Abstract
Setting the cosmological constant to be dynamical, we study the bulk and boundary thermodynamics of charged Anti-de Sitter black holes. We develop mass/energy formulas in terms of thermodynamic state functions for the extended thermodynamics, mixed thermodynamics, and boundary conformal field theory thermodynamics. We employ the residue method to study the topological properties of the phase transitions. Our analysis reveals that the bulk and boundary thermodynamics are topologically equivalent for both criticalities and first-order phase transitions in the canonical ensembles, as well as for the Hawking-Page(-like) phase transitions in the grand canonical ensembles. Additionally, those three kinds of phase transitions are shown to be distinguished by their unique topological charges. Our results exemplify the gravity-gauge duality in terms of topology.
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References
J.M. Bardeen, B. Carter and S.W. Hawking, The four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
S.W. 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, 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].
W. Cong, D. Kubiznak, R.B. Mann and M.R. Visser, Holographic CFT phase transitions and criticality for charged AdS black holes, JHEP 08 (2022) 174 [arXiv:2112.14848] [INSPIRE].
Y.-Z. Cui, W. Xu and B. Zhu, Hawking-Page transition with reentrance and triple point in Gauss-Bonnet gravity, Phys. Rev. D 107 (2023) 044048 [arXiv:2106.13942] [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].
B.P. Dolan, The cosmological constant and the black hole equation of state, Class. Quant. Grav. 28 (2011) 125020 [arXiv:1008.5023] [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].
M. Cvetic, 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].
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. Cvetic 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].
R.A. Hennigar, R.B. Mann and E. Tjoa, Superfluid black holes, Phys. Rev. Lett. 118 (2017) 021301 [arXiv:1609.02564] [INSPIRE].
S.-W. Wei, Y.-X. Liu and R.B. Mann, Repulsive interactions and universal properties of charged anti-de Sitter black hole microstructures, Phys. Rev. Lett. 123 (2019) 071103 [arXiv:1906.10840] [INSPIRE].
M. Tavakoli, J. Wu and R.B. Mann, Multi-critical points in black hole phase transitions, JHEP 12 (2022) 117 [arXiv:2207.03505] [INSPIRE].
J. Wu and R.B. Mann, Multicritical phase transitions in Lovelock AdS black holes, Phys. Rev. D 107 (2023) 084035 [arXiv:2212.08087] [INSPIRE].
A.M. Frassino, J.F. Pedraza, A. Svesko and M.R. Visser, Higher-dimensional origin of extended black hole thermodynamics, Phys. Rev. Lett. 130 (2023) 161501 [arXiv:2212.14055] [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].
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].
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].
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].
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].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
A. Karch and B. Robinson, Holographic black hole chemistry, JHEP 12 (2015) 073 [arXiv:1510.02472] [INSPIRE].
A. Gadde, M. Jagadale, S. Jain and T. Sharma, Bound on the central charge of CFTs in large dimension, JHEP 05 (2023) 146 [arXiv:2301.04980] [INSPIRE].
C.V. Johnson, Holographic heat engines, Class. Quant. Grav. 31 (2014) 205002 [arXiv:1404.5982] [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].
M.B. Ahmed et al., Holographic dual of extended black hole thermodynamics, Phys. Rev. Lett. 130 (2023) 181401 [arXiv:2302.08163] [INSPIRE].
I. Savonije and E.P. Verlinde, CFT and entropy on the brane, Phys. Lett. B 507 (2001) 305 [hep-th/0102042] [INSPIRE].
G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
Y.-S. Duan and M.-L. Ge, SU(2) gauge theory and electrodynamics with N magnetic monopoles, Sci. Sin. 9 (1979) 1072 [INSPIRE].
S.-W. Wei and Y.-X. Liu, Topology of black hole thermodynamics, Phys. Rev. D 105 (2022) 104003 [arXiv:2112.01706] [INSPIRE].
P.K. Yerra, C. Bhamidipati and S. Mukherji, Topology of critical points and Hawking-Page transition, Phys. Rev. D 106 (2022) 064059 [arXiv:2208.06388] [INSPIRE].
