Kerr-Newman-AdS black holes, JHEP 04 (2010) 118 [arXiv:1002.2538] [INSPIRE].
A. Sahay, T. Sarkar and G. Sengupta, On the thermodynamic geometry and critical phenomena of AdS black holes, JHEP 07 (2010) 082 [arXiv:1004.1625] [INSPIRE].
R. Banerjee and D. Roychowdhury, Thermodynamics of phase transition in higher dimensional AdS black holes, JHEP 11 (2011) 004 [arXiv:1109.2433] [INSPIRE].
Y.-D. Tsai, X.N. Wu and Y. Yang, Phase structure of Kerr-AdS black hole, Phys. Rev. D 85 (2012) 044005 [arXiv:1104.0502] [INSPIRE].
S.H. Hendi, B.E. Panah and S. Panahiyan, Einstein-Born-Infeld-massive gravity: AdS-black hole solutions and their thermodynamical properties, JHEP 11 (2015) 157 [arXiv:1508.01311] [INSPIRE].
S.H. Hendi, S. Panahiyan and B.E. Panah, Charged black hole solutions in Gauss-Bonnet-massive gravity, JHEP 01 (2016) 129 [arXiv:1507.06563] [INSPIRE].
K.D. Kokkotas and B.G. Schmidt, Quasinormal modes of stars and black holes, Living Rev. Rel. 2 (1999) 2 [gr-qc/9909058] [INSPIRE].
R.A. Konoplya and A. Zhidenko, Quasinormal modes of black holes: from astrophysics to string theory, Rev. Mod. Phys. 83 (2011) 793 [arXiv:1102.4014] [INSPIRE].
J.S.F. Chan and R.B. Mann, Scalar wave falloff in topological black hole backgrounds, Phys. Rev. D 59 (1999) 064025 [INSPIRE].
G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
B. Wang, C.-Y. Lin and E. Abdalla, Quasinormal modes of Reissner-Nordström anti-de Sitter black holes, Phys. Lett. B 481 (2000) 79 [hep-th/0003295] [INSPIRE].
E. Berti and K.D. Kokkotas, Quasinormal modes of Reissner-Nordström-anti-de Sitter black holes: scalar, electromagnetic and gravitational perturbations, Phys. Rev. D 67 (2003) 064020 [gr-qc/0301052] [INSPIRE].
R.A. Konoplya, Decay of charged scalar field around a black hole: quasinormal modes of R-N, R-N-AdS black hole, Phys. Rev. D 66 (2002) 084007 [gr-qc/0207028] [INSPIRE].
B. Wang, C.-Y. Lin and C. Molina, Quasinormal behavior of massless scalar field perturbation in Reissner-Nordström anti-de Sitter spacetimes, Phys. Rev. D 70 (2004) 064025 [hep-th/0407024] [INSPIRE].
E. Abdalla, R.A. Konoplya and C. Molina, Scalar field evolution in Gauss-Bonnet black holes, Phys. Rev. D 72 (2005) 084006 [hep-th/0507100] [INSPIRE].
G. Koutsoumbas, S. Musiri, E. Papantonopoulos and G. Siopsis, Quasi-normal modes of electromagnetic perturbations of four-dimensional topological black holes with scalar hair, JHEP 10 (2006) 006 [hep-th/0606096] [INSPIRE].
C. Martinez, R. Troncoso and J. Zanelli, Exact black hole solution with a minimally coupled scalar field, Phys. Rev. D 70 (2004) 084035 [hep-th/0406111] [INSPIRE].
J. Shen, B. Wang, C.-Y. Lin, R.-G. Cai and R.-K. Su, The phase transition and the quasi-normal modes of black holes, JHEP 07 (2007) 037 [hep-th/0703102] [INSPIRE].
G. Koutsoumbas, E. Papantonopoulos and G. Siopsis, Phase transitions in charged topological-AdS black holes, JHEP 05 (2008) 107 [arXiv:0801.4921] [INSPIRE].
X.-P. Rao, B. Wang and G.-H. Yang, Quasinormal modes and phase transition of black holes, Phys. Lett. B 649 (2007) 472 [arXiv:0712.0645] [INSPIRE].
Y.S. Myung, Phase transition for black holes with scalar hair and topological black holes, Phys. Lett. B 663 (2008) 111 [arXiv:0801.2434] [INSPIRE].
