Abstract
We study the holographic dual of the extended thermodynamics of spherically symmetric, charged AdS black holes in the context of the AdS/CFT correspondence. The gravitational thermodynamics of AdS black holes can be extended by allowing for variations of the cosmological constant and Newton’s constant. In the dual CFT this corresponds to including the central charge C and its chemical potential μ as a new pair of conjugate thermodynamic variables, in addition to the standard pairs: temperature vs. entropy (T, S), electric potential vs. charge (\( \overset{\sim }{\Phi},\overset{\sim }{Q} \)) and field theory pressure vs. volume (p, \( \mathcal{V} \)). For the (grand) canonical ensembles at fixed (\( \overset{\sim }{Q},\mathcal{V},C \)), (\( \overset{\sim }{\Phi},\mathcal{V},C \)) and (\( \overset{\sim }{Q},\mathcal{V},\mu \)), based on the holographic dictionary, we argue the CFT description of charged AdS black holes contains either critical phenomena or interesting phase behaviour. In the fixed (\( \overset{\sim }{Q},\mathcal{V},\mu \)) we find a new zeroth-order phase transition between a high- and low-entropy phase at some μ-dependent temperature. Finally, we point out there is no critical behaviour in the fixed p ensembles, i.e. there is no p − \( \mathcal{V} \) criticality, and hence the CFT state dual to a classical charged black hole cannot be a Van der Waals fluid. Whether or not this phase structure is supported by CFT computations remains an interesting open question.
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References
S.W. Hawking, Particle creation by black holes, Commun. math. Phys. 43 (1975) 199.
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
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].
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].
M. Cvetič and S.S. Gubser, Phases of R charged black holes, spinning branes and strongly coupled gauge theories, JHEP 04 (1999) 024 [hep-th/9902195] [INSPIRE].
D. Kubiznak and R.B. Mann, P-V criticality of charged AdS black holes, JHEP 07 (2012) 033 [arXiv:1205.0559] [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].
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].
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].
N. Altamirano, D. Kubizňák, R.B. Mann and Z. Sherkatghanad, Kerr-AdS analogue of triple point and solid/liquid/gas phase transition, Class. Quant. Grav. 31 (2014) 042001 [arXiv:1308.2672] [INSPIRE].
S.-W. Wei and Y.-X. Liu, Triple points and phase diagrams in the extended phase space of charged Gauss-Bonnet black holes in AdS space, Phys. Rev. D 90 (2014) 044057 [arXiv:1402.2837] [INSPIRE].
R.A. Hennigar, R.B. Mann and E. Tjoa, Superfluid black holes, Phys. Rev. Lett. 118 (2017) 021301 [arXiv:1609.02564] [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. 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].
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].
A. Karch and B. Robinson, Holographic black hole chemistry, JHEP 12 (2015) 073 [arXiv:1510.02472] [INSPIRE].
D. Sarkar and M. Visser, The first law of differential entropy and holographic complexity, JHEP 11 (2020) 004 [arXiv:2008.12673] [INSPIRE].
M.R. Visser, Holographic thermodynamics requires a chemical potential for color, Phys. Rev. D 105 (2022) 106014 [arXiv:2101.04145] [INSPIRE].
W. Cong, D. Kubiznak and R.B. Mann, Thermodynamics of AdS Black Holes: Critical Behavior of the Central Charge, Phys. Rev. Lett. 127 (2021) 091301 [arXiv:2105.02223] [INSPIRE].
T. Jacobson and M. Visser, Gravitational thermodynamics of causal diamonds in (A)dS, SciPost Phys. 7 (2019) 079 [arXiv:1812.01596] [INSPIRE].
B.P. Dolan, Pressure and volume in the first law of black hole thermodynamics, Class. Quant. Grav. 28 (2011) 235017 [arXiv:1106.6260] [INSPIRE].
B.P. Dolan, The cosmological constant and the black hole equation of state, Class. Quant. Grav. 28 (2011) 125020 [arXiv:1008.5023] [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].
C.V. Johnson, Holographic heat engines, Class. Quant. Grav. 31 (2014) 205002 [arXiv:1404.5982] [INSPIRE].
B.P. Dolan, Bose condensation and branes, JHEP 10 (2014) 179 [arXiv:1406.7267] [INSPIRE].
J.-L. Zhang, R.-G. Cai and H. Yu, Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS5 × S5 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].
