Abstract
Black holes are famous for their universal behavior. New thermodynamic relations have been found recently for the product of gravitational entropies over all the horizons of a given stationary black hole. This product has been found to be independent of the mass for all such solutions of Einstein-Maxwell theory in d = 4, 5. We study the universality of this mass independence by introducing a number of possible higher curvature corrections to the gravitational action. We consider finite temperature black holes with both asymptotically flat and (A)dS boundary conditions. Although we find examples for which mass independence of the horizon entropy product continues to hold, we show that the universality of this property fails in general. We also derive further thermodynamic properties of inner horizons, such as the first law and Smarr relation, in the higher curvature theories under consideration, as well as a set of relations between thermodynamic potentials on the inner and outer horizons that follow from the horizon entropy product, whether or not it is mass independent.
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References
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [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].
A. Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
M. Cvetič, G. Gibbons and C. Pope, Universal Area Product Formulae for Rotating and Charged Black Holes in Four and Higher Dimensions, Phys. Rev. Lett. 106 (2011) 121301 [arXiv:1011.0008] [INSPIRE].
A. Castro and M.J. Rodriguez, Universal properties and the first law of black hole inner mechanics, Phys. Rev. D 86 (2012) 024008 [arXiv:1204.1284] [INSPIRE].
S. Detournay, Inner Mechanics of 3d Black Holes, Phys. Rev. Lett. 109 (2012) 031101 [arXiv:1204.6088] [INSPIRE].
B. Chen, S.-X. Liu and J.-J. Zhang, Thermodynamics of Black Hole Horizons and Kerr/CFT Correspondence, JHEP 11 (2012) 017 [arXiv:1206.2015] [INSPIRE].
B. Chen, Z. Xue and J.-J. Zhang, Note on Thermodynamic Method of Black Hole/CFT Correspondence, JHEP 03 (2013) 102 [arXiv:1301.0429] [INSPIRE].
A. Castro, J.M. Lapan, A. Maloney and M.J. Rodriguez, Black Hole Monodromy and Conformal Field Theory, arXiv:1303.0759 [INSPIRE].
A. Strominger, Black hole entropy from near horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [INSPIRE].
F. Larsen, A string model of black hole microstates, Phys. Rev. D 56 (1997) 1005 [hep-th/9702153] [INSPIRE].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
A. Castro, A. Maloney and A. Strominger, Hidden Conformal Symmetry of the Kerr Black Hole, Phys. Rev. D 82 (2010) 024008 [arXiv:1004.0996] [INSPIRE].
D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498 [INSPIRE].
A. Curir, Spin entropy of a rotating black hole, Nuovo Cimento B 51 (1979) 262.
A. Curir and M. Francaviglia, Spin thermodynamics of a Kerr black hole, Nuovo Cimento B 52 (1979) 165.
M. Ansorg and J. Hennig, The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter, Class. Quant. Grav. 25 (2008) 222001 [arXiv:0810.3998] [INSPIRE].
M. Ansorg and J. Hennig, The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory, Phys. Rev. Lett. 102 (2009) 221102 [arXiv:0903.5405] [INSPIRE].
P. Meessen, T. Ortín, J. Perz and C. Shahbazi, Black holes and black strings of N = 2, D = 5 supergravity in the H-FGK formalism, JHEP 09 (2012) 001 [arXiv:1204.0507] [INSPIRE].
M. Visser, Quantization of area for event and Cauchy horizons of the Kerr-Newman black hole, JHEP 06 (2012) 023 [arXiv:1204.3138] [INSPIRE].
V. Faraoni and A.F.Z. Moreno, Are quantization rules for horizon areas universal?, arXiv:1208.3814 [INSPIRE].
C. Toldo and S. Vandoren, Static nonextremal AdS4 black hole solutions, JHEP 09 (2012) 048 [arXiv:1207.3014] [INSPIRE].
D. Klemm and O. Vaughan, Nonextremal black holes in gauged supergravity and the real formulation of special geometry II, Class. Quant. Grav. 30 (2013) 065003 [arXiv:1211.1618] [INSPIRE].
M. Visser, Area products for black hole horizons, arXiv:1205.6814 [INSPIRE].
A. Gnecchi and C. Toldo, On the non-BPS first order flow in N = 2 U(1)-gauged Supergravity, JHEP 03 (2013) 088 [arXiv:1211.1966] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2+1) black hole, Phys. Rev. D 48 (1993) 1506 [gr-qc/9302012] [INSPIRE].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
H. Saida and J. Soda, Statistical entropy of BTZ black hole in higher curvature gravity, Phys. Lett. B 471 (2000) 358 [gr-qc/9909061] [INSPIRE].
