Abstract
We present a numerical study of fully non-linear, rotating and charged hairy black hole solutions in five-dimensional anti-de Sitter space, which originate from a consistent truncation of \( \mathcal{N}=8 \) supergravity, and can be consistently embedded in type IIB supergravity with AdS5×S5 asymptotics. The hairy black holes have one scalar field charged under a U(1) gauge field, and branch from the near-extremal Cvetič, Lü and Pope solutions. We give numerical evidence that the hairy solutions exist arbitrarily close to the BPS bound for all charges, and saturate it in the T → 0 and T → ∞ limits. We give further evidence for the conjecture of Markevičiūtė and Santos, that on the BPS bound, the rotating hairy black holes form a two-parameter family of solutions with finite entropy, and can be regarded as a one-parameter extension of the supersymmetric Gutowski and Reall black hole. We analyse the approach to the supersymmetric limit and explore the full phase diagram. In the planar horizon limit we find a two parameter family of rotating hairy black brane solutions which cannot be obtained via a Lorentz boost. The field theory dual exhibits a spontaneously generated current. The results of this paper suggest rich and intricate structure of hairy black hole solutions in AdS5×S5, and highlight their importance in understanding the thermodynamics of \( \mathcal{N}=4 \) SYM.
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J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
B. de Wit and H. Nicolai, Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions, JHEP 05 (2013) 077 [arXiv:1302.6219] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Nonlinear Kaluza-Klein theory for dual fields, Phys. Rev. D 88 (2013) 125002 [arXiv:1309.0266] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Testing the non-linear flux ansatz for maximal supergravity, Phys. Rev. D 87 (2013) 085038 [arXiv:1303.1013] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Generalised geometry from the ground up, JHEP 02 (2014) 075 [arXiv:1307.8295] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Embedding tensor of Scherk-Schwarz flux compactifications from eleven dimensions, Phys. Rev. D 89 (2014) 045009 [arXiv:1312.1061] [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, Fortsch. Phys. 65 (2017) 1700048 [arXiv:1401.3360] [INSPIRE].
A. Baguet, O. Hohm and H. Samtleben, Consistent Type IIB Reductions to Maximal 5D Supergravity, Phys. Rev. D 92 (2015) 065004 [arXiv:1506.01385] [INSPIRE].
M. Cvetič, H. Lü, C.N. Pope, A. Sadrzadeh and T.A. Tran, Consistent SO(6) reduction of type IIB supergravity on S 5, Nucl. Phys. B 586 (2000) 275 [hep-th/0003103] [INSPIRE].
S. Bhattacharyya, S. Minwalla and K. Papadodimas, Small Hairy Black Holes in AdS 5 × S 5, JHEP 11 (2011) 035 [arXiv:1005.1287] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
M. Cvetič, H. Lü and C.N. Pope, Charged Kerr-de Sitter black holes in five dimensions, Phys. Lett. B 598 (2004) 273 [hep-th/0406196] [INSPIRE].
M. Cvetič, H. Lü and C.N. Pope, Charged rotating black holes in five dimensional U(1)3 gauged N = 2 supergravity, Phys. Rev. D 70 (2004) 081502 [hep-th/0407058] [INSPIRE].
M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Rotating black holes in gauged supergravities: Thermodynamics, supersymmetric limits, topological solitons and time machines, hep-th/0504080 [INSPIRE].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Five-dimensional gauged supergravity black holes with independent rotation parameters, Phys. Rev. D 72 (2005) 041901 [hep-th/0505112] [INSPIRE].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity, Phys. Rev. Lett. 95 (2005) 161301 [hep-th/0506029] [INSPIRE].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Non-extremal rotating black holes in five-dimensional gauged supergravity, Phys. Lett. B 644 (2007) 192 [hep-th/0606213] [INSPIRE].
S.-Q. Wu, General Nonextremal Rotating Charged AdS Black Holes in Five-dimensional U(1)3 Gauged Supergravity: A Simple Construction Method, Phys. Lett. B 707 (2012) 286 [arXiv:1108.4159] [INSPIRE].
J.B. Gutowski and H.S. Reall, Supersymmetric AdS 5 black holes, JHEP 02 (2004) 006 [hep-th/0401042] [INSPIRE].
J.B. Gutowski and H.S. Reall, General supersymmetric AdS 5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].
H.K. Kunduri, J. Lucietti and H.S. Reall, Supersymmetric multi-charge AdS 5 black holes, JHEP 04 (2006) 036 [hep-th/0601156] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].
J.P. Gauntlett, J.B. Gutowski and N.V. Suryanarayana, A Deformation of AdS 5 × S 5, Class. Quant. Grav. 21 (2004) 5021 [hep-th/0406188] [INSPIRE].
J. Markevičiutė and J.E. Santos, Hairy black holes in AdS 5 × S 5, JHEP 06 (2016) 096 [arXiv:1602.03893] [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, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
O.J.C. Dias, R. Monteiro, H.S. Reall and J.E. Santos, A Scalar field condensation instability of rotating anti-de Sitter black holes, JHEP 11 (2010) 036 [arXiv:1007.3745] [INSPIRE].
