Abstract
We present the computation of logarithmic corrections to near-extremal black hole entropy from one-loop Euclidean gravity path integral around the near-horizon geometry. We extract these corrections employing a suitably modified heat kernel method, where the near-extremal near-horizon geometry is treated as a perturbation around the extremal near-horizon geometry. Using this method we compute the logarithmic corrections to non-rotating solutions in four dimensional Einstein-Maxwell and \( \mathcal{N} \) = 2, 4, 8 supergravity theories. We also discuss the limit that suitably recovers the extremal black hole results.
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References
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
S.W. Hawking, Black Holes and Thermodynamics, Phys. Rev. D 13 (1976) 191 [INSPIRE].
S.N. Solodukhin, The conical singularity and quantum corrections to entropy of black hole, Phys. Rev. D 51 (1995) 609 [hep-th/9407001] [INSPIRE].
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].
A.J.M. Medved, A comment on black hole entropy or does nature abhor a logarithm?, Class. Quant. Grav. 22 (2005) 133 [gr-qc/0406044] [INSPIRE].
R.-G. Cai, L.-M. Cao and N. Ohta, Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy, JHEP 04 (2010) 082 [arXiv:0911.4379] [INSPIRE].
R. Aros, D.E. Diaz and A. Montecinos, Logarithmic correction to BH entropy as Noether charge, JHEP 07 (2010) 012 [arXiv:1003.1083] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
J.W. York Jr., Black hole thermodynamics and the Euclidean Einstein action, Phys. Rev. D 33 (1986) 2092 [INSPIRE].
A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP 09 (2005) 038 [hep-th/0506177] [INSPIRE].
A. Sen, Entropy Function and AdS(2) / CFT(1) Correspondence, JHEP 11 (2008) 075 [arXiv:0805.0095] [INSPIRE].
A. Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
A. Sen, Quantum Entropy Function from AdS(2)/CFT(1) Correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE].
N. Banerjee et al., Supersymmetry, Localization and Quantum Entropy Function, JHEP 02 (2010) 091 [arXiv:0905.2686] [INSPIRE].
S. Banerjee, R.K. Gupta and A. Sen, Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function, JHEP 03 (2011) 147 [arXiv:1005.3044] [INSPIRE].
S. Karan, G. Banerjee and B. Panda, Seeley-DeWitt Coefficients in \( \mathcal{N} \) = 2 Einstein-Maxwell Supergravity Theory and Logarithmic Corrections to \( \mathcal{N} \) = 2 Extremal Black Hole Entropy, JHEP 08 (2019) 056 [arXiv:1905.13058] [INSPIRE].
G. Banerjee, S. Karan and B. Panda, Logarithmic correction to the entropy of extremal black holes in \( \mathcal{N} \) = 1 Einstein-Maxwell supergravity, JHEP 01 (2021) 090 [arXiv:2007.11497] [INSPIRE].
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, JHEP 11 (2011) 143 [arXiv:1106.0080] [INSPIRE].
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].
A. Sen, Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions, JHEP 04 (2013) 156 [arXiv:1205.0971] [INSPIRE].
S. Bhattacharyya, B. Panda and A. Sen, Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory, JHEP 08 (2012) 084 [arXiv:1204.4061] [INSPIRE].
A. Sen, Logarithmic Corrections to N = 2 Black Hole Entropy: An infrared Window into the Microstates, Gen. Rel. Grav. 44 (2012) 1207 [arXiv:1108.3842] [INSPIRE].
S. Karan and B. Panda, Logarithmic corrections to black hole entropy in matter coupled \( \mathcal{N} \) ≥ 1 Einstein-Maxwell supergravity, JHEP 05 (2021) 104 [arXiv:2012.12227] [INSPIRE].
S. Karan and B. Panda, Generalized Einstein-Maxwell theory: Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and nonextremal black holes, Phys. Rev. D 104 (2021) 046010 [arXiv:2104.06381] [INSPIRE].
G. Banerjee and B. Panda, Logarithmic corrections to the entropy of non-extremal black holes in \( \mathcal{N} \) = 1 Einstein-Maxwell supergravity, JHEP 11 (2021) 214 [arXiv:2109.04407] [INSPIRE].
S. Karan and G.S. Punia, Logarithmic correction to black hole entropy in universal low-energy string theory models, JHEP 03 (2023) 028 [arXiv:2210.16230] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
J.C. Breckenridge, R.C. Myers, A.W. Peet and C. Vafa, D-branes and spinning black holes, Phys. Lett. B 391 (1997) 93 [hep-th/9602065] [INSPIRE].
J.R. David, D.P. Jatkar and A. Sen, Dyon Spectrum in N = 4 Supersymmetric Type II String Theories, JHEP 11 (2006) 073 [hep-th/0607155] [INSPIRE].
J.R. David, D.P. Jatkar and A. Sen, Dyon spectrum in generic N = 4 supersymmetric Z(N) orbifolds, JHEP 01 (2007) 016 [hep-th/0609109] [INSPIRE].
R.K. Gupta and A. Sen, Ads(3)/CFT(2) to Ads(2)/CFT(1), JHEP 04 (2009) 034 [arXiv:0806.0053] [INSPIRE].
