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Hairy black hole entropy and the role of solitons in three dimensions. (English) Zbl 1309.81182
Summary: Scalar fields minimally coupled to General Relativity in three dimensions are considered. For certain families of self-interaction potentials, new exact solutions describing solitons and hairy black holes are found. It is shown that they fit within a relaxed set of asymptotically AdS boundary conditions, whose asymptotic symmetry group coincides with the one for pure gravity and its canonical realization possesses the standard central extension. Solitons are devoid of integration constants and their corresponding (negative) mass, fixed and determined by nontrivial functions of the self-interaction couplings, is shown to be bounded from below by the mass of AdS spacetime. Remarkably, assuming that a soliton corresponds to the ground state of the sector of the theory for which the scalar field is switched on, the semiclassical entropy of the corresponding hairy black hole is exactly reproduced from Cardy formula once nonvanishing lowest eigenvalues of the Virasoro operators are taking into account, being precisely given by the ones associated to the soliton. This provides further evidence about the robustness of previous results, for which the ground state energy instead of the central charge appears to play the leading role in order to reproduce the hairy black hole entropy from a microscopic counting.

MSC:
81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
35C08 Soliton solutions
83C57 Black holes
83C15 Exact solutions to problems in general relativity and gravitational theory
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
94A17 Measures of information, entropy
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References:
[1] Strominger, A.; Vafa, C., Microscopic origin of the bekenstein-Hawking entropy, Phys. Lett., B 379, 99, (1996)
[2] Strominger, A., Black hole entropy from near horizon microstates, JHEP, 02, 009, (1998)
[3] Birmingham, D.; Sachs, I.; Sen, S., Entropy of three-dimensional black holes in string theory, Phys. Lett., B 424, 275, (1998)
[4] Carlip, S., Conformal field theory, (2+1)-dimensional gravity and the BTZ black hole, Class. Quant. Grav., 22, r85, (2005)
[5] Guica, M.; Hartman, T.; Song, W.; Strominger, A., The Kerr/CFT correspondence, Phys. Rev., D 80, 124008, (2009)
[6] Carlip, S., Effective conformal descriptions of black hole entropy, Entropy, 13, 1355, (2011)
[7] M. Cvetič and F. Larsen, Conformal Symmetry for General Black Holes, arXiv:1106.3341 [INSPIRE].
[8] M. Cvetič and F. Larsen, Conformal Symmetry for Black Holes in Four Dimensions, arXiv:1112.4846. 24 pages,typos corrected [INSPIRE].
[9] Brown, J.; Henneaux, M., Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys., 104, 207, (1986)
[10] J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2 (1998) 231 [Int. J. Theor. Phys.38 (1999) 1133] [hep-th/9711200] [INSPIRE].
[11] Gubser, S.; Klebanov, IR; Polyakov, AM, Gauge theory correlators from noncritical string theory, Phys. Lett., B 428, 105, (1998)
[12] Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253, (1998)
[13] Cardy, JL, Operator content of two-dimensional conformally invariant theories, Nucl. Phys., B 270, 186, (1986)
[14] Bañados, M.; Teitelboim, C.; Zanelli, J., The black hole in three-dimensional space-time, Phys. Rev. Lett., 69, 1849, (1992)
[15] Bañados, M.; Henneaux, M.; Teitelboim, C.; Zanelli, J., Geometry of the (2+1) black hole, Phys. Rev., D 48, 1506, (1993)
[16] Correa, F.; Martínez, C.; Troncoso, R., Scalar solitons and the microscopic entropy of hairy black holes in three dimensions, JHEP, 01, 034, (2011)
[17] Carlip, S., Entropy from conformal field theory at Killing horizons, Class. Quant. Grav., 16, 3327, (1999)
[18] Park, M-I, Fate of three-dimensional black holes coupled to a scalar field and the bekenstein-Hawking entropy, Phys. Lett., B 597, 237, (2004)
[19] Loran, F.; Sheikh-Jabbari, M.; Vincon, M., Beyond logarithmic corrections to cardy formula, JHEP, 01, 110, (2011)
[20] Henneaux, M.; Martínez, C.; Troncoso, R.; Zanelli, J., Black holes and asymptotics of 2 + 1 gravity coupled to a scalar field, Phys. Rev., D 65, 104007, (2002)
[21] Breitenlohner, P.; Freedman, DZ, Positive energy in anti-de Sitter backgrounds and gauged extended supergravity, Phys. Lett., B 115, 197, (1982)
[22] Breitenlohner, P.; Freedman, DZ, Stability in gauged extended supergravity, Annals Phys., 144, 249, (1982)
[23] Mezincescu, L.; Townsend, P., Stability at a local maximum in higher dimensional anti-de Sitter space and applications to supergravity, Annals Phys., 160, 406, (1985)
[24] Regge, T.; Teitelboim, C., Role of surface integrals in the Hamiltonian formulation of general relativity, Annals Phys., 88, 286, (1974)
[25] E.W. Weisstein, Lambert W-Function, MathWorld-A Wolfram Web Resource.
