Abstract
The low-temperature thermodynamics of near-extremal rotating black holes has recently been revisited to incorporate one-loop contributions that are dominant in this regime. We discuss these quantum corrections to the gravitational path integral for asymptotically Anti de-Sitter black holes in four and five dimensions. In four dimensions we explicitly consider Kerr-AdS4, Kerr-Newman-AdS4 and the rotating black hole in \( \mathcal{N} \) = 4 gauged supergravity with two scalars and two electric charges turned on. In five dimensions we explicitly address the asymptotically flat Myers-Perry black hole and the Kerr-AdS5 black hole. In every case we find that tensor modes contribute \( \frac{3}{2}\log {T}_{\textrm{Hawking}} \) to the low-temperature thermodynamics. We identify the root cause of this universality in two facts: (i) the universal presence of a SL(2, ℝ) subgroup of isometries in the near-horizon geometry and (ii) a set of cancellations in the Lichnerowicz operator. We show that these two conditions hold for near-extremal black holes in asymptotically flat and asymptotically AdS spacetimes of various dimensions.
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References
J. Preskill et al., Limitations on the statistical description of black holes, Mod. Phys. Lett. A 6 (1991) 2353 [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].
J. Boruch, M.T. Heydeman, L.V. Iliesiu and G.J. Turiaci, BPS and near-BPS black holes in AdS5 and their spectrum in \( \mathcal{N} \) = 4 SYM, arXiv:2203.01331 [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
K. Jensen, Chaos in AdS2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
T.G. Mertens and G.J. Turiaci, Solvable models of quantum black holes: a review on Jackiw-Teitelboim gravity, Living Rev. Rel. 26 (2023) 4 [arXiv:2210.10846] [INSPIRE].
G.J. Turiaci, New insights on near-extremal black holes, arXiv:2307.10423 [INSPIRE].
R. Emparan and J.M. Magan, Tearing down spacetime with quantum disentanglement, JHEP 03 (2024) 078 [arXiv:2312.06803] [INSPIRE].
A. Castro and V. Godet, Breaking away from the near horizon of extreme Kerr, SciPost Phys. 8 (2020) 089 [arXiv:1906.09083] [INSPIRE].
A. Castro et al., Gravitational perturbations from NHEK to Kerr, JHEP 07 (2021) 218 [arXiv:2102.08060] [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].
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].
N. Banerjee, M. Saha and S. Srinivasan, Logarithmic corrections for near-extremal black holes, JHEP 02 (2024) 077 [arXiv:2311.09595] [INSPIRE].
M. David, J. Nian and L.A. Pando Zayas, Gravitational Cardy Limit and AdS Black Hole Entropy, JHEP 11 (2020) 041 [arXiv:2005.10251] [INSPIRE].
M. David, V. Godet, Z. Liu and L.A. Pando Zayas, Non-topological logarithmic corrections in minimal gauged supergravity, JHEP 08 (2022) 043 [arXiv:2112.09444] [INSPIRE].
B. Carter, Hamilton-Jacobi and Schrodinger separable solutions of Einstein’s equations, Commun. Math. Phys. 10 (1968) 280 [INSPIRE].
J.F. Plebanski and M. Demianski, Rotating, charged, and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [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].
G.W. Gibbons, M.J. Perry and C.N. Pope, The first law of thermodynamics for Kerr-anti-de Sitter black holes, Class. Quant. Grav. 22 (2005) 1503 [hep-th/0408217] [INSPIRE].
J.M. Bardeen and G.T. Horowitz, The Extreme Kerr throat geometry: A vacuum analog of AdS2 × S2, Phys. Rev. D 60 (1999) 104030 [hep-th/9905099] [INSPIRE].
S.M. Christensen and M.J. Duff, Quantizing Gravity with a Cosmological Constant, Nucl. Phys. B 170 (1980) 480 [INSPIRE].
R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].
A. González Lezcano, I. Jeon and A. Ray, Supersymmetric localization: \( \mathcal{N} \) = (2) theories on S2 and AdS2, JHEP 07 (2023) 056 [Erratum ibid. 09 (2023) 003] [arXiv:2302.10370] [INSPIRE].
