×

Logarithmic corrections to Schwarzschild and other non-extremal black hole entropy in different dimensions. (English) Zbl 1342.83207

Summary: Euclidean gravity method has been successful in computing logarithmic corrections to extremal black hole entropy in terms of low energy data, and gives results in perfect agreement with the microscopic results in string theory. Motivated by this success we apply Euclidean gravity to compute logarithmic corrections to the entropy of various non-extremal black holes in different dimensions, taking special care of integration over the zero modes and keeping track of the ensemble in which the computation is done. These results provide strong constraint on any ultraviolet completion of the theory if the latter is able to give an independent computation of the entropy of non-extremal black holes from microscopic description. For Schwarzschild black holes in four space-time dimensions the macroscopic result seems to disagree with the existing result in loop quantum gravity.

MSC:

83C57 Black holes
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] S.N. Solodukhin, The Conical singularity and quantum corrections to entropy of black hole, Phys. Rev.D 51 (1995) 609 [hep-th/9407001] [INSPIRE].
[2] S.N. Solodukhin, On ’Nongeometric’ contribution to the entropy of black hole due to quantum corrections, Phys. Rev.D 51 (1995) 618 [hep-th/9408068] [INSPIRE].
[3] D.V. Fursaev, Temperature and entropy of a quantum black hole and conformal anomaly, Phys. Rev.D 51 (1995) 5352 [hep-th/9412161] [INSPIRE].
[4] N. Mavromatos and E. Winstanley, Aspects of hairy black holes in spontaneously broken Einstein Yang-Mills systems: Stability analysis and entropy considerations, Phys. Rev.D 53 (1996) 3190 [hep-th/9510007] [INSPIRE].
[5] R.B. Mann and S.N. Solodukhin, Conical geometry and quantum entropy of a charged Kerr black hole, Phys. Rev.D 54 (1996) 3932 [hep-th/9604118] [INSPIRE].
[6] R.B. Mann and S.N. Solodukhin, Universality of quantum entropy for extreme black holes, Nucl. Phys.B 523 (1998) 293 [hep-th/9709064] [INSPIRE]. · Zbl 0953.83015
[7] S. Carlip, Logarithmic corrections to black hole entropy from the Cardy formula, Class. Quant. Grav.17 (2000) 4175 [gr-qc/0005017] [INSPIRE]. · Zbl 0970.83026
[8] T. Govindarajan, R. Kaul and V. Suneeta, Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole, Class. Quant. Grav.18 (2001) 2877 [gr-qc/0104010] [INSPIRE]. · Zbl 0999.83031
[9] K.S. Gupta and S. Sen, Further evidence for the conformal structure of a Schwarzschild black hole in an algebraic approach, Phys. Lett.B 526 (2002) 121 [hep-th/0112041] [INSPIRE]. · Zbl 0981.83030
[10] A. Medved, A Comment on black hole entropy or does nature abhor a logarithm?, Class. Quant. Grav.22 (2005) 133 [gr-qc/0406044] [INSPIRE]. · Zbl 1060.83522
[11] D.N. Page, Hawking radiation and black hole thermodynamics, New J. Phys.7 (2005) 203 [hep-th/0409024] [INSPIRE].
[12] R. Banerjee and B.R. Majhi, Quantum Tunneling Beyond Semiclassical Approximation, JHEP06 (2008) 095 [arXiv:0805.2220] [INSPIRE].
[13] R. Banerjee and B.R. Majhi, Quantum Tunneling, Trace Anomaly and Effective Metric, Phys. Lett.B 674 (2009) 218 [arXiv:0808.3688] [INSPIRE].
[14] B.R. Majhi, Fermion Tunneling Beyond Semiclassical Approximation, Phys. Rev.D 79 (2009) 044005 [arXiv:0809.1508] [INSPIRE].
[15] R.-G. Cai, L.-M. Cao and N. Ohta, Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy, JHEP04 (2010) 082 [arXiv:0911.4379] [INSPIRE]. · Zbl 1272.83042
[16] R. Aros, D. Diaz and A. Montecinos, Logarithmic correction to BH entropy as Noether charge, JHEP07 (2010) 012 [arXiv:1003.1083] [INSPIRE]. · Zbl 1290.83031
[17] S.N. Solodukhin, Entanglement entropy of round spheres, Phys. Lett.B 693 (2010) 605 [arXiv:1008.4314] [INSPIRE].
