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
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]]
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]]
E.J. Copeland, A.I.P. Conference of Proceedings 957(1), 21–29 (2007). https://doi.org/10.1063/1.2823765
K. Hinterbichler, Rev. Mod. Phys. 84, 671–710 (2012). https://doi.org/10.1103/RevModPhys.84.671
C. de Rham, Living Rev. Rel. 17, 7 (2014). https://doi.org/10.12942/lrr-2014-7. [arXiv:1401.4173 [hep-th]]
C. de Rham, G. Gabadadze, A.J. Tolley, Phys. Rev. Lett. 106, 231101 (2011). https://doi.org/10.1103/PhysRevLett.106.231101
M. Fierz, W. Pauli, Proc. Roy. Soc. London A 173, 211–232 (1939). https://doi.org/10.1098/rspa.1939.0140
V.I. Zakharov, JETP Lett. 12, 312 (1970)
D.G. Boulware, S. Deser, Phys. Rev. D 6, 3368–3382 (1972). https://doi.org/10.1103/PhysRevD.6.3368
A.R. Akbarieh, S. Kazempour, L. Shao, Phys. Rev. D 105(2), 023501 (2022). https://doi.org/10.1103/PhysRevD.105.023501
T.M. Nieuwenhuizen, Phys. Rev. D 84, 024038 (2011). https://doi.org/10.1103/PhysRevD.84.024038. [arXiv:1103.5912 [gr-qc]]
P. Li, X.Z. Li, P. Xi, Phys. Rev. D 93(6), 064040 (2016). https://doi.org/10.1103/PhysRevD.93.064040
E. Babichev, A. Fabbri, JHEP 07, 016 (2014). https://doi.org/10.1007/JHEP07(2014)016
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]]
E. Babichev, R. Brito, Class Quant. Gravity 32, 154001 (2015). https://doi.org/10.1088/0264-9381/32/15/154001
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
P. Boonserm, T. Ngampitipan, P. Wongjun, Eur. Phys. J. C 79(4), 330 (2019). https://doi.org/10.1140/epjc/s10052-019-6827-z
S.G. Ghosh, R. Kumar, L. Tannukij, P. Wongjun, Phys. Rev. D 101(10), 104042 (2020). https://doi.org/10.1103/PhysRevD.101.104042
R.A. Rosen, JHEP 10, 206 (2017). https://doi.org/10.1007/JHEP10(2017)206
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
R. Bousso, JHEP 04, 035 (2001). https://doi.org/10.1088/1126-6708/2001/04/035
J.D. Bekenstein, Phys. Rev. D 7, 2333–2346 (1973). https://doi.org/10.1103/PhysRevD.7.2333
J.D. Bekenstein, Phys. Rev. D 23, 287 (1981). https://doi.org/10.1103/PhysRevD.23.287
J.D. Bekenstein, Phys. Rev. D 30, 1669–1679 (1984). https://doi.org/10.1103/PhysRevD.30.1669
M. Schiffer, J.D. Bekenstein, Phys. Rev. D 39, 1109–1115 (1989). https://doi.org/10.1103/PhysRevD.39.1109
D.N. Page, [arXiv:hep-th/0007237 [hep-th]]
J.D. Bekenstein, [arXiv:gr-qc/0006003 [gr-qc]]
R.M. Wald, Living Rev Rel. 4, 6 (2001). https://doi.org/10.12942/lrr-2001-6
J.D. Bekenstein, Lett. Nuovo Cim. 4, 737–740 (1972). https://doi.org/10.1007/BF02757029
J.D. Bekenstein, Phys. Rev. D 9, 3292–3300 (1974). https://doi.org/10.1103/PhysRevD.9.3292
W.G. Unruh, R.M. Wald, Phys. Rev. D 25, 942–958 (1982). https://doi.org/10.1103/PhysRevD.25.942
W.G. Unruh, R.M. Wald, Phys. Rev. D 27, 2271–2276 (1983). https://doi.org/10.1103/PhysRevD.27.2271
M.A. Pelath, R.M. Wald, Phys. Rev. D 60, 104009 (1999). https://doi.org/10.1103/PhysRevD.60.104009
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
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
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
H. Hadi, F. Darabi, Y. Heydarzade, EPL 131(5), 59001 (2020). https://doi.org/10.1209/0295-5075/131/59001
K. Koyama, G. Niz, G. Tasinato, Phys. Rev. D 84, 064033 (2011). https://doi.org/10.1103/PhysRevD.84.064033
K. Koyama, G. Niz, G. Tasinato, Phys. Rev. Lett. 107, 131101 (2011). https://doi.org/10.1103/PhysRevLett.107.131101
F. Sbisa, G. Niz, K. Koyama, G. Tasinato, Phys. Rev. D 86, 024033 (2012). https://doi.org/10.1103/PhysRevD.86.024033
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
V.V. Kiselev, Class. Quant. Gravity 20, 1187–1198 (2003). https://doi.org/10.1088/0264-9381/20/6/310
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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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DOI: https://doi.org/10.1140/epjp/s13360-023-03949-8