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Thermodynamics of charged, rotating, and accelerating black holes

  • Andrés Anabalón
  • Finnian Gray
  • Ruth Gregory
  • David KubizňákEmail author
  • Robert B. Mann
Open Access
Regular Article - Theoretical Physics
  • 29 Downloads

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.

Keywords

Black Holes AdS-CFT Correspondence 

Notes

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.

References

  1. [1]
    J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  2. [2]
    J.D. Bekenstein, Generalized second law of thermodynamics in black hole physics, Phys. Rev. D 9 (1974) 3292 [INSPIRE].ADSGoogle Scholar
  3. [3]
    S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
  4. [4]
    D. Kubizňák, R.B. Mann and M. Teo, Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav. 34 (2017) 063001 [arXiv:1608.06147] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    W. Kinnersley and M. Walker, Uniformly accelerating charged mass in general relativity, Phys. Rev. D 2 (1970) 1359 [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  6. [6]
    J.F. Plebański and M. Demianski, Rotating, charged and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    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].ADSMathSciNetzbMATHGoogle Scholar
  8. [8]
    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].
  9. [9]
    R. Gregory and M. Hindmarsh, Smooth metrics for snapping strings, Phys. Rev. D 52 (1995) 5598 [gr-qc/9506054] [INSPIRE].
  10. [10]
    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].ADSMathSciNetGoogle Scholar
  11. [11]
    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].
  12. [12]
    R. Emparan, Pair creation of black holes joined by cosmic strings, Phys. Rev. Lett. 75 (1995) 3386 [gr-qc/9506025] [INSPIRE].
  13. [13]
    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].
  14. [14]
    R.B. Mann and S.F. Ross, Cosmological production of charged black hole pairs, Phys. Rev. D 52 (1995) 2254 [gr-qc/9504015] [INSPIRE].
  15. [15]
    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].
  16. [16]
    M. Appels, R. Gregory and D. Kubizňák, Thermodynamics of Accelerating Black Holes, Phys. Rev. Lett. 117 (2016) 131303 [arXiv:1604.08812] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    M. Appels, R. Gregory and D. Kubizňák, Black Hole Thermodynamics with Conical Defects, JHEP 05 (2017) 116 [arXiv:1702.00490] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    R. Gregory, Accelerating Black Holes, J. Phys. Conf. Ser. 942 (2017) 012002 [arXiv:1712.04992] [INSPIRE].CrossRefGoogle Scholar
  19. [19]
    M. Astorino, CFT Duals for Accelerating Black Holes, Phys. Lett. B 760 (2016) 393 [arXiv:1605.06131] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  20. [20]
    M. Astorino, Thermodynamics of Regular Accelerating Black Holes, Phys. Rev. D 95 (2017) 064007 [arXiv:1612.04387] [INSPIRE].ADSMathSciNetGoogle Scholar
  21. [21]
    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].ADSGoogle Scholar
  22. [22]
    J. Podolsky, Accelerating black holes in anti-de Sitter universe, Czech. J. Phys. 52 (2002) 1 [gr-qc/0202033] [INSPIRE].
  23. [23]
    L. Smarr, Mass formula for Kerr black holes, Phys. Rev. Lett. 30 (1973) 71 [Erratum ibid. 30 (1973) 521] [INSPIRE].
  24. [24]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    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].ADSMathSciNetGoogle Scholar
  27. [27]
    S.W. Hawking and S.F. Ross, Duality between electric and magnetic black holes, Phys. Rev. D 52 (1995) 5865 [hep-th/9504019] [INSPIRE].ADSMathSciNetGoogle Scholar
  28. [28]
    A. Ashtekar and S. Das, Asymptotically Anti-de Sitter space-times: Conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  29. [29]
    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].ADSCrossRefzbMATHGoogle Scholar
  30. [30]
    I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, JHEP 08 (2005) 004 [hep-th/0505190] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    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].ADSMathSciNetGoogle Scholar
  33. [33]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    J.B. Griffiths, P. Krtouš and J. Podolsky, Interpreting the C-metric, Class. Quant. Grav. 23 (2006) 6745 [gr-qc/0609056] [INSPIRE].
  35. [35]
    E. Bianchi and A. Satz, Mechanical laws of the Rindler horizon, Phys. Rev. D 87 (2013) 124031 [arXiv:1305.4986] [INSPIRE].ADSGoogle Scholar
  36. [36]
    T. De Lorenzo and A. Perez, Light Cone Thermodynamics, Phys. Rev. D 97 (2018) 044052 [arXiv:1707.00479] [INSPIRE].ADSMathSciNetGoogle Scholar
  37. [37]
    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].
  38. [38]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    D.G. Boulware, Radiation From a Uniformly Accelerated Charge, Annals Phys. 124 (1980) 169 [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    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].ADSGoogle Scholar
  41. [41]
    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].ADSGoogle Scholar
  42. [42]
    G. Bernardi de Freitas and H.S. Reall, Algebraically special solutions in AdS/CFT, JHEP 06 (2014) 148 [arXiv:1403.3537] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    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].ADSCrossRefzbMATHGoogle Scholar
  44. [44]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    G.T. Horowitz, J.E. Santos and C. Toldo, Deforming black holes in AdS, JHEP 11 (2018) 146 [arXiv:1809.04081] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Andrés Anabalón
    • 1
  • Finnian Gray
    • 2
    • 3
  • Ruth Gregory
    • 4
    • 2
  • David Kubizňák
    • 2
    • 3
    Email author
  • Robert B. Mann
    • 3
    • 2
  1. 1.Departamento de Ciencias, Facultad de Artes LiberalesUniversidad Adolfo IbáñezViña del MarChile
  2. 2.Perimeter InstituteWaterlooCanada
  3. 3.Department of Physics and AstronomyUniversity of WaterlooWaterlooCanada
  4. 4.Centre for Particle TheoryDurham UniversityDurhamU.K.

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