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On the critical phenomena and thermodynamics of charged topological dilaton AdS black holes

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Abstract

In this paper, we study the phase structure and equilibrium state space geometry of charged topological dilaton black holes in (n+1)-dimensional anti-de Sitter spacetime. By considering the pairs of parameters (P∼V) and (Q∼U) as variables, we analyze the phase structure and critical phenomena of black holes and discuss the relation between the two kinds of critical phenomena. We find that the phase structures and critical phenomena drastically depend on the cosmological constant l (or the static electric charge Q of the black holes), dimensionality n and dilaton field Φ.

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References

  1. J.D. Bekenstein, Black holes and the second law. Lett. Nuovo Cimento 4, 737 (1972)

    Article  ADS  Google Scholar 

  2. J.D. Bekenstein, Generalized second law of thermodynamics in black hole physics. Phys. Rev. D 9, 3292 (1974)

    Article  ADS  Google Scholar 

  3. J.D. Bekenstein, Extraction of energy and charge from a black hole. Phys. Rev. D 7, 949 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  4. J.M. Bardeen, B. Carter, S.W. Hawking, The four laws of black hole mechanics. Commun. Math. Phys. 31, 161 (1973)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. S.W. Hawking, Black hole explosions. Nature 248, 30 (1974)

    Article  ADS  Google Scholar 

  6. S.W. Hawking, Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  7. S. Hawking, D.N. Page, Thermodynamics of black holes in anti-de Sitter space. Commun. Math. Phys. 87, 577 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  8. A. Chamblin, R. Emparan, C. Johnson, R. Myers, Charged AdS black holes and catastrophic holography. Phys. Rev. D 60, 064018 (1999). hep-th/9902170

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Chamblin, R. Emparan, C. Johnson, R. Myers, Holography, thermodynamics and actuations of charged AdS black holes. Phys. Rev. D 60, 104026 (1999). hep-th/9904197

    Article  ADS  MathSciNet  Google Scholar 

  10. C. Peca, J.P.S. Lemos, Thermodynamics of Reissner–Nordstrom–anti-de Sitter black holes in the grand canonical ensemble. Phys. Rev. D 59, 124007 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  11. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri, Y. Oz, Large N field theories, string theory and gravity. Phys. Rep. 323, 183 (2000). arXiv:hep-th/9905111

    Article  ADS  MathSciNet  Google Scholar 

  12. S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon. Phys. Rev. D 78, 065034 (2008). arXiv:0801.2977 [hep-th]

    Article  ADS  Google Scholar 

  13. S.A. Hartnoll, C.P. Herzog, G.T. Horowitz, Building a holographic superconductor. Phys. Rev. Lett. 101, 031601 (2008). arXiv:0803.3295 [hep-th]

    Article  ADS  Google Scholar 

  14. J.P.S. Lemos, V.T. Zanchin, Charged rotating black strings and three dimensional black holes. Phys. Rev. D 54, 3840 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  15. J.P.S. Lemos, Three dimensional black holes and cylindrical general relativity. Phys. Lett. B 352, 46 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  16. J.P.S. Lemos, Three dimensional black holes and cylindrical general relativity. Phys. Lett. B 352, 46 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  17. J.P.S. Lemos, Two Dimensional Black Holes and Planar General Relativity Class. Quantum Gravity 12, 1081 (1995)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  18. A. Sahay, T. Sarkar, G. Sengupta, Thermodynamic geometry and phase transitions in Kerr–Newman–AdS black holes. J. High Energy Phys. 1004, 118 (2010). arXiv:1002.2538 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  19. A. Sahay, T. Sarkar, G. Sengupta, On the thermodynamic geometry and critical phenomena of AdS black holes. J. High Energy Phys. 1007, 082 (2010). arXiv:1004.1625 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  20. A. Sahay, T. Sarkar, G. Sengupta, On the phase structure and thermodynamic geometry of R-charged black holes. J. High Energy Phys. 1011, 125 (2010). arXiv:1009.2236 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  21. D. Kastor, S. Ray, J. Traschen, Enthalpy and the mechanics of AdS black holes. Class. Quantum Gravity 26, 195011 (2009). arXiv:0904.2765 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  22. R. Banerjee, S.K. Modak, S. Samanta, Second order phase transition and thermodynamic geometry in Kerr–AdS black hole. Phys. Rev. D 84, 064024 (2011). arXiv:1005.4832

    Article  ADS  Google Scholar 

  23. R. Banerjee, D. Roychowdhury, Critical behavior of Born Infeld AdS black holes in higher dimensions. Phys. Rev. D 85, 104043 (2012). arXiv:1203.0118

    Article  ADS  Google Scholar 

  24. R. Banerjee, D. Roychowdhury, Critical phenomena in Born–Infeld AdS black holes. Phys. Rev. D 85, 044040 (2012). arXiv:1111.0147

    Article  ADS  Google Scholar 

  25. R. Banerjee, D. Roychowdhury, Thermodynamics of phase transition in higher dimensional AdS black holes. J. High Energy Phys. 11, 004 (2011). arXiv:1109.2433