[18] S. Banerjee, R.K. Gupta and A. Sen, Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function, JHEP03 (2011) 147 [arXiv:1005.3044] [INSPIRE]. · Zbl 1301.81182
[19] S. Banerjee, R.K. Gupta, I. Mandal and A. Sen, Logarithmic Corrections to N = 4 and N = 8 Black Hole Entropy: A One Loop Test of Quantum Gravity, JHEP11 (2011) 143 [arXiv:1106.0080] [INSPIRE]. · Zbl 1306.83038
[20] A. Sen, Logarithmic Corrections to N = 2 Black Hole Entropy: An Infrared Window into the Microstates, arXiv:1108.3842 [INSPIRE]. · Zbl 1241.83051
[21] S. Ferrara and A. Marrani, Generalized Mirror Symmetry and Quantum Black Hole Entropy, Phys. Lett.B 707 (2012) 173 [arXiv:1109.0444] [INSPIRE].
[22] A. Sen, Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions, Gen. Rel. Grav.44 (2012) 1947 [arXiv:1109.3706] [INSPIRE]. · Zbl 1253.83003
[23] A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett.B 379 (1996) 99 [hep-th/9601029] [INSPIRE]. · Zbl 1376.83026
[24] J. Breckenridge, R.C. Myers, A. Peet and C. Vafa, D-branes and spinning black holes, Phys. Lett.B 391 (1997) 93 [hep-th/9602065] [INSPIRE]. · Zbl 0956.83064
[25] I. Mandal and A. Sen, Black Hole Microstate Counting and its Macroscopic Counterpart, Nucl. Phys. Proc. Suppl.216 (2011) 147 [arXiv:1008.3801] [INSPIRE].
[26] S. Bhattacharyya, B. Panda and A. Sen, Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory, JHEP08 (2012) 084 [arXiv:1204.4061] [INSPIRE].
[27] S.N. Solodukhin, Entanglement entropy of black holes, Living Rev. Rel.14 (2011) 8 [arXiv:1104.3712] [INSPIRE]. · Zbl 1320.83015
[28] D.V. Fursaev and S.N. Solodukhin, On one loop renormalization of black hole entropy, Phys. Lett.B 365 (1996) 51 [hep-th/9412020] [INSPIRE].
[29] R.K. Kaul and P. Majumdar, Quantum black hole entropy, Phys. Lett.B 439 (1998) 267 [gr-qc/9801080] [INSPIRE].
[30] R.K. Kaul and P. Majumdar, Logarithmic correction to the Bekenstein-Hawking entropy, Phys. Rev. Lett.84 (2000) 5255 [gr-qc/0002040] [INSPIRE].
[31] S. Das, R.K. Kaul and P. Majumdar, A New holographic entropy bound from quantum geometry, Phys. Rev.D 63 (2001) 044019 [hep-th/0006211] [INSPIRE].
[32] A. Ghosh and P. Mitra, A Bound on the log correction to the black hole area law, Phys. Rev.D 71 (2005) 027502 [gr-qc/0401070] [INSPIRE].
[33] M. Domagala and J. Lewandowski, Black hole entropy from quantum geometry, Class. Quant. Grav.21 (2004) 5233 [gr-qc/0407051] [INSPIRE]. · Zbl 1062.83053
[34] K.A. Meissner, Black hole entropy in loop quantum gravity, Class. Quant. Grav.21 (2004) 5245 [gr-qc/0407052] [INSPIRE]. · Zbl 1062.83056
[35] A. Ghosh and P. Mitra, An Improved lower bound on black hole entropy in the quantum geometry approach, Phys. Lett.B 616 (2005) 114 [gr-qc/0411035] [INSPIRE]. · Zbl 1247.83088
[36] A. Ghosh and P. Mitra, Counting black hole microscopic states in loop quantum gravity, Phys. Rev.D 74 (2006) 064026 [hep-th/0605125] [INSPIRE].
[37] J. Engle, A. Perez and K. Noui, Black hole entropy and SU(2) Chern-Simons theory, Phys. Rev. Lett.105 (2010) 031302 [arXiv:0905.3168] [INSPIRE].
[38] R. Basu, R.K. Kaul and P. Majumdar, Entropy of Isolated Horizons revisited, Phys. Rev.D 82 (2010) 024007 [arXiv:0907.0846] [INSPIRE].
[39] J. Engle, K. Noui, A. Perez and D. Pranzetti, Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons, Phys. Rev.D 82 (2010) 044050 [arXiv:1006.0634] [INSPIRE].
[40] J. Engle, K. Noui, A. Perez and D. Pranzetti, The SU(2) Black Hole entropy revisited, JHEP05 (2011) 016 [arXiv:1103.2723] [INSPIRE]. · Zbl 1296.83037
[41] R.K. Kaul, Entropy of quantum black holes, SIGMA8 (2012) 005 [arXiv:1201.6102] [INSPIRE]. · Zbl 1248.81122
[42] R. Dijkgraaf, J.M. Maldacena, G.W. Moore and E.P. Verlinde, A Black hole Farey tail, hep-th/0005003 [INSPIRE].
