Abstract
We show how to obtain a consistent thermodynamic description of accelerating asymptotically AdS black holes, extending our previous results by including charge and rotation. We find that the key ingredient of consistent thermodynamics is to ensure that the system is not over-constrained by including the possibility of varying the ‘string’ tensions that are responsible for the acceleration of the black hole, yielding a first law of full cohomogeneity. The first law assumes the standard form, with the entropy given by one quarter of the horizon area and other quantities identified by standard methods. In particular we compute the mass in two independent ways: through a Euclidean action calculation and by the method of conformal completion. The ambiguity in the choice of the normalization of the timelike Killing vector can be fixed by explicit coordinate transformation (in the case of rotation) to the standard AdS form or by holographic methods (in the case of charge). This resolves a long-standing problem of formulating the thermodynamics of accelerating black holes, opening the way to detailed studies of their phase behaviour.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
J.D. Bekenstein, Generalized second law of thermodynamics in black hole physics, Phys. Rev. D 9 (1974) 3292 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
D. Kubizňák, R.B. Mann and M. Teo, Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav. 34 (2017) 063001 [arXiv:1608.06147] [INSPIRE].
W. Kinnersley and M. Walker, Uniformly accelerating charged mass in general relativity, Phys. Rev. D 2 (1970) 1359 [INSPIRE].
J.F. Plebański and M. Demianski, Rotating, charged and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [INSPIRE].
O.J.C. Dias and J.P.S. Lemos, Pair of accelerated black holes in anti-de Sitter background: AdS C metric, Phys. Rev. D 67 (2003) 064001 [hep-th/0210065] [INSPIRE].
J.B. Griffiths and J. Podolsky, A New look at the Plebański-Demianski family of solutions, Int. J. Mod. Phys. D 15 (2006) 335 [gr-qc/0511091] [INSPIRE].
R. Gregory and M. Hindmarsh, Smooth metrics for snapping strings, Phys. Rev. D 52 (1995) 5598 [gr-qc/9506054] [INSPIRE].
F. Dowker, J.P. Gauntlett, D.A. Kastor and J.H. Traschen, Pair creation of dilaton black holes, Phys. Rev. D 49 (1994) 2909 [hep-th/9309075] [INSPIRE].
S.W. Hawking, G.T. Horowitz and S.F. Ross, Entropy, Area and black hole pairs, Phys. Rev. D 51 (1995) 4302 [gr-qc/9409013] [INSPIRE].
R. Emparan, Pair creation of black holes joined by cosmic strings, Phys. Rev. Lett. 75 (1995) 3386 [gr-qc/9506025] [INSPIRE].
D.M. Eardley, G.T. Horowitz, D.A. Kastor and J.H. Traschen, Breaking cosmic strings without monopoles, Phys. Rev. Lett. 75 (1995) 3390 [gr-qc/9506041] [INSPIRE].
R.B. Mann and S.F. Ross, Cosmological production of charged black hole pairs, Phys. Rev. D 52 (1995) 2254 [gr-qc/9504015] [INSPIRE].
I.S. Booth and R.B. Mann, Complex instantons and charged rotating black hole pair creation, Phys. Rev. Lett. 81 (1998) 5052 [gr-qc/9806015] [INSPIRE].
M. Appels, R. Gregory and D. Kubizňák, Thermodynamics of Accelerating Black Holes, Phys. Rev. Lett. 117 (2016) 131303 [arXiv:1604.08812] [INSPIRE].
M. Appels, R. Gregory and D. Kubizňák, Black Hole Thermodynamics with Conical Defects, JHEP 05 (2017) 116 [arXiv:1702.00490] [INSPIRE].
R. Gregory, Accelerating Black Holes, J. Phys. Conf. Ser. 942 (2017) 012002 [arXiv:1712.04992] [INSPIRE].
M. Astorino, CFT Duals for Accelerating Black Holes, Phys. Lett. B 760 (2016) 393 [arXiv:1605.06131] [INSPIRE].
M. Astorino, Thermodynamics of Regular Accelerating Black Holes, Phys. Rev. D 95 (2017) 064007 [arXiv:1612.04387] [INSPIRE].