    Article  ADS  Google Scholar 

  26. R. Banerjee, S. Ghosh, D. Roychowdhury, New type of phase transition in Reissner–Nordström–AdS black hole and its thermodynamic geometry. Phys. Lett. B 696, 156–162 (2011). arXiv:1008.2644

    Article  ADS  Google Scholar 

  27. R. Banerjee, S.K. Modak, D. Roychowdhury, A unified picture of phase transition: from liquid-vapour systems to AdS black holes. J. High Energy Phys. 1210, 125 (2012). arXiv:1106.3877

    Article  ADS  Google Scholar 

  28. R. Banerjee, S.K. Modak, S. Samanta, Glassy phase transition and stability in black holes. Eur. Phys. J. C 70, 317–328 (2010). arXiv:1002.0466

    Article  ADS  Google Scholar 

  29. B.R. Majhi, D. Roychowdhury, Phase transition and scaling behavior of topological charged black holes in Horava–Lifshitz gravity. Class. Quantum Gravity 29, 245012 (2012). arXiv:1205.0146 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  30. R.-G. Cai, Gauss–Bonnet black holes in AdS spaces. Phys. Rev. D 65, 084014 (2002). arXiv:hep-th/0109133

    Article  ADS  MathSciNet  Google Scholar 

  31. H.-C. Kim, R.-G. Cai, Slowly rotating charged Gauss–Bonnet black holes in AdS spaces. Phys. Rev. D 77, 024045 (2008). arXiv:0711.0885 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  32. Y.S. Myung, Y.-W. Kim, Y.-J. Park, Thermodynamics of Gauss–Bonnet black holes revisited. Eur. Phys. J. C 58, 337 (2008). arXiv:0806.4452 [gr-qc]

    Article  ADS  MATH  MathSciNet  Google Scholar 

  33. Y. Liu, Q. Pan, B. Wang, R.-G. Cai, Dynamical perturbations and critical phenomena in Gauss–Bonnet–AdS black holes. Phys. Lett. B 693, 343 (2010). arXiv:1007.2536 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  34. D. Astefanesei, N. Banerjee, S. Dutta, (Un)attractor black holes in higher derivative AdS gravity. J. High Energy Phys. 0811, 070 (2008). arXiv:0806.1334 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  35. A. Lala, Critical phenomena in higher curvature charged AdS black holes. arXiv:1205.6121 [gr-qc]

  36. T.K. Dey, S. Mukherji, S. Mukhopadhyay, S. Sarkar, Phase transitions in higher derivative gravity. J. High Energy Phys. 0704, 014 (2007). arXiv:hep-th/0609038

    Article  ADS  MathSciNet  Google Scholar 

  37. D. Anninos, G. Pastras, Thermodynamics of the Maxwell–Gauss–Bonnet anti-de Sitter black hole with higher derivative gauge corrections. J. High Energy Phys. 0907, 030 (2009). arXiv:0807.3478 [hep-th]

    Article  ADS  Google Scholar 

  38. S.-W. Wei, Y.-X. Liu, Critical phenomena and thermodynamic geometry of charged Gauss–Bonnet AdS black holes. Phys. Rev. D 87, 044014 (2013). arXiv:1209.1707

    Article  ADS  Google Scholar 

  39. D. Kubiznak, R.B. Mann, P–V criticality of charged AdS black holes. J. High Energy Phys. 1207, 033 (2012). arXiv:1205.0559

    Article  ADS  MathSciNet  Google Scholar 

  40. B.P. Dolan, D. Kastor, D. Kubiznak, R.B. Mann, J. Traschen, Thermodynamic volumes and isoperimetric inequalities for de Sitter black holes. arXiv:1301.5926

  41. S. Gunasekaran, D. Kubiznak, R.B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization. arXiv:1208.6251

  42. B.P. Dolan, Where is the PdV term in the first law of black hole thermodynamics? arXiv:1209.1272 [gr-qc]

  43. M. Cvetic, G.W. Gibbons, D. Kubiznak, C.N. Pope, Black hole enthalpy and an entropy inequality for the thermodynamic volume. Phys. Rev. D 84, 024037 (2011). arXiv:1012.2888

    Article  ADS  Google Scholar 

  44. C. Peca, J.P.S. Lemos, Thermodynamics of toroidal black holes. J. Math. Phys. 41, 4783 (2000)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  45. C.J. Gao, H.N. Zhang, Topological black holes in dilaton gravity theory. Phys. Lett. B 612, 127–136 (2006)

    Article  ADS  Google Scholar 

  46. M.H. Dehghani, S.H. Hendi, A. Sheykhi, H. Rastegar Sedehi, Thermodynamics of rotating black branes in Einstein–Born–Infeld-dilaton gravity. J. Cosmol. Astropart. Phys. 02, 020 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  47. S.H. Hendi, A. Sheykhi, M.H. Dehghani, Thermodynamics of higher dimensional topological charged AdS black branes in dilaton gravity. Eur. Phys. J. C 70, 703 (2010)