P. Kraus and F. Larsen, Microscopic black hole entropy in theories with higher derivatives, JHEP 09 (2005) 034 [hep-th/0506176] [INSPIRE].
R.K. Gupta and A. Sen, Consistent Truncation to Three Dimensional (Super-)gravity, JHEP 03 (2008) 015 [arXiv:0710.4177] [INSPIRE].
B. Chen, J.-j. Zhang, J.-d. Zhang and D.-l. Zhong, Aspects of Warped AdS 3 /CFT 2 Correspondence, JHEP 04 (2013) 055 [arXiv:1302.6643] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive Gravity in Three Dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
G. Clement, Warped AdS 3 black holes in new massive gravity, Class. Quant. Grav. 26 (2009) 105015 [arXiv:0902.4634] [INSPIRE].
A. Sheykhi, Higher-dimensional charged f(R) black holes, Phys. Rev. D 86 (2012) 024013 [arXiv:1209.2960] [INSPIRE].
T.P. Sotiriou and V. Faraoni, f(R) Theories Of Gravity, Rev. Mod. Phys. 82 (2010) 451 [arXiv:0805.1726] [INSPIRE].
T. Moon, Y.S. Myung and E.J. Son, f(R) black holes, Gen. Rel. Grav. 43 (2011) 3079 [arXiv:1101.1153] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav. 26 (2009) 195011 [arXiv:0904.2765] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Smarr Formula and an Extended First Law for Lovelock Gravity, Class. Quant. Grav. 27 (2010) 235014 [arXiv:1005.5053] [INSPIRE].
M. Cvetič, G. Gibbons, D. Kubiznak and C. Pope, Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume, Phys. Rev. D 84 (2011) 024037 [arXiv:1012.2888] [INSPIRE].
B.P. Dolan, D. Kastor, D. Kubiznak, R.B. Mann and J. Traschen, Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes, arXiv:1301.5926 [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Mass and Free Energy of Lovelock Black Holes, Class. Quant. Grav. 28 (2011) 195022 [arXiv:1106.2764] [INSPIRE].
I. Okamoto and O. Kaburaki, The ‘inner-horizon thermodynamics’ of Kerr black holes, Mon. Not. Roy. Astron. Soc. 255 (1992) 539.
T. Jacobson, G. Kang and R.C. Myers, On black hole entropy, Phys. Rev. D 49 (1994) 6587 [gr-qc/9312023] [INSPIRE].
D.G. Boulware and S. Deser, String Generated Gravity Models, Phys. Rev. Lett. 55 (1985) 2656 [INSPIRE].
J.T. Wheeler, Symmetric Solutions to the Gauss-Bonnet Extended Einstein Equations, Nucl. Phys. B 268 (1986) 737 [INSPIRE].
C. Charmousis, Higher order gravity theories and their black hole solutions, Lect. Notes Phys. 769 (2009) 299 [arXiv:0805.0568] [INSPIRE].
C. Garraffo and G. Giribet, The Lovelock Black Holes, Mod. Phys. Lett. A 23 (2008) 1801 [arXiv:0805.3575] [INSPIRE].
D.L. Wiltshire, Spherically symmetric solutions of Einstein-Maxwell theory with a Gauss-Bonnet term, Phys. Lett. B 169 (1986) 36 [INSPIRE].
D.L. Wiltshire, Black holes in string generated gravity models, Phys. Rev. D 38 (1988) 2445 [INSPIRE].
T. Mohaupt, Black hole entropy, special geometry and strings, Fortsch. Phys. 49 (2001) 3 [hep-th/0007195] [INSPIRE].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, String Theory Effects on Five-Dimensional Black Hole Physics, Int. J. Mod. Phys. A 23 (2008) 613 [arXiv:0801.1863] [INSPIRE].
T. Jacobson and R.C. Myers, Black hole entropy and higher curvature interactions, Phys. Rev. Lett. 70 (1993) 3684 [hep-th/9305016] [INSPIRE].
M. Dehghani, Charged rotating black branes in anti-de Sitter Einstein-Gauss-Bonnet gravity, Phys. Rev. D 67 (2003) 064017 [hep-th/0211191] [INSPIRE].
G. Gibbons and P. Townsend, Self-gravitating Yang Monopoles in all Dimensions, Class. Quant. Grav. 23 (2006) 4873 [hep-th/0604024] [INSPIRE].
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ArXiv ePrint: 1304.1696
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Castro, A., Dehmami, N., Giribet, G. et al. On the universality of inner black hole mechanics and higher curvature gravity. J. High Energ. Phys. 2013, 164 (2013). https://doi.org/10.1007/JHEP07(2013)164
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DOI: https://doi.org/10.1007/JHEP07(2013)164