Abstract
In this paper, we check the universality of the entropy product for some black hole and black ring solutions. Applying the asymptotic symmetry group (ASG) analysis, we also find the central charges of the dual CFTs for these solutions. It has been observed [16] that if the entropy product for a solution is universal, it is possible to read the central charges of the dual CFTs from the entropy product as \( {c}_i\sim \frac{\partial }{\partial {N}_i}\left({S}_{+}{S}_{-}\right), \) where Ni is a conserved charge of the solution like angular momentum or electric charge. In this work we consider some other families of solutions and we check that the same behavior is valid for them. Moreover, in the case of solutions containing the conical singularity, we find the central charges using the ASG analysis. We show that the central charges receive a contribution from the conical characteristic κ of the solution, however it is still possible to read the central charges from the entropy product.
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References
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
F. Loran and H. Soltanpanahi, Near the horizon of 5D black rings, JHEP 03 (2009) 035 [arXiv:0810.2620] [INSPIRE].
H. Lü, J. Mei and C.N. Pope, Kerr/CFT Correspondence in Diverse Dimensions, JHEP 04 (2009) 054 [arXiv:0811.2225] [INSPIRE].
T. Azeyanagi, N. Ogawa and S. Terashima, Holographic Duals of Kaluza-Klein Black Holes, JHEP 04 (2009) 061 [arXiv:0811.4177] [INSPIRE].
T. Hartman, K. Murata, T. Nishioka and A. Strominger, CFT Duals for Extreme Black Holes, JHEP 04 (2009) 019 [arXiv:0811.4393] [INSPIRE].
D.D.K. Chow, M. Cvetǐc, H. Lü and C.N. Pope, Extremal Black Hole/CFT Correspondence in (Gauged) Supergravities, Phys. Rev. D 79 (2009) 084018 [arXiv:0812.2918] [INSPIRE].
H. Isono, T.-S. Tai and W.-Y. Wen, Kerr/CFT correspondence and five-dimensional BMPV black holes, Int. J. Mod. Phys. A 24 (2009) 5659 [arXiv:0812.4440] [INSPIRE].
H. Golchin, M.M. Sheikh-Jabbari and A. Ghodsi, Dual 2d CFT Identification of Extremal Black Rings from Holes, JHEP 10 (2013) 194 [arXiv:1308.1478] [INSPIRE].
A. Ghodsi, H. Golchin and M.M. Sheikh-Jabbari, More on Five Dimensional EVH Black Rings, JHEP 09 (2014) 036 [arXiv:1407.7484] [INSPIRE].
S. Sadeghian and H. Yavartanoo, Black rings in U(1)3 supergravity and their dual 2d CFT, Class. Quant. Grav. 33 (2016) 095006 [arXiv:1510.01209] [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 and J.-j. Zhang, Holographic Descriptions of Black Rings, JHEP 11 (2012) 022 [arXiv:1208.4413] [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].
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].
M. Ansorg, J. Hennig and C. Cederbaum, Universal properties of distorted Kerr-Newman black holes, Gen. Rel. Grav. 43 (2011) 1205 [arXiv:1005.3128] [INSPIRE].
M. Cvetǐc, G.W. Gibbons and C.N. 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].
M. Visser, Area products for stationary black hole horizons, Phys. Rev. D 88 (2013) 044014 [arXiv:1205.6814] [INSPIRE].
M. Cvetǐc, H. Lü and C.N. Pope, Entropy-Product Rules for Charged Rotating Black Holes, Phys. Rev. D 88 (2013) 044046 [arXiv:1306.4522] [INSPIRE].
A. Castro, N. Dehmami, G. Giribet and D. Kastor, On the Universality of Inner Black Hole Mechanics and Higher Curvature Gravity, JHEP 07 (2013) 164 [arXiv:1304.1696] [INSPIRE].
W. Xu, J. Wang and X.-h. Meng, Entropy bound of horizons for charged and rotating black holes, Phys. Lett. B 746 (2015) 53 [INSPIRE].
U. Debnath, Entropy bound of horizons for accelerating, rotating and charged Plebanski-Demianski black hole, Annals Phys. 372 (2016) 449 [arXiv:1507.00901] [INSPIRE].
J. Wang, W. Xu and X.-H. Meng, The ‘universal property’ of horizon entropy sum of black holes in four dimensional asymptotical (anti-)de-Sitter spacetime background, JHEP 01 (2014) 031 [arXiv:1310.6811] [INSPIRE].
P. Pradhan, Area (or entropy) product formula for a regular black hole, Gen. Rel. Grav. 48 (2016) 19 [arXiv:1512.06187] [INSPIRE].
D. Mahdavian Yekta, Entropy product of rotating black holes in three-dimensions, Phys. Rev. D 95 (2017) 064027 [arXiv:1612.01135] [INSPIRE].
H. Golchin, Universality of the area product: Solutions with conical singularity, Phys. Rev. D 100 (2019) 126016 [arXiv:1910.11449] [INSPIRE].
E.T. Newman, R. Couch, K. Chinnapared, A. Exton, A. Prakash and R. Torrence, Metric of a Rotating, Charged Mass, J. Math. Phys. 6 (1965) 918 [INSPIRE].
B. Chen and J.-j. Zhang, Novel CFT Duals for Extreme Black Holes, Nucl. Phys. B 856 (2012) 449 [arXiv:1106.4148] [INSPIRE].
A.A. Pomeransky and R.A. Sen’kov, Black ring with two angular momenta, hep-th/0612005 [INSPIRE].
R. Emparan, Rotating circular strings and infinite nonuniqueness of black rings, JHEP 03 (2004) 064 [hep-th/0402149] [INSPIRE].
R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys. 172 (1986) 304 [INSPIRE].
S.W. Hawking, C.J. Hunter and M. Taylor, Rotation and the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 064005 [hep-th/9811056] [INSPIRE].
Y. Chen, K. Hong and E. Teo, A Doubly rotating black ring with dipole charge, JHEP 06 (2012) 148 [arXiv:1204.5785] [INSPIRE].
W. Kinnersley and M. Walker, Uniformly accelerating charged mass in general relativity, Phys. Rev. D 2 (1970) 1359 [INSPIRE].
M. Astorino, Thermodynamics of Regular Accelerating Black Holes, Phys. Rev. D 95 (2017) 064007 [arXiv:1612.04387] [INSPIRE].
K. Hong and E. Teo, A New form of the rotating C-metric, Class. Quant. Grav. 22 (2005) 109 [gr-qc/0410002] [INSPIRE].
Y. Chen, K. Hong and E. Teo, Unbalanced Pomeransky-Sen’kov black ring, Phys. Rev. D 84 (2011) 084030 [arXiv:1108.1849] [INSPIRE].
R. Emparan and H.S. Reall, A Rotating black ring solution in five-dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [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].
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Golchin, H. More on the entropy product and dual CFTs. J. High Energ. Phys. 2020, 127 (2020). https://doi.org/10.1007/JHEP03(2020)127
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DOI: https://doi.org/10.1007/JHEP03(2020)127