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Kerr/CFT correspondence on Kerr-Newman-NUT-Quintessence black hole

  • Muhammad F. A. R. SaktiEmail author
  • Agus Suroso
  • Freddy P. Zen
Regular Article
  • 15 Downloads

Abstract.

Rotating black hole solution surrounded by quintessential matter is recently discussed because it might be the promising solution to study the effect of dark energy in small scale of the universe. This quintessential solution is originally derived from the condition of additivity and linearity for the energy-momentum tensor. We carry out the thermodynamic properties of this solution using the Kerr/CFT correspondence for several specific quintessential equation-of-state parameters. A problem arises when we compute the central charge because the canonical conserved charge is needed to be calculated from the Lagrangian. However, the exact Lagrangian of the quintessence is not defined yet in the original derivation. Yet we solve this problem by the assumption that there is only a contribution from gravitational field to the central charge. Then we could find the entropy of this black hole after calculating the temperature and using Cardy entropy formula. Another problem comes out when the spin goes to zero to find the Reissner-Nordström-NUT-Quintessence solution. To solve it, we extend to the 5-dimensional solution. In the end, we obtain the entropy for this 5-dimensional solution. So the quintessential black hole solution is dual with the CFT.

References

  1. 1.
    E.J. Copeland, M. Sami, S. Tsujikawa, Int. J. Mod. Phys. D 15, 1753 (2006)ADSGoogle Scholar
  2. 2.
    Arianto, F.P. Zen, B.E. Gunara, Triyanta, Supardi, J. High Energy Phys. 09, 048 (2007)ADSGoogle Scholar
  3. 3.
    Arianto, F.P. Zen, Triyanta, B.E. Gunara, Phys. Rev. D 77, 123517 (2008)ADSMathSciNetGoogle Scholar
  4. 4.
    F.P. Zen, Arianto, B.E. Gunara, Triyanta, A. Purwanto, Eur. Phys. J. C 63, 477 (2009)ADSGoogle Scholar
  5. 5.
    Arianto, F.P. Zen, B.E. Gunara, Gen. Relativ. Gravit. 42, 909 (2010)ADSGoogle Scholar
  6. 6.
    S. Feranie, Arianto, F.P. Zen, Phys. Rev. D 81, 084058 (2010)ADSGoogle Scholar
  7. 7.
    Arianto, F.P. Zen, S. Feranie, I.P. Widyatmika, B.E. Gunara, Phys. Rev. D 84, 044008 (2011)ADSGoogle Scholar
  8. 8.
    A. Suroso, F.P. Zen, Gen. Relativ. Gravit. 45, 799 (2013)ADSGoogle Scholar
  9. 9.
    A. Suroso, F.P. Zen, Adv. Stud. Theor. Phys. 9, 423 (2015)Google Scholar
  10. 10.
    G. Hikmawan, J. Soda, A. Suroso, F.P. Zen, Phys. Rev. D 93, 068301 (2016)ADSMathSciNetGoogle Scholar
  11. 11.
    V.V. Kiselev, Class. Quantum Grav. 20, 1187 (2003)ADSGoogle Scholar
  12. 12.
    B. Toshmatov, Z. Stuchlík, B. Ahmedov, Eur. Phys. J. Plus 132, 98 (2017)Google Scholar
  13. 13.
    Z. Xu, J. Wang, Phys. Rev. D 95, 064015 (2017)ADSMathSciNetGoogle Scholar
  14. 14.
    E.T. Newman, A.I. Janis, J. Math. Phys. 6, 915 (1965)ADSGoogle Scholar
  15. 15.
    E.T. Newman, E. Couch, K. Chinnapared, A. Exton, A. Prakash, R. Torrence, J. Math. Phys. 6, 918 (1965)ADSGoogle Scholar
  16. 16.
    M.F.A.R. Sakti, A. Suroso, F.P. Zen, arXiv:1901.09163 [gr-qc]Google Scholar
  17. 17.
    H. Erbin, Gen. Relativ. Gravit. 47, 19 (2015)ADSMathSciNetGoogle Scholar
  18. 18.
    H. Erbin, L. Heurtier, Class. Quantum Grav. 32, 165005 (2015)ADSGoogle Scholar
  19. 19.
    H. Erbin, Gen. Relativ. Gravit. 48, 56 (2016)ADSMathSciNetGoogle Scholar
  20. 20.
    H. Erbin, Universe 3, 19 (2017)ADSGoogle Scholar
  21. 21.
    R. Kumar, S.G. Ghosh, Eur. Phys. J. C 78, 750 (2018)ADSGoogle Scholar