K. Maeda, S. Fujii and J.-I. Koga, The final fate of instability of Reissner-Nordström-anti-de Sitter black holes by charged complex scalar fields, Phys. Rev. D 81 (2010) 124020 [arXiv:1003.2689] [INSPIRE].
X. He, B. Wang, R.-G. Cai and C.-Y. Lin, Signature of the black hole phase transition in quasinormal modes, Phys. Lett. B 688 (2010) 230 [arXiv:1002.2679] [INSPIRE].
Y. Liu, D.-C. Zou and B. Wang, Signature of the Van der Waals like small-large charged AdS black hole phase transition in quasinormal modes, JHEP 09 (2014) 179 [arXiv:1405.2644] [INSPIRE].
J. de Boer, M. Kulaxizi and A. Parnachev, AdS 7 /CFT 6 , Gauss-Bonnet gravity and viscosity bound, JHEP 03 (2010) 087 [arXiv:0910.5347] [INSPIRE].
R. Gregory, S. Kanno and J. Soda, Holographic superconductors with higher curvature corrections, JHEP 10 (2009) 010 [arXiv:0907.3203] [INSPIRE].
A. Dey, S. Mahapatra and T. Sarkar, Generalized holographic superconductors with higher derivative couplings, JHEP 06 (2014) 147 [arXiv:1404.2190] [INSPIRE].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [INSPIRE].
R.C. Myers, S. Sachdev and A. Singh, Holographic quantum critical transport without self-duality, Phys. Rev. D 83 (2011) 066017 [arXiv:1010.0443] [INSPIRE].
A. Ritz and J. Ward, Weyl corrections to holographic conductivity, Phys. Rev. D 79 (2009) 066003 [arXiv:0811.4195] [INSPIRE].
R.C. Myers, S. Sachdev and A. Singh, Holographic quantum critical transport without self-duality, Phys. Rev. D 83 (2011) 066017 [arXiv:1010.0443] [INSPIRE].
A. Dey, S. Mahapatra and T. Sarkar, Holographic thermalization with Weyl corrections, JHEP 01 (2016) 088 [arXiv:1510.00232] [INSPIRE].
A. Dey, S. Mahapatra and T. Sarkar, Thermodynamics and entanglement entropy with Weyl corrections, arXiv:1512.07117 [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
D.M. Hofman, Higher derivative gravity, causality and positivity of energy in a UV complete QFT, Nucl. Phys. B 823 (2009) 174 [arXiv:0907.1625] [INSPIRE].
J.-P. Wu, Y. Cao, X.-M. Kuang and W.-J. Li, The 3 + 1 holographic superconductor with Weyl corrections, Phys. Lett. B 697 (2011) 153 [arXiv:1010.1929] [INSPIRE].
D. Momeni, N. Majd and R. Myrzakulov, p-wave holographic superconductors with Weyl corrections, Europhys. Lett. 97 (2012) 61001 [arXiv:1204.1246] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
O. Mišković, R. Olea and M. Tsoukalas, Renormalized AdS action and critical gravity, JHEP 08 (2014) 108 [arXiv:1404.5993] [INSPIRE].
A. Ashtekar and S. Das, Asymptotically anti-de Sitter space-times: conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [INSPIRE].
N. Okuyama and J.-I. Koga, Asymptotically anti-de Sitter spacetimes and conserved quantities in higher curvature gravitational theories, Phys. Rev. D 71 (2005) 084009 [hep-th/0501044] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038] [INSPIRE].
R.A. Konoplya, On quasinormal modes of small Schwarzschild-anti-de Sitter black hole, Phys. Rev. D 66 (2002) 044009 [hep-th/0205142] [INSPIRE].
V. Cardoso, R. Konoplya and J.P.S. Lemos, Quasinormal frequencies of Schwarzschild black holes in anti-de Sitter space-times: a complete study on the asymptotic behavior, Phys. Rev. D 68 (2003) 044024 [gr-qc/0305037] [INSPIRE].
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Mahapatra, S. Thermodynamics, phase transition and quasinormal modes with Weyl corrections. J. High Energ. Phys. 2016, 142 (2016). https://doi.org/10.1007/JHEP04(2016)142
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DOI: https://doi.org/10.1007/JHEP04(2016)142