Abstract
In this paper we provide the first non-trivial evidence for universality of the entropy formula 4πJ +0 J −0 beyond pure Einstein gravity in 4-dimensions. We consider the Einstein-Maxwell theory in the presence of cosmological constant, then write near horizon metric of the Kerr-Newman (A)dS black hole in the Gaussian null coordinate system. We consider near horizon fall-off conditions for metric and U(1) gauge field. We find asymptotic combined symmetry generator, consists of diffeomorphism and U(1) gauge transformation, so that it preserves fall-off conditions. Consequently, we find supertranslation, supperrotation and multiple-charge modes and then we show that the entropy formula is held for the Kerr-Newman (A)dS black hole. Supperrotation modes suffer from a problem. By introducing new combined symmetry generator, we cure that problem.
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References
J.D. Bekenstein, Black holes and the second law, Lett. Nuovo Cim. 4 (1972) 737 [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
J.D. Bekenstein, Generalized second law of thermodynamics in black hole physics, Phys. Rev. D 9 (1974) 3292 [INSPIRE].
S.W. Hawking, Black holes in general relativity, Commun. Math. Phys. 25 (1972) 152 [INSPIRE].
J.M. Bardeen, B. Carter and S.W. Hawking, The four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Soft Hair on Black Holes, Phys. Rev. Lett. 116 (2016) 231301 [arXiv:1601.00921] [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Superrotation Charge and Supertranslation Hair on Black Holes, JHEP 05 (2017) 161 [arXiv:1611.09175] [INSPIRE].
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
H. Afshar, D. Grumiller, W. Merbis, A. Perez, D. Tempo and R. Troncoso, Soft hairy horizons in three spacetime dimensions, Phys. Rev. D 95 (2017) 106005 [arXiv:1611.09783] [INSPIRE].
M.R. Setare and H. Adami, Near Horizon Geometry of Warped Black Holes in Generalized Minimal Massive Gravity, arXiv:1711.08344 [INSPIRE].
D. Grumiller, P. Hacker and W. Merbis, Soft hairy warped black hole entropy, JHEP 02 (2018) 010 [arXiv:1711.07975] [INSPIRE].
M.R. Setare, On the Generalized Minimal Massive Gravity, Nucl. Phys. B 898 (2015) 259 [arXiv:1412.2151] [INSPIRE].
M.R. Setare and H. Adami, The Heisenberg algebra as near horizon symmetry of the black flower solutions of Chern-Simons-like theories of gravity, Nucl. Phys. B 914 (2017) 220 [arXiv:1606.05260] [INSPIRE].
H. Gonzalez, D. Grumiller, W. Merbis and R. Wutte, New entropy formula for Kerr black holes, EPJ Web Conf. 168 (2018) 01009 [INSPIRE].
J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
K. Prabhu, The First Law of Black Hole Mechanics for Fields with Internal Gauge Freedom, Class. Quant. Grav. 34 (2017) 035011 [arXiv:1511.00388] [INSPIRE].
K. Hajian and M.M. Sheikh-Jabbari, Solution Phase Space and Conserved Charges: A General Formulation for Charges Associated with Exact Symmetries, Phys. Rev. D 93 (2016) 044074 [arXiv:1512.05584] [INSPIRE].
M.R. Setare and H. Adami, Quasi-local conserved charges in the Einstein-Maxwell theory, Class. Quant. Grav. 34 (2017) 105008 [arXiv:1609.06168] [INSPIRE].
M.M. Caldarelli, G. Cognola and D. Klemm, Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories, Class. Quant. Grav. 17 (2000) 399 [hep-th/9908022] [INSPIRE].
K. Hajian, Conserved charges and first law of thermodynamics for Kerr-de Sitter black holes, Gen. Rel. Grav. 48 (2016) 114 [arXiv:1602.05575] [INSPIRE].
I. Booth, Spacetime near isolated and dynamical trapping horizons, Phys. Rev. D 87 (2013) 024008 [arXiv:1207.6955] [INSPIRE].
L.A. Tamburino and J.H. Winicour, Gravitational Fields in Finite and Conformal Bondi Frames, Phys. Rev. 150 (1966) 1039 [INSPIRE].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
L. Donnay, G. Giribet, H.A. González and M. Pino, Extended Symmetries at the Black Hole Horizon, JHEP 09 (2016) 100 [arXiv:1607.05703] [INSPIRE].
L. Donnay, G. Giribet, H.A. González and M. Pino, Supertranslations and Superrotations at the Black Hole Horizon, Phys. Rev. Lett. 116 (2016) 091101 [arXiv:1511.08687] [INSPIRE].
G. Barnich and C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited, Phys. Rev. Lett. 105 (2010) 111103 [arXiv:0909.2617] [INSPIRE].
G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].
M.R. Setare and H. Adami, Near Horizon Symmetries of the Non-Extremal Black Hole Solutions of Generalized Minimal Massive Gravity, Phys. Lett. B 760 (2016) 411 [arXiv:1606.02273] [INSPIRE].
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Setare, M.R., Adami, H. Near horizon symmetry and entropy formula for Kerr-Newman (A)dS black holes. J. High Energ. Phys. 2018, 133 (2018). https://doi.org/10.1007/JHEP04(2018)133
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DOI: https://doi.org/10.1007/JHEP04(2018)133