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Massive gravity solution of black holes and entropy bounds

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Abstract

The dRGT massive gravity represents a comprehensive theory which properly describes massive graviton field. Latterly, the exact spherical solutions are identified for the black hole in the dRGT massive gravity theory. In this paper, we derive Bousso’s D-bound entropy for the black hole solutions of dRGT massive gravity. By an entropic consideration which provides a criterion, it is demonstrated that the relation between the D-bound and Bekenstein entropy bound imposes some constraints on the structure parameters of black hole solutions in dRGT massive gravity.

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References

  1. T. Clifton, P. G. Ferreira, A. Padilla, C. Skordis, Phys. Rep. 513, 1-189 (2012) https://doi.org/10.1016/j.physrep.2012.01.001[arXiv:1106.2476 [astro-ph.CO]]

  2. A.G. Riess et al. [Supernova Search Team], Astron. J. 116 (1998), 1009-1038 https://doi.org/10.1086/300499[arXiv:astro-ph/9805201 [astro-ph]]

  3. E.J. Copeland, A.I.P. Conference of Proceedings 957(1), 21–29 (2007). https://doi.org/10.1063/1.2823765

  4. K. Hinterbichler, Rev. Mod. Phys. 84, 671–710 (2012). https://doi.org/10.1103/RevModPhys.84.671

    Article  ADS  Google Scholar 

  5. C. de Rham, Living Rev. Rel. 17, 7 (2014). https://doi.org/10.12942/lrr-2014-7. [arXiv:1401.4173 [hep-th]]

  6. C. de Rham, G. Gabadadze, A.J. Tolley, Phys. Rev. Lett. 106, 231101 (2011). https://doi.org/10.1103/PhysRevLett.106.231101

    Article  ADS  Google Scholar 

  7. M. Fierz, W. Pauli, Proc. Roy. Soc. London A 173, 211–232 (1939). https://doi.org/10.1098/rspa.1939.0140

    Article  ADS  Google Scholar 

  8. V.I. Zakharov, JETP Lett. 12, 312 (1970)

    ADS  Google Scholar 

  9. D.G. Boulware, S. Deser, Phys. Rev. D 6, 3368–3382 (1972). https://doi.org/10.1103/PhysRevD.6.3368

    Article  ADS  Google Scholar 

  10. A.R. Akbarieh, S. Kazempour, L. Shao, Phys. Rev. D 105(2), 023501 (2022). https://doi.org/10.1103/PhysRevD.105.023501

    Article  ADS  Google Scholar 

  11. T.M. Nieuwenhuizen, Phys. Rev. D 84, 024038 (2011). https://doi.org/10.1103/PhysRevD.84.024038. [arXiv:1103.5912 [gr-qc]]

    Article  ADS  Google Scholar 

  12. P. Li, X.Z. Li, P. Xi, Phys. Rev. D 93(6), 064040 (2016). https://doi.org/10.1103/PhysRevD.93.064040

    Article  ADS  MathSciNet  Google Scholar 

  13. E. Babichev, A. Fabbri, JHEP 07, 016 (2014). https://doi.org/10.1007/JHEP07(2014)016

    Article  ADS  Google Scholar 

  14. M.S. Volkov, Lect. Notes Phys. 892, 161-180 (2015) https://doi.org/10.1007/978-3-319-10070-8_6[arXiv:1405.1742 [hep-th]]

  15. E. Babichev, R. Brito, Class Quant. Gravity 32, 154001 (2015). https://doi.org/10.1088/0264-9381/32/15/154001

    Article  ADS  Google Scholar 

  16. L. Tannukij, P. Wongjun, S.G. Ghosh, Eur. Phys. J. C 77(12), 846 (2017). https://doi.org/10.1140/epjc/s10052-017-5426-0

    Article  ADS  Google Scholar 

  17. P. Boonserm, T. Ngampitipan, P. Wongjun, Eur. Phys. J. C 79(4), 330 (2019). https://doi.org/10.1140/epjc/s10052-019-6827-z

    Article  ADS  Google Scholar 

  18. S.G. Ghosh, R. Kumar, L. Tannukij, P. Wongjun, Phys. Rev. D 101(10), 104042 (2020). https://doi.org/10.1103/PhysRevD.101.104042

    Article  ADS  MathSciNet  Google Scholar 

  19. R.A. Rosen, JHEP 10, 206 (2017). https://doi.org/10.1007/JHEP10(2017)206

    Article  ADS  Google Scholar 

  20. G. Jafari, M.R. Setare, H.R. Bakhtiarizadeh, Phys. Lett. B 773, 395–400 (2017). https://doi.org/10.1016/j.physletb.2017.08.057