P. Basu, J. Bhattacharya, S. Bhattacharyya, R. Loganayagam, S. Minwalla and V. Umesh, Small Hairy Black Holes in Global AdS Spacetime, JHEP 10 (2010) 045 [arXiv:1003.3232] [INSPIRE].
O.J.C. Dias, P. Figueras, S. Minwalla, P. Mitra, R. Monteiro and J.E. Santos, Hairy black holes and solitons in global AdS 5, JHEP 08 (2012) 117 [arXiv:1112.4447] [INSPIRE].
S.A. Gentle, M. Rangamani and B. Withers, A Soliton Menagerie in AdS, JHEP 05 (2012) 106 [arXiv:1112.3979] [INSPIRE].
Y. Brihaye and B. Hartmann, A Scalar field instability of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time, JHEP 03 (2012) 050 [arXiv:1112.6315] [INSPIRE].
Z.W. Chong, H. Lü and C.N. Pope, BPS geometries and AdS bubbles, Phys. Lett. B 614 (2005) 96 [hep-th/0412221] [INSPIRE].
J.T. Liu, H. Lü, C.N. Pope and J.F. Vazquez-Poritz, New supersymmetric solutions of N = 2, D = 5 gauged supergravity with hyperscalars, JHEP 10 (2007) 093 [arXiv:0705.2234] [INSPIRE].
J.T. Liu, H. Lü, C.N. Pope and J.F. Vazquez-Poritz, Bubbling AdS black holes, JHEP 10 (2007) 030 [hep-th/0703184] [INSPIRE].
B. Chen et al., Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity, JHEP 10 (2007) 003 [arXiv:0704.2233] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
A. Strominger, Black hole entropy from near horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS 4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Exact microstate counting for dyonic black holes in AdS4, Phys. Lett. B 771 (2017) 462 [arXiv:1608.07294] [INSPIRE].
J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An Index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].
M. Berkooz, D. Reichmann and J. Simon, A Fermi Surface Model for Large Supersymmetric AdS 5 Black Holes, JHEP 01 (2007) 048 [hep-th/0604023] [INSPIRE].
H.K. Kunduri and J. Lucietti, Near-horizon geometries of supersymmetric AdS 5 black holes, JHEP 12 (2007) 015 [arXiv:0708.3695] [INSPIRE].
J. Markevičiūtė and J.E. Santos, Evidence for the existence of a novel class of supersymmetric black holes with AdS 5 × S 5 asymptotics, Class. Quant. Grav. 36 (2019) 02LT01 [arXiv:1806.01849] [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].
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].
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].
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].
A. Ashtekar and A. Magnon, Asymptotically anti-de Sitter space-times, Class. Quant. Grav. 1 (1984) L39 [INSPIRE].
M. Henneaux and C. Teitelboim, Asymptotically anti-de Sitter Spaces, Commun. Math. Phys. 98 (1985) 391 [INSPIRE].
M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [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].
O. Madden and S.F. Ross, On uniqueness of charged Kerr-AdS black holes in five dimensions, Class. Quant. Grav. 22 (2005) 515 [hep-th/0409188] [INSPIRE].
D. Klemm and W.A. Sabra, General (anti-)de Sitter black holes in five-dimensions, JHEP 02 (2001) 031 [hep-th/0011016] [INSPIRE].
R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys. 172 (1986) 304 [INSPIRE].
M. Headrick, S. Kitchen and T. Wiseman, A New approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav. 27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].
P. Figueras, J. Lucietti and T. Wiseman, Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua, Class. Quant. Grav. 28 (2011) 215018 [arXiv:1104.4489] [INSPIRE].
T. Wiseman, Numerical construction of static and stationary black holes, in Black holes in higher dimensions, G.T. Horowitz, ed., pp. 233-270 (2012) [arXiv:1107.5513] [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Numerical Methods for Finding Stationary Gravitational Solutions, Class. Quant. Grav. 33 (2016) 133001 [arXiv:1510.02804] [INSPIRE].
P. Figueras and T. Wiseman, On the existence of stationary Ricci solitons, Class. Quant. Grav. 34 (2017) 145007 [arXiv:1610.06178] [INSPIRE].
A. Ashtekar and S. Das, Asymptotically Anti-de Sitter space-times: Conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [INSPIRE].
J. Markevičiūtė and J.E. Santos, Stirring a black hole, JHEP 02 (2018) 060 [arXiv:1712.07648] [INSPIRE].
G.T. Horowitz and S.F. Ross, Naked black holes, Phys. Rev. D 56 (1997) 2180 [hep-th/9704058] [INSPIRE].
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].
J.F. Pedraza, W. Sybesma and M.R. Visser, Hyperscaling violating black holes with spherical and hyperbolic horizons, Class. Quant. Grav. 36 (2019) 054002 [arXiv:1807.09770] [INSPIRE].
S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) R5412 [hep-th/9508072] [INSPIRE].
A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B 383 (1996) 39 [hep-th/9602111] [INSPIRE].
