Advertisement

Area (or entropy) products in modified gravity and Kerr-MG/CFT correspondence

  • Parthapratim Pradhan
Regular Article
  • 17 Downloads

Abstract.

We examine the thermodynamic features of inner and outer horizons of modified gravity (MOG) and its consequences on the holographic duality. We derive the thermodynamic product relations for this gravity. We consider both spherically symmetric solutions and axisymmetric solutions of MOG. We find that the area product formula for both cases is not mass-independent because they depend on the ADM mass parameter while, in Einstein gravity, this formula is mass-independent (universal). We also explicitly verify the first law, which is fulfilled at the inner horizon (IH) as well as at the outer horizon (OH). We derive thermodynamic products and sums for this kind of gravity. We further derive the Smarr-like mass formula for this kind of black hole (BH) in MOG. Moreover, we derive the area bound for both horizons. Furthermore, we show that the central charges of the left and right moving sectors are the same via universal thermodynamic relations. We also discuss the most important result of the Kerr-MOG/CFT correspondence. We derive the central charges for Kerr-MOG BH, which is \(c_{L}=12J\) and it is similar to Kerr BH. We also derive the dimensionless temperature for extreme Kerr-MOG BH which is \(T_{L} = \frac{1}{4\pi} \frac{\alpha+2}{\sqrt{1+\alpha}}\), where \(\alpha\) is a MOG parameter. This is actually the dual CFT temperature of the Frolov-Thorne thermal vacuum state. In the limit \(\alpha = 0\), we find the dimensionless temperature of a Kerr BH. Consequently, the Cardy formula gives us microscopic entropy for extreme Kerr-MOG BH, \(S_{\rm micro}=\frac{\alpha+2}{\sqrt{1+\alpha}} \pi J\), for the CFT, which is completely in agreement with the macroscopic Bekenstein-Hawking entropy. Therefore we may conjecture that, in the extremal limit, the Kerr-MOG BH is holographically dual to a chiral 2D CFT with central charge \(c_{L}=12J\). Finally, we derive the mass-independent area (or entropy) product relations for regular MOG BH.

References

  1. 1.
    J.M. Bardeen et al., Commun. Math. Phys. 31, 161 (1973)ADSCrossRefGoogle Scholar
  2. 2.
    J.D. Bekenstein, Phys. Rev. D 7, 2333 (1973)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    M. Ansorg, J. Hennig, Phys. Rev. Lett. 102, 221102 (2009)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    M. Visser, Phys. Rev. D 88, 044014 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    P. Pradhan, Phys. Lett. B 747, 64 (2015)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    P. Pradhan, Eur. Phys. J. C 74, 2887 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    P. Pradhan, Gen. Relativ. Gravit. 48, 19 (2016)ADSCrossRefGoogle Scholar
  8. 8.
    P. Pradhan, Int. J. Mod. Phys. D 26, 1750010 (2017)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    P. Pradhan, Mod. Phys. Lett. A 30, 1550170 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    P. Pradhan, JETP Lett. 102, 481 (2015)CrossRefGoogle Scholar
  11. 11.
    P. Pradhan, Gen. Relativ. Gravit. 48, 98 (2016)ADSCrossRefGoogle Scholar
  12. 12.
    P. Pradhan, Eur. Phys. J. C 76, 131 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    M. Cvetič et al., Phys. Rev. Lett. 106, 121301 (2011)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    F. Larsen, Phys. Rev. D 56, 1005 (1997)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    A. Castro, M.J. Rodriguez, Phys. Rev. D 86, 024008 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    S. Detournay, Phys. Rev. Lett. 109, 031101 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    V. Faraoni, A.F.Z. Moreno, Phys. Rev. D. 88, 044011 (2013)ADSCrossRefGoogle Scholar
  18. 18.
    B. Chen et al., J. High Energy Phys. 11, 017 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    J. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    A. Strominger, C. Vafa, Phys. Lett. B. 379, 99 (1996)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    J.D. Brown, M. Henneaux, Commun. Math. Phys. 104, 207 (1986)ADSCrossRefGoogle Scholar
  22. 22.
    M. Guica et al., Phys. Rev. D 80, 124008 (2009)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    A. Castro et al., Phys. Rev. D 82, 024008 (2010)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    V.P. Frolov, K.S. Thorne, Phys. Rev. D. 39, 2125 (1989)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    J.W. Moffat, JCAP 03, 004 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    B. Chen, J. Zhang, Phys. Rev. D. 87, 081505(R) (2013)ADSCrossRefGoogle Scholar
  27. 27.
    J.W. Moffat, S. Rahvar, Mon. Not. R. Acad. Sci. 436, 1439 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    J.W. Moffat, S. Rahvar, Mon. Not. R. Acad. Sci. 441, 3724 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    J.W. Moffat, V.T. Toth, Phys. Rev. D. 91, 043004 (2015)ADSCrossRefGoogle Scholar
  30. 30.
    J.R. Brownstein, J.W. Moffat, Mon. Not. R. Acad. Sci. 382, 29 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    J.R. Mureika et al., Phys. Lett. B 757, 528 (2016)ADSCrossRefGoogle Scholar
  32. 32.
    J.W. Moffat, Eur. Phys. J. C 75, 175 (2015)ADSCrossRefGoogle Scholar
  33. 33.
    J.W. Moffat, Eur. Phys. J. C 75, 130 (2015)ADSCrossRefGoogle Scholar
  34. 34.
    W. Xu et al., Phys. Lett. B 746, 53 (2015)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    E.T. Newman et al., J. Math. Phys. 6, 918 (1965)ADSCrossRefGoogle Scholar
  36. 36.
    C.A.R. Herdeiro, E. Radu, Int. J. Mod. Phys. D 24, 1542014 (2015) and references thereinADSCrossRefGoogle Scholar
  37. 37.
    M. Cvetič, D. Youm, Phys. Rev. D 54, 2612 (1996)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    M. Cvetič, F. Larsen, Nucl. Phys. B 506, 107 (1997)ADSCrossRefGoogle Scholar
  39. 39.
    M. Cvetič, F. Larsen, Phys. Rev. D 56, 4994 (1997)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    T. Hartman et al., J. High Energy Phys. 04, 019 (2009)ADSCrossRefGoogle Scholar
  41. 41.
    J. Bardeen, Conference Proceedings in GR5 (Tiflis, U.S.S.R., 1968)Google Scholar
  42. 42.
    E. Ayón-Beato, A. García, Phys. Rev. Lett. 80, 5056 (1998)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsHiralal Mazumdar Memorial College For WomenKolkataIndia

Personalised recommendations