B.P. Dolan, Pressure and compressibility of conformal field theories from the AdS/CFT correspondence, Entropy 18 (2016) 169 [arXiv:1603.06279] [INSPIRE].
J.F. Pedraza, A. Svesko, W. Sybesma and M.R. Visser, Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity, JHEP 12 (2021) 134 [arXiv:2107.10358] [INSPIRE].
J.P. Gauntlett, R.C. Myers and P.K. Townsend, Black holes of D = 5 supergravity, Class. Quant. Grav. 16 (1999) 1 [hep-th/9810204] [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].
D. Kubiznak, R.B. Mann and M. Teo, Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav. 34 (2017) 063001 [arXiv:1608.06147] [INSPIRE].
E. Caceres, P.H. Nguyen and J.F. Pedraza, Holographic entanglement chemistry, Phys. Rev. D 95 (2017) 106015 [arXiv:1605.00595] [INSPIRE].
F. Rosso and A. Svesko, Novel aspects of the extended first law of entanglement, JHEP 08 (2020) 008 [arXiv:2003.10462] [INSPIRE].
M. Sinamuli and R.B. Mann, Higher order corrections to holographic black hole chemistry, Phys. Rev. D 96 (2017) 086008 [arXiv:1706.04259] [INSPIRE].
J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82 (2010) 046006 [arXiv:1006.1263] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
L.-Y. Hung, R.C. Myers, M. Smolkin and A. Yale, Holographic calculations of Renyi entropy, JHEP 12 (2011) 047 [arXiv:1110.1084] [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].
I. Savonije and E.P. Verlinde, CFT and entropy on the brane, Phys. Lett. B 507 (2001) 305 [hep-th/0102042] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
M. Henneaux and C. Teitelboim, Asymptotically Anti-de Sitter spaces, Commun. Math. Phys. 98 (1985) 391 [INSPIRE].
A. Ashtekar and A. Magnon, Asymptotically Anti-de Sitter space-times, Class. Quant. Grav. 1 (1984) L39 [INSPIRE].
A. Ashtekar and S. Das, Asymptotically Anti-de Sitter space-times: conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [INSPIRE].
S. Hollands, A. Ishibashi and D. Marolf, Comparison between various notions of conserved charges in asymptotically AdS-spacetimes, Class. Quant. Grav. 22 (2005) 2881 [hep-th/0503045] [INSPIRE].
J. Tarrio and S. Vandoren, Black holes and black branes in Lifshitz spacetimes, JHEP 09 (2011) 017 [arXiv:1105.6335] [INSPIRE].
J.F. Pedraza, W. Sybesma and M.R. Visser, Hyperscaling violating black holes with spherical and hyperbolic horizons, Class. Quant. Grav. 36 (2019) 054002 [arXiv:1807.09770] [INSPIRE].
C. Niu, Y. Tian and X.-N. Wu, Critical phenomena and thermodynamic geometry of RN-AdS black holes, Phys. Rev. D 85 (2012) 024017 [arXiv:1104.3066] [INSPIRE].
V. P. Maslov, Zeroth-order phase transitions, Math. Notes 76 (2004) 697.
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].
J. Couch, W. Fischler and P.H. Nguyen, Noether charge, black hole volume, and complexity, JHEP 03 (2017) 119 [arXiv:1610.02038] [INSPIRE].
C.V. Johnson, V.L. Martin and A. Svesko, Microscopic description of thermodynamic volume in extended black hole thermodynamics, Phys. Rev. D 101 (2020) 086006 [arXiv:1911.05286] [INSPIRE].
M. Rafiee, S.A.H. Mansoori, S.-W. Wei and R.B. Mann, Universal criticality of thermodynamic geometry for boundary conformal field theories in gauge/gravity duality, Phys. Rev. D 105 (2022) 024058 [arXiv:2107.08883] [INSPIRE].
G. Zeyuan and L. Zhao, Restricted phase space thermodynamics for AdS black holes via holography, Class. Quant. Grav. 39 (2022) 075019 [arXiv:2112.02386] [INSPIRE].
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Cong, W., Kubizňák, D., Mann, R.B. et al. Holographic CFT phase transitions and criticality for charged AdS black holes. J. High Energ. Phys. 2022, 174 (2022). https://doi.org/10.1007/JHEP08(2022)174
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DOI: https://doi.org/10.1007/JHEP08(2022)174