  22. 22.
    Z. Xu, X. Hou, X. Gong, J. Wang, Eur. Phys. J. C 78, 513 (2018)ADSGoogle Scholar
  23. 23.
    S.G. Ghosh, M. Amir, S.D. Maharaj, Eur. Phys. J. C 77, 530 (2017)ADSGoogle Scholar
  24. 24.
    S.G. Ghosh, S.D. Maharaj, D. Baboolal, T. Lee, Eur. Phys. J. C 78, 90 (2018)ADSGoogle Scholar
  25. 25.
    A. Strominger, C. Vafa, Phys. Lett. B 379, 99 (1996)ADSMathSciNetGoogle Scholar
  26. 26.
    M. Guica, T. Hartman, W. Song, A. Strominger, Phys. Rev. D 80, 124008 (2009)ADSMathSciNetGoogle Scholar
  27. 27.
    T. Hartman, K. Murata, T. Nishioka, A. Strominger, J. High Energy Phys. 04, 019 (2009)ADSGoogle Scholar
  28. 28.
    A.M. Ghezelbash, J. High Energy Phys. 08, 045 (2009)ADSGoogle Scholar
  29. 29.
    H. Lü, J. Mei, C.N. Pope, J. High Energy Phys. 04, 054 (2009)ADSGoogle Scholar
  30. 30.
    R. Li, J.R. Ren, J. High Energy Phys. 09, 039 (2010)ADSGoogle Scholar
  31. 31.
    D. Anninos, T. Hartman, J. High Energy Phys. 03, 096 (2010)ADSGoogle Scholar
  32. 32.
    A. Ghodsi, M.R. Garousi, Phys. Lett. B 687, 79 (2010)ADSMathSciNetGoogle Scholar
  33. 33.
    A.M. Ghezelbash, Mod. Phys. Lett. A 27, 1250046 (2012)ADSMathSciNetGoogle Scholar
  34. 34.
    M. Astorino, J. High Energy Phys. 10, 016 (2015)ADSMathSciNetGoogle Scholar
  35. 35.
    M. Astorino, Phys. Lett. B 751, 96 (2015)ADSGoogle Scholar
  36. 36.
    H.M. Siahaan, Class. Quantum Grav. 33, 155013 (2016)ADSMathSciNetGoogle Scholar
  37. 37.
    M. Astorino, Phys. Lett. B 760, 393 (2016)ADSGoogle Scholar
  38. 38.
    M. Sinamuli, R.B. Mann, J. High Energy Phys. 08, 148 (2016)ADSGoogle Scholar
  39. 39.
    G. Compére, Living Rev. Relativ. 20, 1 (2017)ADSGoogle Scholar
  40. 40.
    M.F.A.R. Sakti, A. Suroso, F.P. Zen, Int. J. Mod. Phys. D 27, 1850109 (2018)ADSGoogle Scholar
  41. 41.
    M.F.A.R. Sakti, A. Suroso, F.P. Zen, J. Phys.: Conf. Ser. 1204, 012009 (2019)Google Scholar
  42. 42.
    M.F.A.R. Sakti, P.Y.D. Sagita, A. Suroso, F.P. Zen, arXiv:1612.00701 [hep-th]Google Scholar
  43. 43.
    M.F.A.R. Sakti, P.Y.D. Sagita, A. Suroso, F.P. Zen, J. Phys.: Conf. Ser. 1127, 012002 (2019)Google Scholar
  44. 44.
    J. Podolský, H. Kadlecová, Class. Quantum Grav. 26, 105007 (2006)ADSGoogle Scholar
  45. 45.
    S. Chen, B. Wang, R. Su, Phys. Rev. D 77, 124011 (2008)ADSMathSciNetGoogle Scholar
  46. 46.
    Y. Sekiwa, Phys. Rev. D 73, 084009 (2006)ADSMathSciNetGoogle Scholar
  47. 47.
    J.D. Brown, M. Henneaux, Commun. Math. Phys. 104, 207 (1986)ADSGoogle Scholar
  48. 48.
    G. Barnich, F. Brandt, Nucl. Phys. B 633, 3 (2002)ADSGoogle Scholar
  49. 49.
    G. Barnich, G. Compere, J. Math. Phys. (N.Y.) 49, 042901 (2008)ADSGoogle Scholar
  50. 50.
    P. Di Francesco, P. Mathieu, D. Senechal, Conformal Field Theory (Springer, New York, 1997)Google Scholar
  51. 51.
    D.A. Lowe, A. Skanata, J. Phys. A 45, 475401 (2012)ADSMathSciNetGoogle Scholar
  52. 52.
    A.M. Ghezelbash, H.M. Siahaan, Class. Quantum Grav. 30, 135005 (2013)ADSGoogle Scholar
  53. 53.
    A.M. Ghezelbash, H.M. Siahaan, Gen. Relativ. Gravit. 46, 1783 (2014)ADSGoogle Scholar
  54. 54.
    M.F.A.R. Sakti, A.M. Ghezelbash, A. Suroso, F.P. Zen, Gen. Relativ. Gravit. 51, 151 (2019) arXiv:1911.05459 [gr-qc]ADSGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Theoretical Physics Laboratory, THEPI DivisionInstitut Teknologi BandungBandungIndonesia
  2. 2.Indonesia Center for Theoretical and Mathematical Physics (ICTMP)Institut Teknologi BandungBandungIndonesia

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