Abstract
Kerr-AdSd+1 black holes for d ≥ 3 suffer from classical superradiant instabilities over a range of masses above extremality. We conjecture that these instabilities settle down into Grey Galaxies (GGs) — a new class of coarse-grained solutions to Einstein’s equations which we construct in d = 3. Grey Galaxies are made up of a black hole with critical angular velocity ω = 1 in the ‘centre’ of AdS, surrounded by a large flat disk of thermal bulk gas that revolves around the centre of AdS at the speed of light. The gas carries a finite fraction of the total energy, as its parametrically low energy density and large radius are inversely related. GGs exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr-AdS black holes and the bulk gas. Their boundary stress tensor is the sum of a smooth ‘black hole’ contribution and a peaked gas contribution that is delta function localized around the equator of the boundary sphere in the large N limit. We also construct another class of solutions with the same charges; ‘Revolving Black Holes (RBHs)’. RBHs are macroscopically charged SO(d, 2) descendants of AdS-Kerr solutions, and consist of ω = 1 black holes revolving around the centre of AdS at a fixed radial location but in a quantum wave function in the angular directions. RBH solutions are marginally entropically subdominant to GG solutions and do not constitute the endpoint of the superradiant instability. Nonetheless, we argue that supersymmetric versions of these solutions have interesting implications for the spectrum of supersymmetric states in, e.g. \( \mathcal{N} \) = 4 Yang-Mills theory.
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References
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].
Y.B. Zel’Dovich, Generation of Waves by a Rotating Body, JETP Lett. 14 (1971) 180.
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
B. Carter, Black holes equilibrium states, in the proceedings of the Les Houches Summer School of Theoretical Physics: Black Holes, Les Houches France, August (1972), p. 57–214 [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Black holes with a single Killing vector field: black resonators, JHEP 12 (2015) 171 [arXiv:1505.04793] [INSPIRE].
T. Ishii and K. Murata, Black resonators and geons in AdS5, Class. Quant. Grav. 36 (2019) 125011 [arXiv:1810.11089] [INSPIRE].
P.M. Chesler and D.A. Lowe, Nonlinear Evolution of the AdS4 Superradiant Instability, Phys. Rev. Lett. 122 (2019) 181101 [arXiv:1801.09711] [INSPIRE].
T. Ishii, K. Murata, J.E. Santos and B. Way, Superradiant instability of black resonators and geons, JHEP 07 (2020) 206 [arXiv:2005.01201] [INSPIRE].
P.M. Chesler, Hairy black resonators and the AdS4 superradiant instability, Phys. Rev. D 105 (2022) 024026 [arXiv:2109.06901] [INSPIRE].
P. Basu et al., Small Hairy Black Holes in Global AdS Spacetime, JHEP 10 (2010) 045 [arXiv:1003.3232] [INSPIRE].
S. Bhattacharyya, S. Minwalla and K. Papadodimas, Small Hairy Black Holes in AdS5 × S5, JHEP 11 (2011) 035 [arXiv:1005.1287] [INSPIRE].
O.J.C. Dias et al., Hairy black holes and solitons in global AdS5, JHEP 08 (2012) 117 [arXiv:1112.4447] [INSPIRE].
S.R. Green, S. Hollands, A. Ishibashi and R.M. Wald, Superradiant instabilities of asymptotically anti-de Sitter black holes, Class. Quant. Grav. 33 (2016) 125022 [arXiv:1512.02644] [INSPIRE].
H.K. Kunduri, J. Lucietti and H.S. Reall, Gravitational perturbations of higher dimensional rotating black holes: Tensor perturbations, Phys. Rev. D 74 (2006) 084021 [hep-th/0606076] [INSPIRE].
K. Murata, Instabilities of Kerr-AdS5 × S5 Spacetime, Prog. Theor. Phys. 121 (2009) 1099 [arXiv:0812.0718] [INSPIRE].
V. Cardoso et al., Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS, JHEP 04 (2014) 183 [arXiv:1312.5323] [INSPIRE].
B.E. Niehoff, J.E. Santos and B. Way, Towards a violation of cosmic censorship, Class. Quant. Grav. 33 (2016) 185012 [arXiv:1510.00709] [INSPIRE].
H. Kodama, R.A. Konoplya and A. Zhidenko, Gravitational instability of simply rotating AdS black holes in higher dimensions, Phys. Rev. D 79 (2009) 044003 [arXiv:0812.0445] [INSPIRE].
S. Minwalla, A. Mishra, N. Prabhakar and T. Sharma, The Hilbert space of large N Chern-Simons matter theories, JHEP 07 (2022) 025 [arXiv:2201.08410] [INSPIRE].
O.J.C. Dias, G.T. Horowitz and J.E. Santos, Black holes with only one Killing field, JHEP 07 (2011) 115 [arXiv:1105.4167] [INSPIRE].
T. Ishii, K. Murata, J.E. Santos and B. Way, Multioscillating black holes, JHEP 05 (2021) 011 [arXiv:2101.06325] [INSPIRE].
Ó.J.C. Dias and J.E. Santos, Boundary Conditions for Kerr-AdS Perturbations, JHEP 10 (2013) 156 [arXiv:1302.1580] [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].
O. Aharony et al., The Hagedorn-deconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla and T. Wiseman, Black hole-black string phase transitions in thermal 1 + 1 dimensional supersymmetric Yang-Mills theory on a circle, Class. Quant. Grav. 21 (2004) 5169 [hep-th/0406210] [INSPIRE].