[26] Valluri, SR; Jeffrey, DJ; Corless, RM, Some applications of the Lambert W function to physics, Can. J. Phys., 78, 823, (2000)
[27] G. Barnich, Conserved charges in gravitational theories: Contribution from scalar fields, gr-qc/0211031 [INSPIRE].
[28] Barnich, G., Boundary charges in gauge theories: using Stokes theorem in the bulk, Class. Quant. Grav., 20, 3685, (2003)
[29] Gegenberg, J.; Martínez, C.; Troncoso, R., A finite action for three-dimensional gravity with a minimally coupled scalar field, Phys. Rev., D 67, 084007, (2003)
[30] Clement, G., Black hole mass and angular momentum in 2+1 gravity, Phys. Rev., D 68, 024032, (2003)
[31] Hortaçsu, M.; Özçelik, HT; Yapıskan, B., Properties of solutions in (2+1)-dimensions, Gen. Rel. Grav., 35, 1209, (2003)
[32] Bañados, M.; Theisen, S., Scale invariant hairy black holes, Phys. Rev., D 72, 064019, (2005)
[33] Myung, YS, Phase transition for black holes with scalar hair and topological black holes, Phys. Lett., B 663, 111, (2008)
[34] Lashkari, N., Holographic symmetry-breaking phases in ads_{3}/CFT_{2}, JHEP, 11, 104, (2011)
[35] P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Springer, New York, U.S.A. (1997) [INSPIRE].
[36] Pérez, A.; Tempo, D.; Troncoso, R., Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity, JHEP, 07, 093, (2011)
[37] González, HA; Tempo, D.; Troncoso, R., Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes, JHEP, 11, 066, (2011)
[38] Bergshoeff, EA; Hohm, O.; Townsend, PK, Massive gravity in three dimensions, Phys. Rev. Lett., 102, 201301, (2009)
[39] Bergshoeff, EA; Hohm, O.; Rosseel, J.; Sezgin, E.; Townsend, PK, More on massive 3D supergravity, Class. Quant. Grav., 28, 015002, (2011)
[40] Oliva, J.; Tempo, D.; Troncoso, R., Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity, JHEP, 07, 011, (2009)
[41] Giribet, G.; Oliva, J.; Tempo, D.; Troncoso, R., Microscopic entropy of the three-dimensional rotating black hole of BHT massive gravity, Phys. Rev., D 80, 124046, (2009)
[42] Ayón-Beato, E.; Garbarz, A.; Giribet, G.; Hassaïne, M., Lifshitz black hole in three dimensions, Phys. Rev., D 80, 104029, (2009)
[43] Martínez, C.; Zanelli, J., Conformally dressed black hole in (2+1)-dimensions, Phys. Rev., D 54, 3830, (1996)
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