A. Anabalón, M. Appels, R. Gregory, D. Kubizňák, R.B. Mann and A. Ovgün, Holographic Thermodynamics of Accelerating Black Holes, Phys. Rev. D 98 (2018) 104038 [arXiv:1805.02687] [INSPIRE].
J. Podolsky, Accelerating black holes in anti-de Sitter universe, Czech. J. Phys. 52 (2002) 1 [gr-qc/0202033] [INSPIRE].
L. Smarr, Mass formula for Kerr black holes, Phys. Rev. Lett. 30 (1973) 71 [Erratum ibid. 30 (1973) 521] [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].
V.E. Hubeny, D. Marolf and M. Rangamani, Black funnels and droplets from the AdS C-metrics, Class. Quant. Grav. 27 (2010) 025001 [arXiv:0909.0005] [INSPIRE].
C. Herdeiro, B. Kleihaus, J. Kunz and E. Radu, On the Bekenstein-Hawking area law for black objects with conical singularities, Phys. Rev. D 81 (2010) 064013 [arXiv:0912.3386] [INSPIRE].
S.W. Hawking and S.F. Ross, Duality between electric and magnetic black holes, Phys. Rev. D 52 (1995) 5865 [hep-th/9504019] [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. Das and R.B. Mann, Conserved quantities in Kerr-anti-de Sitter space-times in various dimensions, JHEP 08 (2000) 033 [hep-th/0008028] [INSPIRE].
I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, JHEP 08 (2005) 004 [hep-th/0505190] [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].
M. Astorino, G. Compère, R. Oliveri and N. Vandevoorde, Mass of Kerr-Newman black holes in an external magnetic field, Phys. Rev. D 94 (2016) 024019 [arXiv:1602.08110] [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.B. Griffiths, P. Krtouš and J. Podolsky, Interpreting the C-metric, Class. Quant. Grav. 23 (2006) 6745 [gr-qc/0609056] [INSPIRE].
E. Bianchi and A. Satz, Mechanical laws of the Rindler horizon, Phys. Rev. D 87 (2013) 124031 [arXiv:1305.4986] [INSPIRE].
T. De Lorenzo and A. Perez, Light Cone Thermodynamics, Phys. Rev. D 97 (2018) 044052 [arXiv:1707.00479] [INSPIRE].
J. Podolsky, M. Ortaggio and P. Krtouš, Radiation from accelerated black holes in an anti-de Sitter universe, Phys. Rev. D 68 (2003) 124004 [gr-qc/0307108] [INSPIRE].
J. Podolsky and H. Kadlecova, Radiation generated by accelerating and rotating charged black holes in (anti-)de Sitter space, Class. Quant. Grav. 26 (2009) 105007 [arXiv:0903.3577] [INSPIRE].
D.G. Boulware, Radiation From a Uniformly Accelerated Charge, Annals Phys. 124 (1980) 169 [INSPIRE].
B.P. Dolan, D. Kastor, D. Kubizňák, R.B. Mann and J. Traschen, Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes, Phys. Rev. D 87 (2013) 104017 [arXiv:1301.5926] [INSPIRE].
M. Cvetič, G.W. Gibbons, D. Kubizňák 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].
G. Bernardi de Freitas and H.S. Reall, Algebraically special solutions in AdS/CFT, JHEP 06 (2014) 148 [arXiv:1403.3537] [INSPIRE].
J. Zhang, Y. Li and H. Yu, Thermodynamics of charged accelerating AdS black holes and holographic heat engines, JHEP 02 (2019) 144 [arXiv:1808.10299] [INSPIRE].
K. Dutta, S. Ray and J. Traschen, Boost mass and the mechanics of accelerated black holes, Class. Quant. Grav. 23 (2006) 335 [hep-th/0508041] [INSPIRE].
G.T. Horowitz, J.E. Santos and C. Toldo, Deforming black holes in AdS, JHEP 11 (2018) 146 [arXiv:1809.04081] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1811.04936
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Anabalón, A., Gray, F., Gregory, R. et al. Thermodynamics of charged, rotating, and accelerating black holes. J. High Energ. Phys. 2019, 96 (2019). https://doi.org/10.1007/JHEP04(2019)096
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2019)096