    Article  ADS  Google Scholar 

  48. Y.C. Ong, Stringy stability of dilaton black holes in 5-dimensional anti-de-sitter space, in Proceedings of the Conference in Honor of Murray Gell-Mann’s 80th Birthday (World Scientific, Singapore, 2010), pp. 583–590. arXiv:1101.5776v1 [hep-th]

    Google Scholar 

  49. K. Goldstein, S. Kachru, S. Prakash, S.P. Trivedi, Holography of charged dilaton black holes. J. High Energy Phys. 1008, 078 (2010). arXiv:0911.3586v4 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  50. C.-M. Chen, D.-W. Peng, Holography of charged dilaton black holes in general dimensions. J. High Energy Phys. 1006, 093 (2010). arXiv:1003.5064

    Article  ADS  Google Scholar 

  51. B. Gout’eraux, B.S. Kim, R. Meyer, Charged dilatonic black holes and their transport properties. Fortschr. Phys. 59, 723 (2011). arXiv:1102.4440v1 [hep-th]

    Article  MathSciNet  Google Scholar 

  52. N. Lizuka, N. Kundu, P. Narayan, S.P. Trivedi, Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity. J. High Energy Phys. 1201, 094 (2012). arXiv:1105.1162v3 [hep-th]

    Google Scholar 

  53. J.-P. Wu, Some properties of the holographic fermions in an extremal charged dilatonic black holes. Phys. Rev. D 84, 064008 (2011). arXiv:1108.6134v1 [hep-th]

    Article  ADS  Google Scholar 

  54. W.-J. Li, R. Meyer, H. Zhang, Holographic non-relativistic fermionic fixed point by the charged dilatonic black hole. J. High Energy Phys. 01, 153 (2012). 1111.3783v3 [hep-th]

    Article  ADS  Google Scholar 

  55. S.S. Gubser, F.D. Rocha, Peculiar properties of a charged dilatonic black hole in AdS5. Phys. Rev. D 81, 046001 (2010). arXiv:0911.2898v2 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  56. A. Sheykhi, M.H. Dehghani, S.H. Hendi, Thermodynamic instability of charged dilaton black holes in AdS spaces. Phys. Rev. D 81, 084040 (2010). arXiv:0912.4199v2 [hep-th]

    Article  ADS  Google Scholar 

  57. K. Goldstein, N. Lizuka, S. Kachru, S. Prakash, S.P. Trivedi, A. Westphal, Holography of dyonic dilaton black branes. J. High Energy Phys. 1010, 027 (2010). arXiv:1007.2490v1 [hep-th]

    Article  ADS  Google Scholar 

  58. Yen Chin Ong, P. Chen, Stringy stability of charged dilaton black holes with flat event horizon. J. High Energy Phys. 8, 79 (2012). arXiv:1205.4398 [hep-th]

    Google Scholar 

  59. A. Lala, D. Roychowdhury, Ehrenfest’s scheme and thermodynamic geometry in Born–Infeld AdS black holes. Phys. Rev. D 86, 084027 (2012)

    Article  ADS  Google Scholar 

  60. L.F. Abbott, S. Deser, Stability of gravity with a cosmological constant. Nucl. Phys. B 195, 76 (1982)

    Article  ADS  MATH  Google Scholar 

  61. R. Olea, Mass, angular momentum and thermodynamics in four-dimensional Kerr–AdS black holes. J. High Energy Phys. 0506, 023 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  62. R. Olea, Regularization of odd-dimensional AdS gravity: counterterms. J. High Energy Phys. 0704, 073 (2007). hep-th/0610230

    Article  ADS  MathSciNet  Google Scholar 

  63. G. Kofinas, R. Olea, J. High Energy Phys. 0711, 069 (2007). arXiv:0708.0782 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  64. G. Kofinas, R. Olea, Phys. Rev. D 74, 084035 (2006). hep-th/0606253

    Article  ADS  MathSciNet  Google Scholar 

  65. A. Sheykhi, Thermodynamics of charged topological dilaton black holes. Phys. Rev. D 76, 124025 (2007). arXiv:0709.3619 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

This work is supported by NSFC under Grant Nos. 11175109; 11075098; 11205097.

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Authors and Affiliations

  1. Institute of Theoretical Physics, Shanxi Datong University, 037009, Datong, China

    Ren Zhao, Hui-Hua Zhao, Meng-Sen Ma & Li-Chun Zhang

  2. Department of Physics, Shanxi Datong University, 037009, Datong, China

    Hui-Hua Zhao, Meng-Sen Ma & Li-Chun Zhang

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  1. Ren Zhao
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Zhao, R., Zhao, HH., Ma, MS. et al. On the critical phenomena and thermodynamics of charged topological dilaton AdS black holes. Eur. Phys. J. C 73, 2645 (2013). https://doi.org/10.1140/epjc/s10052-013-2645-x

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