N. Banerjee, D.P. Jatkar and A. Sen, Adding Charges to N = 4 Dyons, JHEP 07 (2007) 024 [arXiv:0705.1433] [INSPIRE].
N. Banerjee, D.P. Jatkar and A. Sen, Asymptotic Expansion of the N = 4 Dyon Degeneracy, JHEP 05 (2009) 121 [arXiv:0810.3472] [INSPIRE].
N. Banerjee, I. Mandal and A. Sen, Black Hole Hair Removal, JHEP 07 (2009) 091 [arXiv:0901.0359] [INSPIRE].
A.A. H., P.V. Athira, C. Chowdhury and A. Sen, Logarithmic Correction to BPS Black Hole Entropy from Supersymmetric Index at Finite Temperature, arXiv:2306.07322 [INSPIRE].
A.H. Anupam, C. Chowdhury and A. Sen, Revisiting Logarithmic Correction to Five Dimensional BPS Black Hole Entropy, arXiv:2308.00038 [INSPIRE].
P. Nayak et al., On the Dynamics of Near-Extremal Black Holes, JHEP 09 (2018) 048 [arXiv:1802.09547] [INSPIRE].
U. Moitra, S.K. Sake, S.P. Trivedi and V. Vishal, Jackiw-Teitelboim Gravity and Rotating Black Holes, JHEP 11 (2019) 047 [arXiv:1905.10378] [INSPIRE].
L.V. Iliesiu and G.J. Turiaci, The statistical mechanics of near-extremal black holes, JHEP 05 (2021) 145 [arXiv:2003.02860] [INSPIRE].
M. Heydeman, L.V. Iliesiu, G.J. Turiaci and W. Zhao, The statistical mechanics of near-BPS black holes, J. Phys. A 55 (2022) 014004 [arXiv:2011.01953] [INSPIRE].
K.S. Kolekar and K. Narayan, AdS2 dilaton gravity from reductions of some nonrelativistic theories, Phys. Rev. D 98 (2018) 046012 [arXiv:1803.06827] [INSPIRE].
N. Banerjee, T. Mandal, A. Rudra and M. Saha, Equivalence of JT gravity and near-extremal black hole dynamics in higher derivative theory, JHEP 01 (2022) 124 [arXiv:2110.04272] [INSPIRE].
A. Bhattacharyya, S. Ghosh and S. Pal, Aspects of \( T\overline{T}+J\overline{T} \) deformed 2D topological gravity: from partition function to late-time SFF, arXiv:2309.16658 [INSPIRE].
L.V. Iliesiu, S. Murthy and G.J. Turiaci, Revisiting the Logarithmic Corrections to the Black Hole Entropy, arXiv:2209.13608 [INSPIRE].
N. Banerjee and M. Saha, Revisiting leading quantum corrections to near extremal black hole thermodynamics, JHEP 07 (2023) 010 [arXiv:2303.12415] [INSPIRE].
A. Fotopoulos, S. Stieberger, T.R. Taylor and B. Zhu, Extended BMS Algebra of Celestial CFT, JHEP 03 (2020) 130 [arXiv:1912.10973] [INSPIRE].
W. Fan, A. Fotopoulos and T.R. Taylor, Soft Limits of Yang-Mills Amplitudes and Conformal Correlators, JHEP 05 (2019) 121 [arXiv:1903.01676] [INSPIRE].
A. Fotopoulos, S. Stieberger, T.R. Taylor and B. Zhu, Extended Super BMS Algebra of Celestial CFT, JHEP 09 (2020) 198 [arXiv:2007.03785] [INSPIRE].
N. Banerjee, T. Rahnuma and R.K. Singh, Asymptotic symmetry of four dimensional Einstein-Yang-Mills and Einstein-Maxwell theory, JHEP 01 (2022) 033 [arXiv:2110.15657] [INSPIRE].
N. Banerjee, T. Rahnuma and R.K. Singh, Soft and collinear limits in \( \mathcal{N} \) = 8 supergravity using double copy formalism, JHEP 04 (2023) 126 [arXiv:2212.11480] [INSPIRE].
N. Banerjee, T. Rahnuma and R.K. Singh, Asymptotic Symmetry algebra of \( \mathcal{N} \) = 8 Supergravity, arXiv:2212.12133 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
D. Kapec, A. Sheta, A. Strominger and C. Toldo, Logarithmic Corrections to Kerr Thermodynamics, arXiv:2310.00848 [INSPIRE].
I. Rakic, M. Rangamani and G.J. Turiaci, Thermodynamics of the near-extremal Kerr spacetime, arXiv:2310.04532 [INSPIRE].
Acknowledgments
We are extremely grateful to Ashoke Sen for discussions and his comments on the work. MS would like to thank ICTS, Bengaluru for their hospitality during an important stage of the work. MS would also like to thank Arindam Bhattacharjee and Rajesh Kumar Gupta for useful discussions. The work of NB is partially supported by SERB POWER grant. Finally, we are thankful to the people of India for their generous support towards fundamental research.
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Banerjee, N., Saha, M. & Srinivasan, S. Logarithmic corrections for near-extremal black holes. J. High Energ. Phys. 2024, 77 (2024). https://doi.org/10.1007/JHEP02(2024)077
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DOI: https://doi.org/10.1007/JHEP02(2024)077