Z.-W. Chong, M. Cvetic, H. Lu and C.N. Pope, Charged rotating black holes in four-dimensional gauged and ungauged supergravities, Nucl. Phys. B 717 (2005) 246 [hep-th/0411045] [INSPIRE].
M. Cvetic, G.W. Gibbons, H. Lu and C.N. Pope, Rotating black holes in gauged supergravities: Thermodynamics, supersymmetric limits, topological solitons and time machines, hep-th/0504080 [INSPIRE].
D.D.K. Chow and G. Compère, Dyonic AdS black holes in maximal gauged supergravity, Phys. Rev. D 89 (2014) 065003 [arXiv:1311.1204] [INSPIRE].
S. Choi, C. Hwang, S. Kim and J. Nahmgoong, Entropy Functions of BPS Black Holes in AdS4 and AdS6, J. Korean Phys. Soc. 76 (2020) 101 [arXiv:1811.02158] [INSPIRE].
D. Cassani and L. Papini, The BPS limit of rotating AdS black hole thermodynamics, JHEP 09 (2019) 079 [arXiv:1906.10148] [INSPIRE].
S. Choi, C. Hwang and S. Kim, Quantum vortices, M2-branes and black holes, arXiv:1908.02470 [INSPIRE].
J. Nian and L.A. Pando Zayas, Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization, JHEP 03 (2020) 081 [arXiv:1909.07943] [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].
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].
J.T. Liu, L.A. Pando Zayas, V. Rathee and W. Zhao, Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity, JHEP 01 (2018) 026 [arXiv:1707.04197] [INSPIRE].
I. Jeon and S. Lal, Logarithmic Corrections to Entropy of Magnetically Charged AdS4 Black Holes, Phys. Lett. B 774 (2017) 41 [arXiv:1707.04208] [INSPIRE].
J.T. Liu, L.A. Pando Zayas, V. Rathee and W. Zhao, One-Loop Test of Quantum Black Holes in anti-de Sitter Space, Phys. Rev. Lett. 120 (2018) 221602 [arXiv:1711.01076] [INSPIRE].
L.A. Pando Zayas and Y. Xin, Universal logarithmic behavior in microstate counting and the dual one-loop entropy of AdS4 black holes, Phys. Rev. D 103 (2021) 026003 [arXiv:2008.03239] [INSPIRE].
D. Gang, N. Kim and L.A. Pando Zayas, Precision Microstate Counting for the Entropy of Wrapped M5-branes, JHEP 03 (2020) 164 [arXiv:1905.01559] [INSPIRE].
F. Benini, D. Gang and L.A. Pando Zayas, Rotating Black Hole Entropy from M5 Branes, JHEP 03 (2020) 057 [arXiv:1909.11612] [INSPIRE].
M. David and J. Nian, Universal entropy and hawking radiation of near-extremal AdS4 black holes, JHEP 04 (2021) 256 [arXiv:2009.12370] [INSPIRE].
F. Larsen and S. Paranjape, Thermodynamics of near BPS black holes in AdS4 and AdS7, JHEP 10 (2021) 198 [arXiv:2010.04359] [INSPIRE].
A. Castro, F. Larsen and I. Papadimitriou, 5D rotating black holes and the nAdS2/nCFT1 correspondence, JHEP 10 (2018) 042 [arXiv:1807.06988] [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].
A. Castro, J.F. Pedraza, C. Toldo and E. Verheijden, Rotating 5D Black Holes: Interactions and deformations near extremality, SciPost Phys. 11 (2021) 102 [arXiv:2106.00649] [INSPIRE].
R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys. 172 (1986) 304 [INSPIRE].
R.C. Myers, Myers-Perry black holes, in Black holes in higher dimensions, G.T. Horowitz ed., Cambridge University Press (2012), p. 101–133 [arXiv:1111.1903] [INSPIRE].
A. Galajinsky, Near horizon black holes in diverse dimensions and integrable models, Phys. Rev. D 87 (2013) 024023 [arXiv:1209.5034] [INSPIRE].
A. Galajinsky, A. Nersessian and A. Saghatelian, Superintegrable models related to near horizon extremal Myers-Perry black hole in arbitrary dimension, JHEP 06 (2013) 002 [arXiv:1303.4901] [INSPIRE].