[43] S. Das, P. Majumdar and R.K. Bhaduri, General logarithmic corrections to black hole entropy, Class. Quant. Grav.19 (2002) 2355 [hep-th/0111001] [INSPIRE]. · Zbl 1003.83025
[44] M. Duff, Observations on Conformal Anomalies, Nucl. Phys.B 125 (1977) 334 [INSPIRE].
[45] S. Christensen and M. Duff, New Gravitational Index Theorems and Supertheorems, Nucl. Phys.B 154 (1979) 301 [INSPIRE]. · Zbl 0967.83535
[46] S. Christensen and M. Duff, Quantizing Gravity with a Cosmological Constant, Nucl. Phys.B 170 (1980) 480 [INSPIRE]. · Zbl 0967.83510
[47] M. Duff and P. van Nieuwenhuizen, Quantum Inequivalence of Different Field Representations, Phys. Lett.B 94 (1980) 179 [INSPIRE].
[48] S. Christensen, M. Duff, G. Gibbons and M. Roček, VANISHING ONE LOOP β-function IN GAUGED N ¿ 4 SUPERGRAVITY, Phys. Rev. Lett.45 (1980) 161 [INSPIRE].
[49] N.D. Birrel and P.C.W. Davis, Quantum Fields in Curved Space, Cambridge University Press, New York U.S.A. (1982). · Zbl 0476.53017
[50] P.B. Gilkey, Invariance theory, the heat equation and the Atiyah-Singer index theorem, Publish or Perish Inc. U.S.A. (1984)
[51] D. Vassilevich, Heat kernel expansion: User’s manual, Phys. Rept.388 (2003) 279 [hep-th/0306138] [INSPIRE]. · Zbl 1042.81093
[52] M. Duff and S. Ferrara, Generalized mirror symmetry and trace anomalies, Class. Quant. Grav.28 (2011) 065005 [arXiv:1009.4439] [INSPIRE]. · Zbl 1211.83030
[53] T. Jacobson, Renormalization and black hole entropy in Loop Quantum Gravity, Class. Quant. Grav.24 (2007) 4875 [arXiv:0707.4026] [INSPIRE]. · Zbl 1128.83018
[54] G. Gibbons and S. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev.D 15 (1977) 2752 [INSPIRE].
[55] R.C. Henry, Kretschmann scalar for a Kerr-Newman black hole, astro-ph/9912320 [INSPIRE].
[56] C. Cherubini, D. Bini, S. Capozziello and R. Ruffini, Second order scalar invariants of the Riemann tensor: Applications to black hole space-times, Int. J. Mod. Phys.D 11 (2002) 827 [gr-qc/0302095] [INSPIRE]. · Zbl 1070.83524
[57] S. Mukherji and S.S. Pal, Logarithmic corrections to black hole entropy and AdS/CFT correspondence, JHEP05 (2002) 026 [hep-th/0205164] [INSPIRE].
[58] A. Chatterjee and P. Majumdar, Universal canonical black hole entropy, Phys. Rev. Lett.92 (2004) 141301 [gr-qc/0309026] [INSPIRE]. · Zbl 1267.83053
[59] M.-I. Park, Testing holographic principle from logarithmic and higher order corrections to black hole entropy, JHEP12 (2004) 041 [hep-th/0402173] [INSPIRE].
[60] A. Majhi and P. Majumdar, Charged Quantum Black Holes: Thermal Stability Criterion, Class. Quant. Grav.29 (2012) 135013 [arXiv:1108.4670] [INSPIRE]. · Zbl 1246.83078
[61] L. Smolin, Linking topological quantum field theory and nonperturbative quantum gravity, J. Math. Phys.36 (1995) 6417 [gr-qc/9505028] [INSPIRE]. · Zbl 0856.58055
[62] K.V. Krasnov, On Quantum statistical mechanics of Schwarzschild black hole, Gen. Rel. Grav.30 (1998) 53 [gr-qc/9605047] [INSPIRE]. · Zbl 0910.58045
[63] A. Ashtekar, J. Baez, A. Corichi and K. Krasnov, Quantum geometry and black hole entropy, Phys. Rev. Lett.80 (1998) 904 [gr-qc/9710007] [INSPIRE]. · Zbl 0949.83024
[64] A. Ashtekar, J.C. Baez and K. Krasnov, Quantum geometry of isolated horizons and black hole entropy, Adv. Theor. Math. Phys.4 (2000) 1 [gr-qc/0005126] [INSPIRE]. · Zbl 0981.83028
[65] 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]. · Zbl 0968.83514
[66] P. Kraus and F. Larsen, Microscopic black hole entropy in theories with higher derivatives, JHEP09 (2005) 034 [hep-th/0506176] [INSPIRE].
[67] R.C. Myers and M. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys.172 (1986) 304 [INSPIRE]. · Zbl 0601.53081
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.