Journal of High Energy Physics

, 2013:146 | Cite as

Thermodynamical, geometrical and Poincaré methods for charged black holes in presence of quintessence

Article

Abstract

Properties pertaining to thermodynamical local stability of Reissner-Nordström black holes surrounded by quintessence as well as adiabatic invariance, adiabatic charging and a generalized Smarr formula are discussed. Limits for the entropy, temperature and electric potential ensuring stability of canonical ensembles are determined by the classical thermodynamical and Poincaré methods. By the latter approach we show that microcanonical ensembles (isolated black holes) are stable. Two geometrical approaches lead to determine the same states corresponding to second order phase transitions.

Keywords

Classical Theories of Gravity Black Holes 

References

  1. [1]
    A.D. Chernin, D.I. Santiago and A.S. Silbergleit, Interplay between gravity and quintessence: a set of new GR solutions, Phys. Lett. A 294 (2002) 79 [astro-ph/0106144] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    P.F. González-Díaz, Eternally accelerating universe without event horizon, Phys. Lett. B 522 (2001) 211 [astro-ph/0110335] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    V. Kiselev, Quintessence and black holes, Class. Quant. Grav. 20 (2003) 1187 [gr-qc/0210040] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  4. [4]
    S. Chen, B. Wang and R. Su, Hawking radiation in a d-dimensional static spherically-symmetric black Hole surrounded by quintessence, Phys. Rev. D 77 (2008) 124011 [arXiv:0801.2053] [INSPIRE].MathSciNetADSGoogle Scholar
  5. [5]
    P.F. González-Díaz, Cosmological models from quintessence, Phys. Rev. D 62 (2000) 023513 [astro-ph/0004125] [INSPIRE].ADSGoogle Scholar
  6. [6]
    M. DePies, Survey of dark energy and quintessence, http://faculty.washington.edu/mrdepies/Survey_of_Dark_Energy2.pdf.
  7. [7]
    WMAP collaboration, E. Komatsu et al., Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation, Astrophys. J. Suppl. 192 (2011) 18 [arXiv:1001.4538] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    J.A. Newman et al., The DEEP2 galaxy redshift survey: design, observations, data reduction and redshifts, Astrophys. J. Suppl. 208 (2013) 5 [arXiv:1203.3192] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    SDSS collaboration, D.G. York et al., The Sloan Digital Sky Survey: technical summary, Astron. J. 120 (2000) 1579 [astro-ph/0006396] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    B.A. Bassett and R. Hlozek, Baryon acoustic oscillations, in Dark energy: observational and theoretical approaches, P. Ruiz-Lapuente ed., Cambridge University Press, Cambridge U.K. (2010), arXiv:0910.5224 [INSPIRE].Google Scholar
  11. [11]
    J.D. Bekenstein, Novelno scalar hairtheorem for black holes, Phys. Rev. D 51 (1995) 6608 [INSPIRE].MathSciNetADSGoogle Scholar
  12. [12]
    A.E. Mayo and J.D. Bekenstein, No hair for spherical black holes: charged and nonminimally coupled scalar field with self-interaction, Phys. Rev. D 54 (1996) 5059 [gr-qc/9602057] [INSPIRE].MathSciNetADSGoogle Scholar
  13. [13]
    M. Azreg-Aïnou, G. Clément, J.C. Fabris and M.E. Rodrigues, Phantom Black Holes and σ-models, Phys. Rev. D 83 (2011) 124001 [arXiv:1102.4093] [INSPIRE].ADSGoogle Scholar
  14. [14]
    J.D. Brown and V. Husain, Black holes with short hair, Int. J. Mod. Phys. D 6 (1997) 563 [gr-qc/9707027] [INSPIRE].
  15. [15]
    D. Garfinkle, G.T. Horowitz and A. Strominger, Charged black holes in string theory, Phys. Rev. D 43 (1991) 3140 [Erratum ibid. D 45 (1992) 3888] [INSPIRE].Google Scholar
  16. [16]
    G. Gibbons and K.-i. Maeda, Black holes and membranes in higher dimensional theories with dilaton fields, Nucl. Phys. B 298 (1988) 741 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    N. Mavromatos and E. Winstanley, Aspects of hairy black holes in spontaneously broken Einstein Yang-Mills systems: stability analysis and entropy considerations, Phys. Rev. D 53 (1996) 3190 [hep-th/9510007] [INSPIRE].MathSciNetADSGoogle Scholar
  18. [18]
    S. Hawking, Black holes and thermodynamics, Phys. Rev. D 13 (1976) 191 [INSPIRE].MathSciNetADSGoogle Scholar
  19. [19]
    G.W. Gibbons and M.J. Perry, Black holes and thermal Greens functions, Proc. Roy. Soc. Lond. A 358 (1978) 467 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    P.C.W. Davies, The thermodynamic theory of black holes, Proc. Roy. Soc. London A 353 (1977) 499.ADSCrossRefGoogle Scholar
  21. [21]