H.K. Kunduri, J. Lucietti and H.S. Reall, Near-horizon symmetries of extremal black holes, Class. Quant. Grav. 24 (2007) 4169 [arXiv:0705.4214] [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes, JHEP 10 (2019) 062 [arXiv:1810.11442] [INSPIRE].
S. Choi, J. Kim, S. Kim and J. Nahmgoong, Large AdS black holes from QFT, arXiv:1810.12067 [INSPIRE].
F. Benini and E. Milan, Black Holes in 4D \( \mathcal{N} \) = 4 Super-Yang-Mills Field Theory, Phys. Rev. X 10 (2020) 021037 [arXiv:1812.09613] [INSPIRE].
A. González Lezcano, J. Hong, J.T. Liu and L.A. Pando Zayas, Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions, JHEP 01 (2021) 001 [arXiv:2007.12604] [INSPIRE].
M. David, A. Lezcano González, J. Nian and L.A. Pando Zayas, Logarithmic corrections to the entropy of rotating black holes and black strings in AdS5, JHEP 04 (2022) 160 [arXiv:2106.09730] [INSPIRE].
D. Astefanesei et al., Rotating attractors, JHEP 10 (2006) 058 [hep-th/0606244] [INSPIRE].
H.K. Kunduri and J. Lucietti, A classification of near-horizon geometries of extremal vacuum black holes, J. Math. Phys. 50 (2009) 082502 [arXiv:0806.2051] [INSPIRE].
P. Figueras, H.K. Kunduri, J. Lucietti and M. Rangamani, Extremal vacuum black holes in higher dimensions, Phys. Rev. D 78 (2008) 044042 [arXiv:0803.2998] [INSPIRE].
F. Benini, S. Soltani and Z. Zhang, A quantum mechanics for magnetic horizons, JHEP 05 (2023) 070 [arXiv:2212.00672] [INSPIRE].
Y.B. Zel’Dovich, Generation of Waves by a Rotating Body, JETP Lett. 14 (1971) 180.
V. Cardoso and O.J.C. Dias, Small Kerr-anti-de Sitter black holes are unstable, Phys. Rev. D 70 (2004) 084011 [hep-th/0405006] [INSPIRE].
V. Cardoso, O.J.C. Dias, J.P.S. Lemos and S. Yoshida, The black hole bomb and superradiant instabilities, Phys. Rev. D 70 (2004) 044039 [Erratum ibid. 70 (2004) 049903] [hep-th/0404096] [INSPIRE].
S. Kim et al., Grey Galaxies’ as an endpoint of the Kerr-AdS superradiant instability, JHEP 11 (2023) 024 [arXiv:2305.08922] [INSPIRE].
J.K. Ghosh and L.A. Pando Zayas, Comments on Sen’s classical entropy function for static and rotating AdS4 black holes, Nucl. Phys. B 993 (2023) 116270 [arXiv:2009.11147] [INSPIRE].
Acknowledgments
We are grateful to Alejandra Castro, Marina David, Matt Heydeman, Imtak Jeon, Alfredo Gonzàlez Lezcano, Juan Maldacena, Jun Nian and Joaquín Turiaci for discussions on related topics. This work is supported in part by the U.S. Department of Energy under grant DESC0007859. LPZ gratefully acknowledges support from an IBM Einstein fellowship during 2022/2023 while at the Institute for Advanced Study. AR is supported by an appointment to the JRG program at the APCTP through the Science and Technology Promotion Fund and the Lottery Fund of the Korean Government, by the Korean Local Governments - Gyeongsangbuk-do Province and Pohang City and by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2021R1F1A1048531). SM acknowledges the warm hospitality of APCTP, Postech, South Korea during the APCTP Winter School on Fundamental Physics 2024, where a part of this work was carried out. SM is financially supported by the institute post-doctoral fellowship of IITK.
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Maulik, S., Pando Zayas, L.A., Ray, A. et al. Universality in logarithmic temperature corrections to near-extremal rotating black hole thermodynamics in various dimensions. J. High Energ. Phys. 2024, 34 (2024). https://doi.org/10.1007/JHEP06(2024)034
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DOI: https://doi.org/10.1007/JHEP06(2024)034