Abstract
Thermodynamic quantities associated with black holes in Anti-de Sitter space obey an interesting identity when the cosmological constant is included as one of the dynamical variables, the generalized Smarr relation. We show that this relation can easily be understood from the point of view of the dual holographic field theory. It amounts to the simple statement that the extensive thermodynamic quantities of a large N gauge theory only depend on the number of colors, N , via an overall factor of N 2.
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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].
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].
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].
M.M. Caldarelli, G. Cognola and D. Klemm, Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories, Class. Quant. Grav. 17 (2000) 399 [hep-th/9908022] [INSPIRE].
J.D.E. Creighton and R.B. Mann, Quasilocal thermodynamics of dilaton gravity coupled to gauge fields, Phys. Rev. D 52 (1995) 4569 [gr-qc/9505007] [INSPIRE].
G.W. Gibbons, M.J. Perry and C.N. Pope, The First law of thermodynamics for Kerr-anti-de Sitter black holes, Class. Quant. Grav. 22 (2005) 1503 [hep-th/0408217] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Smarr Formula and an Extended First Law for Lovelock Gravity, Class. Quant. Grav. 27 (2010) 235014 [arXiv:1005.5053] [INSPIRE].
B.P. Dolan, Where is the PdV term in the fist law of black hole thermodynamics?, arXiv:1209.1272 [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].
D. Kubiznak and R.B. Mann, Black hole chemistry, Can. J. Phys. 93 (2015) 999 [arXiv:1404.2126] [INSPIRE].
L. Smarr, Mass formula for Kerr black holes, Phys. Rev. Lett. 30 (1973) 71 [Erratum ibid. 30 (1973) 521] [INSPIRE].
R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys. 172 (1986) 304 [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Chemical Potential in the First Law for Holographic Entanglement Entropy, JHEP 11 (2014) 120 [arXiv:1409.3521] [INSPIRE].
C.V. Johnson, Holographic Heat Engines, Class. Quant. Grav. 31 (2014) 205002 [arXiv:1404.5982] [INSPIRE].
J.-L. Zhang, R.-G. Cai and H. Yu, Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS 5 × S 5 spacetime, JHEP 02 (2015) 143 [arXiv:1409.5305] [INSPIRE].
J.-L. Zhang, R.-G. Cai and H. Yu, Phase transition and thermodynamical geometry of Reissner-Nordström-AdS black holes in extended phase space, Phys. Rev. D 91 (2015) 044028 [arXiv:1502.01428] [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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [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].
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].
A. Karch, M. Kulaxizi and A. Parnachev, Notes on Properties of Holographic Matter, JHEP 11 (2009) 017 [arXiv:0908.3493] [INSPIRE].
D. Kubiznak and R.B. Mann, P-V criticality of charged AdS black holes, JHEP 07 (2012) 033 [arXiv:1205.0559] [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].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
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Karch, A., Robinson, B. Holographic black hole chemistry. J. High Energ. Phys. 2015, 1–15 (2015). https://doi.org/10.1007/JHEP12(2015)073
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DOI: https://doi.org/10.1007/JHEP12(2015)073