N.-C. Bai, L. Li and J. Tao, Topology of black hole thermodynamics in Lovelock gravity, Phys. Rev. D 107 (2023) 064015 [arXiv:2208.10177] [INSPIRE].
C. Fang, J. Jiang and M. Zhang, Revisiting thermodynamic topologies of black holes, JHEP 01 (2023) 102 [arXiv:2211.15534] [INSPIRE].
S.-W. Wei, Y.-X. Liu and R.B. Mann, Black hole solutions as topological thermodynamic defects, Phys. Rev. Lett. 129 (2022) 191101 [arXiv:2208.01932] [INSPIRE].
P.V.P. Cunha and C.A.R. Herdeiro, Stationary black holes and light rings, Phys. Rev. Lett. 124 (2020) 181101 [arXiv:2003.06445] [INSPIRE].
C.S. Peca and J.P.S. Lemos, Thermodynamics of Reissner-Nordström anti-de Sitter black holes in the grand canonical ensemble, Phys. Rev. D 59 (1999) 124007 [gr-qc/9805004] [INSPIRE].
S.-W. Wei, Y.-X. Liu and R.B. Mann, Novel dual relation and constant in Hawking-Page phase transitions, Phys. Rev. D 102 (2020) 104011 [arXiv:2006.11503] [INSPIRE].
X.N. Wu, Multicritical phenomena of Reissner-Nordström anti-de Sitter black holes, Phys. Rev. D 62 (2000) 124023 [INSPIRE].
Z.-Y. Fan, Topological interpretation for phase transitions of black holes, Phys. Rev. D 107 (2023) 044026 [arXiv:2211.12957] [INSPIRE].
R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133] [INSPIRE].
T.-F. Gong, J. Jiang and M. Zhang, Holographic thermodynamics of rotating black holes, arXiv:2305.00267 [INSPIRE].
M.B. Ahmed et al., Holographic CFT phase transitions and criticality for rotating AdS black holes, arXiv:2305.03161 [INSPIRE].
S. Dutta and G.S. Punia, String theory corrections to holographic black hole chemistry, Phys. Rev. D 106 (2022) 026003 [arXiv:2205.15593] [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].
A. Gnecchi et al., Rotating black holes in 4d gauged supergravity, JHEP 01 (2014) 127 [arXiv:1311.1795] [INSPIRE].
G.W. Gibbons, M.J. Perry and C.N. Pope, Bulk/boundary thermodynamic equivalence, and the Bekenstein and cosmic-censorship bounds for rotating charged AdS black holes, Phys. Rev. D 72 (2005) 084028 [hep-th/0506233] [INSPIRE].
M. Cvetic, G.W. Gibbons, C.N. Pope and B.F. Whiting, Supergravity black holes, Love numbers, and harmonic coordinates, Phys. Rev. D 105 (2022) 084035 [arXiv:2109.03254] [INSPIRE].
N. Ezroura, F. Larsen, Z. Liu and Y. Zeng, The phase diagram of BPS black holes in AdS5, JHEP 09 (2022) 033 [arXiv:2108.11542] [INSPIRE].
S.-W. Wei and Y.-X. Liu, Clapeyron equations and fitting formula of the coexistence curve in the extended phase space of charged AdS black holes, Phys. Rev. D 91 (2015) 044018 [arXiv:1411.5749] [INSPIRE].
Acknowledgments
We would like to acknowledge the referee for insightful comments on the paper which have been incorporated in the final version. MZ is supported by the National Natural Science Foundation of China with Grant No. 12005080. JJ is supported by the National Natural Science Foundation of China with Grant No. 210510101, the Guangdong Basic and Applied Research Foundation with Grant No. 217200003, and the Talents Introduction Foundation of Beijing Normal University with Grant No. 310432102.
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Zhang, M., Jiang, J. Bulk-boundary thermodynamic equivalence: a topology viewpoint. J. High Energ. Phys. 2023, 115 (2023). https://doi.org/10.1007/JHEP06(2023)115
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DOI: https://doi.org/10.1007/JHEP06(2023)115