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Interaction potential and thermo-correction to the equation of state for thermally stable Schwarzschild anti-de Sitter black holes

  • Yan-Gang Miao
  • Zhen-Ming Xu
Article
  • 2 Downloads

Abstract

The microscopic structure of black holes remains a challenging subject. In this paper, based on the well-accepted fact that black holes can be mapped to thermodynamic systems, we make a preliminary exploration of the microscopic structure of the thermodynamically stable Schwarzschild anti-de-Sitter (SAdS) black hole. In accordance with the number density and thermodynamic scalar curvature, we give the interaction potential among the molecules of thermodynamically stable SAdS black holes and analyze its effectiveness. Moreover, we derive the thermo-correction to the equation of state for such black holes that arises from interactions among black-hole molecules using virial coefficients.

Keywords

molecular potential number density equation of state 

References

  1. 1.
    B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 (2016), arXiv: 1602.03837.ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    S. W. Hawking, Commun. Math. Phys. 43, 199 (1975); Erratum ibid. 46, 206 (1976).ADSCrossRefGoogle Scholar
  3. 3.
    J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973).ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 161 (1973).ADSCrossRefGoogle Scholar
  5. 5.
    S.W. Hawking, and D. N. Page, Commun. Math. Phys. 87, 577 (1983).ADSCrossRefGoogle Scholar
  6. 6.
    T. Padmanabhan, Rep. Prog. Phys. 73, 046901 (2010), arXiv: 0911.5004.ADSCrossRefGoogle Scholar
  7. 7.
    A. Chamblin, R. Emparan, C. V. Johnson, and R. C. Myers, Phys. Rev. D 60, 104026 (1999), arXiv: hep-th/9904197.ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    D. Kastor, S. Ray, and J. Traschen, Class. Quantum Grav. 26, 195011 (2009), arXiv: 0904.2765.ADSCrossRefGoogle Scholar
  9. 9.
    B. P. Dolan, Class. Quantum Grav. 28, 125020 (2011), arXiv: 1008.5023.ADSCrossRefGoogle Scholar
  10. 10.
    D. Kubizňák, and R. B. Mann, J. High Energ. Phys. 2012, 33 (2012), arXiv: 1205.0559.ADSCrossRefGoogle Scholar
  11. 11.
    D. Kubizňák, R. B. Mann, and M. Teo, Class. Quantum Grav. 34, 063001 (2017), arXiv: 1608.06147.ADSCrossRefGoogle Scholar
  12. 12.
    A. Strominger, and C. Vafa, Phys. Lett. B 379, 99 (1996), arXiv: hepth/9601029.ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    G. T. Horowitz, and A. Strominger, Phys. Rev. Lett. 77, 2368 (1996), arXiv: hep-th/9602051.ADSCrossRefGoogle Scholar
  14. 14.
    J. M. Maldacena, and A. Strominger, Phys. Rev. Lett. 77, 428 (1996), arXiv: hep-th/9603060.ADSCrossRefGoogle Scholar
  15. 15.
    R. Emparan, and G. T. Horowitz, Phys. Rev. Lett. 97, 141601 (2006), arXiv: hep-th/0607023.ADSCrossRefGoogle Scholar
  16. 16.
    O. Lunin, and S. D. Mathur, Phys. Rev. Lett. 88, 211303 (2002), arXiv: hep-th/0202072.ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    S. W. Wei, and Y. X. Liu, Phys. Rev. Lett. 115, 111302 (2015), arXiv: 1502.00386; Erratum ibid. 116, 169903 (2016).ADSCrossRefGoogle Scholar
  18. 18.
    S. Carlip, Phys. Rev. Lett. 120, 101301 (2018), arXiv: 1702.04439.ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    T. Padmanabhan, Int. J. Mod. Phys. D 19, 2275 (2010).ADSCrossRefGoogle Scholar
  20. 20.
    T. Padmanabhan, Phys. Rev. D 81, 124040 (2010), arXiv: 1003.5665.ADSCrossRefGoogle Scholar
  21. 21.
    A. F. Vargas, E. Contreras, and P. Bargue˜no, arXiv: 1712.01159.Google Scholar
  22. 22.
    G. Ruppeiner, Rev. Mod. Phys. 67, 605 (1995); Rev. Mod. Phys. 68, 313 (1996).ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    G. Ruppeiner, in Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity. Springer Proceedings in Physics, Vol 153, edited by S. Bellucci (Springer, Cham, 2014), p. 179.Google Scholar
  24. 24.
    G. Ruppeiner, Phys. Rev. D 78, 024016 (2008), arXiv: 0802.1326.ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    G. Arcioni, and E. Lozano-Tellechea, Phys. Rev. D 72, 104021 (2005), arXiv: hep-th/0412118.ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    B. Mirza, and M. Zamaninasab, J. High Energ Phys. 2007, 059 (2007), arXiv: 0706.3450.CrossRefGoogle Scholar
  27. 27.
    C. Niu, Y. Tian, and X. N. Wu, Phys. Rev. D 85, 024017 (2012), arXiv: 1104.3066.ADSCrossRefGoogle Scholar
  28. 28.
    M. K. Zangeneh, A. Dehyadegari, and A. Sheykhi, arXiv: 1602.03711.Google Scholar
  29. 29.
    A. Dehyadegari, A. Sheykhi, and A. Montakhab, Phys. Lett. B 768, 235 (2017), arXiv: 1607.05333.ADSCrossRefGoogle Scholar
  30. 30.
    A. Sahay, and R. Jha, Phys. Rev. D 96, 126017 (2017), arXiv: 1707.03629.ADSCrossRefGoogle Scholar
  31. 31.
    M. K. Zangeneh, A. Dehyadegari, A. Sheykhi, and R. B. Mann, Phys. Rev. D 97, 084054 (2018), arXiv: 1709.04432.ADSCrossRefGoogle Scholar
  32. 32.
    Y.-G. Miao, and Z.-M. Xu, arXiv: 1711.01757.Google Scholar
  33. 33.
    Y.-G. Miao, and Z.-M. Xu, arXiv: 1712.00545.Google Scholar
  34. 34.
    G. Ruppeiner, arXiv: 1803.08990.Google Scholar
  35. 35.
    E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998), arXiv: hepth/9803131.MathSciNetCrossRefGoogle Scholar
  36. 36.
    E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998), arXiv: hepth/9802150.ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    E. Spallucci, and A. Smailagic, J. Gravity 2013, 1 (2013), arXiv: 1310.2186.CrossRefGoogle Scholar
  38. 38.
    A. Belhaj, M. Chabab, H. El Moumni, K. Masmar, M. B. Sedra, and A. Segui, J. High Energ. Phys. 2015, 149 (2015), arXiv: 1503.07308.CrossRefGoogle Scholar
  39. 39.
    E. Spallucci, and A. Smailagic, Phys. Lett. B 723, 436 (2013), arXiv: 1305.3379.ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    D. C. Johnston, Advances in Thermodynamics of the van der Waals Fluid (Morgan & Claypool Publishers, California, 2014), p. 6–1.Google Scholar
  41. 41.
    F. Weinhold, J. Chem. Phys. 63, 2479 (1975).ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    H. Janyszek, and R. Mrugaa, J. Phys. A-Math. Gen. 23, 467 (1990).ADSCrossRefGoogle Scholar
  43. 43.
    J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, The Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954), p. 131.MATHGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of PhysicsNankai UniversityTianjinChina

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