    P.C.W. Davies, Thermodynamics of black holes, Rept. Prog. Phys. 41 (1978) 1313 [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    R. Banerjee, S.K. Modak and D. Roychowdhury, A unified picture of phase transition: from liquid-vapour systems to AdS black holes, JHEP 10 (2012) 125 [arXiv:1106.3877] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    R. Banerjee, S. Ghosh and D. Roychowdhury, New type of phase transition in Reissner Nordstrom-AdS black hole and its thermodynamic geometry, Phys. Lett. B 696 (2011) 156 [arXiv:1008.2644] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    C.S. Peça and J.P.S. Lemos, Thermodynamics of Reissner-Nordstrom Anti-de Sitter black holes in the grand canonical ensemble, Phys. Rev. D 59 (1999) 124007 [gr-qc/9805004] [INSPIRE].ADSGoogle Scholar
  25. [25]
    H. Poincaré, Sur léquilibre dune masse fluide animée dun mouvement de rotation, Acta. Math 7 (1885) 259.MathSciNetCrossRefGoogle Scholar
  26. [26]
    O. Kaburaki, I. Okamoto and J. Katz, Thermodynamic stability of Kerr black holes, Phys. Rev. D 47 (1993) 2234 [INSPIRE].MathSciNetADSGoogle Scholar
  27. [27]
    G. Arcioni and E. Lozano-Tellechea, Stability and critical phenomena of black holes and black rings, Phys. Rev. D 72 (2005) 104021 [hep-th/0412118] [INSPIRE].MathSciNetADSGoogle Scholar
  28. [28]
    R. Parentani, J. Katz and I. Okamoto, Thermodynamics of a black hole in a cavity, Class. Quant. Grav. 12 (1995) 1663 [gr-qc/9410015] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    R. Parentani, The inequivalence of thermodynamic ensembles, gr-qc/9410017 [INSPIRE].
  30. [30]
    J. Katz, I. Okamoto and O. Kaburaki, Thermodynamic stability of pure black holes, Class. Quant. Grav. 10 (1993) 1323 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    J. Katz, On the number of unstable modes of an equilibrium, Mon. Not. Roy. Astron. Soc. 183 (1978) 765.ADSMATHGoogle Scholar
  32. [32]
    J. Katz, On the number of unstable modes of an equilibrium-II, Mon. Not. Roy. Astron. Soc. 189 (1979) 817.ADSGoogle Scholar
  33. [33]
    J.H. Jeans, Astronomy and cosmogony, Dover, New York U.S.A. (1961).Google Scholar
  34. [34]
    R.A. Lyttleton, Theory of rotating fluid masses, Cambridge University Press, Cambridge U.K. (1953).Google Scholar
  35. [35]
    R.D. Sorkin, A stability criterion for many parameter equilibrium families, Astrophys. J. 257 (1982) 847 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  36. [36]
    H. Quevedo, Geometrothermodynamics, J. Math. Phys. 48 (2007) 013506 [physics/0604164] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  37. [37]
    H. Quevedo and A. Vázquez, The geometry of thermodynamics, AIP Conf. Proc. 977 (2008) 165 [arXiv:0712.0868] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    H. Quevedo, Geometrothermodynamics of black holes, Gen. Rel. Grav. 40 (2008) 971 [arXiv:0704.3102] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  39. [39]
    H. Liu, H. Lü, M. Luo and K.-N. Shao, Thermodynamical metrics and black hole phase transitions, JHEP 12 (2010) 054 [arXiv:1008.4482] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    H. Quevedo and A. Sánchez, Geometrothermodynamics of asymptotically de Sitter black holes, JHEP 09 (2008) 034 [arXiv:0805.3003] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    S.W Hawking and D.N. Page, Thermodynamics of black holes in Anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  42. [42]
    Y. Sekiwa, Thermodynamics of de Sitter black holes: thermal cosmological constant, Phys. Rev. D 73 (2006) 084009 [hep-th/0602269] [INSPIRE].MathSciNetADSGoogle Scholar
  43. [43]
    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].MathSciNetADSCrossRefMATHGoogle Scholar
  44. [44]
    J.D. Bekenstein, Black holes: classical properties, thermodynamics and heuristic quantization, in Cosmology and gravitation, M. Novello ed., Atlantisciences, France (2000), gr-qc/9808028.
  45. [45]
    G. Gibbons, Vacuum polarization and the spontaneous loss of charge by black holes, Commun. Math. Phys. 44 (1975) 245 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  46. [46]
    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].MathSciNetADSGoogle Scholar
  47. [47]
    M.E. Rodrigues and Z.A. Oporto, Thermodynamics of phantom black holes in Einstein-Maxwell-Dilaton theory, Phys. Rev. D 85 (2012) 104022 [arXiv:1201.5337] [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Baskent University, Department of MathematicsAnkaraTurkey
  2. 2.Universidade Federal do Espírito Santo, Centro de Ciências Exatas, Departamento de FísicaVitóriaBrazil
  3. 3.Faculdade de Física, Universidade Federal do ParáBelém-ParáBrazil
  4. 4.Faculdade de Ciências Exatas e Tecnologia, Universidade Federal do ParáAbaetetubaBrazil

Personalised recommendations