S. Ferrara and R. Kallosh, Supersymmetry and attractors, Phys. Rev. D 54 (1996) 1514 [hep-th/9602136] [INSPIRE].
S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525 [hep-th/9603090] [INSPIRE].
A.H. Chamseddine, S. Ferrara, G.W. Gibbons and R. Kallosh, Enhancement of supersymmetry near 5-D black hole horizon, Phys. Rev. D 55 (1997) 3647 [hep-th/9610155] [INSPIRE].
R. Kallosh, A. Rajaraman and W.K. Wong, Supersymmetric rotating black holes and attractors, Phys. Rev. D 55 (1997) R3246 [hep-th/9611094] [INSPIRE].
S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, An extremization principle for the entropy of rotating BPS black holes in AdS 5, JHEP 07 (2017) 106 [arXiv:1705.05383] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, A note on the entropy of rotating BPS AdS 7 × S 4 black holes, JHEP 05 (2018) 121 [arXiv:1803.07568] [INSPIRE].
S. Kim and K.-M. Lee, 1/16-BPS Black Holes and Giant Gravitons in the AdS 5 × S 5 Space, JHEP 12 (2006) 077 [hep-th/0607085] [INSPIRE].
M. Cvetič and S.S. Gubser, Phases of R charged black holes, spinning branes and strongly coupled gauge theories, JHEP 04 (1999) 024 [hep-th/9902195] [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].
H.K. Kunduri and J. Lucietti, Notes on non-extremal, charged, rotating black holes in minimal D = 5 gauged supergravity, Nucl. Phys. B 724 (2005) 343 [hep-th/0504158] [INSPIRE].
B.P. Dolan, Thermodynamic stability of asymptotically anti-de Sitter rotating black holes in higher dimensions, Class. Quant. Grav. 31 (2014) 165011 [arXiv:1403.1507] [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
H.B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd Edition, Wiley (1985).
G.T. Horowitz, Introduction to Holographic Superconductors, Lect. Notes Phys. 828 (2011) 313 [arXiv:1002.1722] [INSPIRE].
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
F. Aprile, D. Roest and J.G. Russo, Holographic Superconductors from Gauged Supergravity, JHEP 06 (2011) 040 [arXiv:1104.4473] [INSPIRE].
J. Sonner and B. Withers, A gravity derivation of the Tisza-Landau Model in AdS/CFT, Phys. Rev. D 82 (2010) 026001 [arXiv:1004.2707] [INSPIRE].
D. Arean, M. Bertolini, C. Krishnan and T. Prochazka, Type IIB Holographic Superfluid Flows, JHEP 03 (2011) 008 [arXiv:1010.5777] [INSPIRE].
A. Buchel and C. Pagnutti, Exotic Hairy Black Holes, Nucl. Phys. B 824 (2010) 85 [arXiv:0904.1716] [INSPIRE].
A. Donos and J.P. Gauntlett, Superfluid black branes in AdS 4 × S 7, JHEP 06 (2011) 053 [arXiv:1104.4478] [INSPIRE].
S.A. Gentle and B. Withers, Superconducting instabilities of R-charged black branes, JHEP 10 (2012) 006 [arXiv:1207.3086] [INSPIRE].
R.-G. Cai, L. Li and L.-F. Li, A Holographic P-wave Superconductor Model, JHEP 01 (2014) 032 [arXiv:1309.4877] [INSPIRE].
E. Banks and J.P. Gauntlett, A new phase for the anisotropic N = 4 super Yang-Mills plasma, JHEP 09 (2015) 126 [arXiv:1506.07176] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].
C.P. Herzog, An Analytic Holographic Superconductor, Phys. Rev. D 81 (2010) 126009 [arXiv:1003.3278] [INSPIRE].
J. Sonner, A Rotating Holographic Superconductor, Phys. Rev. D 80 (2009) 084031 [arXiv:0903.0627] [INSPIRE].
J. Fernandez-Gracia and B. Fiol, A No-hair theorem for extremal black branes, JHEP 11 (2009) 054 [arXiv:0906.2353] [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].
F. Aprile, D. Rodriguez-Gomez and J.G. Russo, p-wave Holographic Superconductors and five-dimensional gauged Supergravity, JHEP 01 (2011) 056 [arXiv:1011.2172] [INSPIRE].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from Superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].
Ó.J.C. Dias and R. Masachs, Hairy black holes and the endpoint of AdS4 charged superradiance, JHEP 02 (2017) 128 [arXiv:1610.03496] [INSPIRE].
O.J.C. Dias and R. Masachs, Charged black hole bombs in a Minkowski cavity, Class. Quant. Grav. 35 (2018) 184001 [arXiv:1801.10176] [INSPIRE].
O.J.C. Dias and R. Masachs, Evading no-hair theorems: hairy black holes in a Minkowski box, Phys. Rev. D 97 (2018) 124030 [arXiv:1802.01603] [INSPIRE].
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Markevičiūtė, J. Rotating hairy black holes in AdS5 × S5. J. High Energ. Phys. 2019, 110 (2019). https://doi.org/10.1007/JHEP03(2019)110
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DOI: https://doi.org/10.1007/JHEP03(2019)110