O. Aharony et al., A First order deconfinement transition in large N Yang-Mills theory on a small S3, Phys. Rev. D 71 (2005) 125018 [hep-th/0502149] [INSPIRE].
O. Aharony et al., The Phase structure of low dimensional large N gauge theories on Tori, JHEP 01 (2006) 140 [hep-th/0508077] [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].
S.W. Hawking and H.S. Reall, Charged and rotating AdS black holes and their CFT duals, Phys. Rev. D 61 (2000) 024014 [hep-th/9908109] [INSPIRE].
S. Bhattacharyya, S. Lahiri, R. Loganayagam and S. Minwalla, Large rotating AdS black holes from fluid mechanics, JHEP 09 (2008) 054 [arXiv:0708.1770] [INSPIRE].
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 783 [hep-th/9712074] [INSPIRE].
D.J. Gross, M.J. Perry and L.G. Yaffe, Instability of Flat Space at Finite Temperature, Phys. Rev. D 25 (1982) 330 [INSPIRE].
D. Marolf and J.E. Santos, Stability of the microcanonical ensemble in Euclidean Quantum Gravity, JHEP 11 (2022) 046 [arXiv:2202.12360] [INSPIRE].
F. Denef, S.A. Hartnoll and S. Sachdev, Black hole determinants and quasinormal modes, Class. Quant. Grav. 27 (2010) 125001 [arXiv:0908.2657] [INSPIRE].
F. Denef, S.A. Hartnoll and S. Sachdev, Quantum oscillations and black hole ringing, Phys. Rev. D 80 (2009) 126016 [arXiv:0908.1788] [INSPIRE].
J. Kaplan, Lectures on AdS/CFT from the Bottom Up, https://sites.krieger.jhu.edu/jared-kaplan/files/2016/05/AdSCFTCourseNotesCurrentPublic.pdf.
L.F. Alday, M. Kologlu and A. Zhiboedov, Holographic correlators at finite temperature, JHEP 06 (2021) 082 [arXiv:2009.10062] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
J.B. Gutowski and H.S. Reall, Supersymmetric AdS5 black holes, JHEP 02 (2004) 006 [hep-th/0401042] [INSPIRE].
J. Markeviciute and J.E. Santos, Evidence for the existence of a novel class of supersymmetric black holes with AdS5 × S5 asymptotics, Class. Quant. Grav. 36 (2019) 02LT01 [arXiv:1806.01849] [INSPIRE].
J. Markeviciute, Rotating Hairy Black Holes in AdS5 × S5, JHEP 03 (2019) 110 [arXiv:1809.04084] [INSPIRE].
S. Choi et al., Towards quantum black hole microstates, arXiv:2304.10155 [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
K. Murata, S. Kinoshita and N. Tanahashi, Non-equilibrium Condensation Process in a Holographic Superconductor, JHEP 07 (2010) 050 [arXiv:1005.0633] [INSPIRE].
G. Cuomo and Z. Komargodski, Giant Vortices and the Regge Limit, JHEP 01 (2023) 006 [arXiv:2210.15694] [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].
H. Elvang and P. Figueras, Black Saturn, JHEP 05 (2007) 050 [hep-th/0701035] [INSPIRE].
A.A. Kirillov, Lectures on the Orbit Method, AMS (2004) [ISBN: 9780821835302].
J.M. Maldacena and A. Strominger, AdS3 black holes and a stringy exclusion principle, JHEP 12 (1998) 005 [hep-th/9804085] [INSPIRE].
C. Grosche and F. Steiner, Handbook of Feynman Path Integrals, Springer Berlin Heidelberg (1998) [https://doi.org/10.1007/bfb0109520] [INSPIRE].
Acknowledgments
We would like to thank O. Aharony, J. Choi, F. Denef, S. Hellerman, I. Halder, S. Hartnoll, G. Horowitz, T. Ishii, D. Jain, D. Jatkar, V. Krishna, K. Lee, S. Lee, G. Mandal, H. Ooguri, O. Parrikar, D. Simmons-Duffin, S. Trivedi, A. Virmani, S. Wadia, H. Yavartanoo and especially N. Benjamin, A. Gadde and J. Santos for very useful discussions. We would also like to thank N. Benjamin, I. Halder, S. Hartnoll, G. Horowitz, T. Ishii, Z. Komargodski, J. Maldacena, K. Murata, J. Santos, A. Virmani, S. Wadia and A. Zhiboedov for comments on the manuscript. The work of SK and EL was supported by the NRF grant 2021R1A2C2012350. The work of CP and SM was supported by the Infosys Endowment for the study of the Quantum Structure of Spacetime. The work of SM and CP is supported by the J C Bose Fellowship JCB/2019/000052. The work of SK was supported in part by an ISF, center for excellence grant (grant number 2289/18), Simons Foundation grant 994296, and Koshland Fellowship. The work of JL was supported in part by the US Department of Energy under the award number DE-SC0011632. SK, SM and CP would also like to acknowledge their debt to the people of India for their steady support to the study of the basic sciences.
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Kim, S., Kundu, S., Lee, E. et al. Grey Galaxies’ as an endpoint of the Kerr-AdS superradiant instability. J. High Energ. Phys. 2023, 24 (2023). https://doi.org/10.1007/JHEP11(2023)024
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DOI: https://doi.org/10.1007/JHEP11(2023)024