Abstract
We study local temperature fluctuations in a 2+1 dimensional CFT on the sphere, dual to a black hole in asymptotically AdS spacetime. The fluctuation spectrum is governed by the lowest-lying hydrodynamic modes of the system whose frequency and damping rate determine whether temperature fluctuations are thermal or quantum. We calculate numerically the corresponding quasinormal frequencies and match the result with the hydrodynamics of the dual CFT at high temperature. As a by-product of our analysis we determine the appropriate boundary conditions for calculating low-lying quasinormal modes for a four-dimensional Reissner-Nordström black hole in global AdS.
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References
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
S. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [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. 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, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
E.J. Brynjolfsson and L. Thorlacius, Taking the temperature of a black hole, JHEP 09 (2008) 066 [arXiv:0805.1876] [INSPIRE].
A. Balatsky and J.-X. Zhu, Quantum Nyquist temperature fluctuations, Physica E 18 (2003) 341 [cond-mat/0202521].
E. Lifshitz and L. Landau, Statistical physics, Course of Theoretical Physics volume 5, Butterworth-Heinemann (1980).
H. Nyquist, Thermal agitation of electric charge in conductors, Phys. Rev. 32 (1928) 110 [INSPIRE].
C.S. Peca and P.S. Lemos, Jose, Thermodynamics of Reissner-Nordstrom Anti-de Sitter black holes in the grand canonical ensemble, Phys. Rev. D 59 (1999) 124007 [gr-qc/9805004] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics. 2. Sound waves, JHEP 12 (2002) 054 [hep-th/0210220] [INSPIRE].
J.J. Friess, S.S. Gubser, G. Michalogiorgakis and S.S. Pufu, Expanding plasmas and quasinormal modes of anti-de Sitter black holes, JHEP 04 (2007) 080 [hep-th/0611005] [INSPIRE].
G. Michalogiorgakis and S.S. Pufu, Low-lying gravitational modes in the scalar sector of the global AdS 4 black hole, JHEP 02 (2007) 023 [hep-th/0612065] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].
P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
P. Kovtun and A. Ritz, Universal conductivity and central charges, Phys. Rev. D 78 (2008) 066009 [arXiv:0806.0110] [INSPIRE].
J.S.F. Chan and R.B. Mann, Scalar wave falloff in asymptotically Anti-de Sitter backgrounds, Phys. Rev. D 55 (1997) 7546 [gr-qc/9612026] [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].
V. Cardoso and J.P.S. Lemos, Quasinormal modes of Schwarzschild anti-de Sitter black holes: Electromagnetic and gravitational perturbations, Phys. Rev. D 64 (2001) 084017 [gr-qc/0105103] [INSPIRE].
I.G. Moss and J.P. Norman, Gravitational quasinormal modes for Anti-de Sitter black holes, Class. Quant. Grav. 19 (2002) 2323 [gr-qc/0201016] [INSPIRE].
E. Berti and K.D. Kokkotas, Quasinormal modes of Reissner-Nordstrom-Anti-de Sitter black holes: scalar, electromagnetic and gravitational perturbations, Phys. Rev. D 67 (2003) 064020 [gr-qc/0301052] [INSPIRE].
E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [INSPIRE].
F. Mellor and I. Moss, Stability of black holes in de Sitter space, Phys. Rev. D 41 (1990) 403 [INSPIRE].
G. Siopsis, Low frequency quasi-normal modes of AdS black holes, JHEP 05 (2007) 042 [hep-th/0702079] [INSPIRE].
V. Cardoso, O.J.C. Dias, G.S. Hartnett, L. Lehner and J.E. Santos, Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS, JHEP 04 (2014) 183 [arXiv:1312.5323] [INSPIRE].
O.J.C. Dias and J.E. Santos, Boundary conditions for Kerr-AdS perturbations, JHEP 10 (2013) 156 [arXiv:1302.1580] [INSPIRE].
R.A. Konoplya and A. Zhidenko, Stability of higher dimensional Reissner-Nordstrom-Anti-de Sitter black holes, Phys. Rev. D 78 (2008) 104017 [arXiv:0809.2048] [INSPIRE].
S. Chandrasekhar, The mathematical theory of black holes, Oxford University Press, Oxford U.K. (1998).
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].
J. Sonner and A.G. Green, Hawking radiation and non-equilibrium quantum critical current noise, Phys. Rev. Lett. 109 (2012) 091601 [arXiv:1203.4908] [INSPIRE].
A. Kundu and S. Kundu, Steady-state physics, effective temperature dynamics in holography, arXiv:1307.6607 [INSPIRE].
S. Nakamura and H. Ooguri, Out of equilibrium temperature from holography, Phys. Rev. D 88 (2013) 126003 [arXiv:1309.4089] [INSPIRE].
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Balatsky, A., Gudnason, S.B., Kedem, Y. et al. Classical and quantum temperature fluctuations via holography. J. High Energ. Phys. 2015, 11 (2015). https://doi.org/10.1007/JHEP01(2015)011
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DOI: https://doi.org/10.1007/JHEP01(2015)011