    Article  ADS  Google Scholar 

  21. R. Bousso, JHEP 04, 035 (2001). https://doi.org/10.1088/1126-6708/2001/04/035

    Article  ADS  Google Scholar 

  22. J.D. Bekenstein, Phys. Rev. D 7, 2333–2346 (1973). https://doi.org/10.1103/PhysRevD.7.2333

    Article  ADS  MathSciNet  Google Scholar 

  23. J.D. Bekenstein, Phys. Rev. D 23, 287 (1981). https://doi.org/10.1103/PhysRevD.23.287

    Article  ADS  MathSciNet  Google Scholar 

  24. J.D. Bekenstein, Phys. Rev. D 30, 1669–1679 (1984). https://doi.org/10.1103/PhysRevD.30.1669

    Article  ADS  MathSciNet  Google Scholar 

  25. M. Schiffer, J.D. Bekenstein, Phys. Rev. D 39, 1109–1115 (1989). https://doi.org/10.1103/PhysRevD.39.1109

    Article  ADS  MathSciNet  Google Scholar 

  26. D.N. Page, [arXiv:hep-th/0007237 [hep-th]]

  27. J.D. Bekenstein, [arXiv:gr-qc/0006003 [gr-qc]]

  28. R.M. Wald, Living Rev Rel. 4, 6 (2001). https://doi.org/10.12942/lrr-2001-6

    Article  Google Scholar 

  29. J.D. Bekenstein, Lett. Nuovo Cim. 4, 737–740 (1972). https://doi.org/10.1007/BF02757029

  30. J.D. Bekenstein, Phys. Rev. D 9, 3292–3300 (1974). https://doi.org/10.1103/PhysRevD.9.3292

    Article  ADS  Google Scholar 

  31. W.G. Unruh, R.M. Wald, Phys. Rev. D 25, 942–958 (1982). https://doi.org/10.1103/PhysRevD.25.942

    Article  ADS  Google Scholar 

  32. W.G. Unruh, R.M. Wald, Phys. Rev. D 27, 2271–2276 (1983). https://doi.org/10.1103/PhysRevD.27.2271

    Article  ADS  Google Scholar 

  33. M.A. Pelath, R.M. Wald, Phys. Rev. D 60, 104009 (1999). https://doi.org/10.1103/PhysRevD.60.104009

    Article  ADS  MathSciNet  Google Scholar 

  34. Y. Heydarzade, H. Hadi, C. Corda, F. Darabi, Phys. Lett. B 776, 457–463 (2018). https://doi.org/10.1016/j.physletb.2017.11.061

    Article  ADS  MathSciNet  Google Scholar 

  35. H. Hadi, Y. Heydarzade, F. Darabi, K. Atazadeh, Eur. Phys. J. Plus 135(7), 584 (2020). https://doi.org/10.1140/epjp/s13360-020-00601-7

    Article  Google Scholar 

  36. H. Hadi, F. Darabi, K. Atazadeh, Y. Heydarzade, Eur. Phys. J. C 80(12), 1126 (2020). https://doi.org/10.1140/epjc/s10052-020-08699-w

    Article  ADS  Google Scholar 

  37. H. Hadi, F. Darabi, Y. Heydarzade, EPL 131(5), 59001 (2020). https://doi.org/10.1209/0295-5075/131/59001

    Article  ADS  Google Scholar 

  38. K. Koyama, G. Niz, G. Tasinato, Phys. Rev. D 84, 064033 (2011). https://doi.org/10.1103/PhysRevD.84.064033

    Article  ADS  Google Scholar 

  39. K. Koyama, G. Niz, G. Tasinato, Phys. Rev. Lett. 107, 131101 (2011). https://doi.org/10.1103/PhysRevLett.107.131101

    Article  ADS  Google Scholar 

  40. F. Sbisa, G. Niz, K. Koyama, G. Tasinato, Phys. Rev. D 86, 024033 (2012). https://doi.org/10.1103/PhysRevD.86.024033

    Article  ADS  Google Scholar 

  41. S.G. Ghosh, L. Tannukij, P. Wongjun, Eur. Phys. J. C 76(3), 119 (2016). https://doi.org/10.1140/epjc/s10052-016-3943-x

    Article  ADS  Google Scholar 

  42. V.V. Kiselev, Class. Quant. Gravity 20, 1187–1198 (2003). https://doi.org/10.1088/0264-9381/20/6/310

    Article  ADS  Google Scholar 

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Correspondence to Hamed Hadi.

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Hadi, H., Rezaei Akbarieh, A. & Safarzadeh Ilkhchi, P. Massive gravity solution of black holes and entropy bounds. Eur. Phys. J. Plus 138, 330 (2023). https://doi.org/10.1140/epjp/s13360-023-03949-8

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