Abstract
In this work we explore ideas in quantizing AdS3 Einstein gravity. We start with the most general solution to the 3d gravity theory which respects Brown-Henneaux boundary conditions. These solutions are specified by two holomorphic functions and satisfy simple superposition rule. These geometries generically have a bifurcate Killing horizon (with a noncompact or not simply connected bifurcation curve) which is not an event horizon. Nonetheless, there are superpositions of these geometries which have event horizon. We propose to view these geometries as “semiclassical fuzzball microstates” of BTZ black holes appearing as superposition of these geometries. The details of quantization of these semiclassical microstates will be discussed in an upcoming work.
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References
E. Witten, (2 + 1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
S. Deser, R. Jackiw and G. ’t Hooft, Three-Dimensional Einstein Gravity: Dynamics of Flat Space, Annals Phys. 152 (1984) 220 [INSPIRE].
J.D. Brown, Lower Dimensional Gravity, World Scientific, Singapore (1988).
S. Carlip, Lectures on (2 + 1) dimensional gravity, J. Korean Phys. Soc. 28 (1995) S447 [gr-qc/9503024] [INSPIRE].
S. Deser and R. Jackiw, Three-Dimensional Cosmological Gravity: Dynamics of Constant Curvature, Annals Phys. 153 (1984) 405 [INSPIRE].
J.M. Maldacena and L. Maoz, Desingularization by rotation, JHEP 12 (2002) 055 [hep-th/0012025] [INSPIRE].
E. Witten, Three-Dimensional Gravity Revisited, arXiv:0706.3359 [INSPIRE].
A. Maloney and E. Witten, Quantum gravity partition functions in three dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [gr-qc/9302012] [INSPIRE].
O. Coussaert and M. Henneaux, Selfdual solutions of (2 + 1) Einstein gravity with a negative cosmological constant, hep-th/9407181 [INSPIRE].
V. Balasubramanian, A. Naqvi and J. Simon, A multiboundary AdS orbifold and DLCQ holography: a universal holographic description of extremal black hole horizons, JHEP 08 (2004) 023 [hep-th/0311237] [INSPIRE].
F. Loran and M.M. Sheikh-Jabbari, Orientifolded Locally AdS 3 Geometries, Class. Quant. Grav. 28 (2011) 025013 [arXiv:1008.0462] [INSPIRE].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
G. Barnich, A. Gomberoff and H.A. Gonzalez, The flat limit of three dimensional asymptotically anti-de Sitter spacetimes, Phys. Rev. D 86 (2012) 024020 [arXiv:1204.3288] [INSPIRE].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
C. Fefferman and C. Graham, Élie Cartan et les Mathématiques d’aujourd’hui, Astérisque; numéro hors série, Société Mathématique de France, Paris France (1985), pg. 95.
C. Graham and J. Lee, Einstein metrics with prescribed conformal infinity on the ball, Adv. Math. 87 (1991) 186.
M. Bañados, Three-dimensional quantum geometry and black holes, hep-th/9901148 [INSPIRE].
K. Skenderis and S.N. Solodukhin, Quantum effective action from the AdS /CFT correspondence, Phys. Lett. B 472 (2000) 316 [hep-th/9910023] [INSPIRE].
C. Li and J. Lucietti, Three-dimensional black holes and descendants, arXiv:1312.2626 [INSPIRE].
A. Garbarz and M. Leston, Classification of Boundary Gravitons in AdS 3 Gravity, JHEP 05 (2014) 141 [arXiv:1403.3367] [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].
J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept. 369 (2002) 549 [hep-th/0203048] [INSPIRE].
S.D. Mathur, The Fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].
P.K. Townsend, Black holes: lecture notes, gr-qc/9707012 [INSPIRE].
V. Balasubramanian, J. de Boer, M.M. Sheikh-Jabbari and J. Simon, What is a chiral 2d CFT? And what does it have to do with extremal black holes?, JHEP 02 (2010) 017 [arXiv:0906.3272] [INSPIRE].
S. Carlip, The statistical mechanics of the (2 + 1)-dimensional black hole, Phys. Rev. D 51 (1995) 632 [gr-qc/9409052] [INSPIRE].
S. Carlip, Dynamics of asymptotic diffeomorphisms in (2 + 1)-dimensional gravity, Class. Quant. Grav. 22 (2005) 3055 [gr-qc/0501033] [INSPIRE].
S. Bahcall and L. Susskind, Fluid dynamics, Chern-Simons theory and the quantum Hall effect, Int. J. Mod. Phys. B 5 (1991) 2735 [INSPIRE].
L. Susskind, The quantum Hall fluid and noncommutative Chern-Simons theory, hep-th/0101029 [INSPIRE].
A.P. Polychronakos, Integrable systems from gauged matrix models, Phys. Lett. B 266 (1991) 29 [INSPIRE].
A.P. Polychronakos, Quantum Hall states as matrix Chern-Simons theory, JHEP 04 (2001) 011 [hep-th/0103013] [INSPIRE].
A.P. Balachandran, L. Chandar and A. Momen, Edge states in gravity and black hole physics, Nucl. Phys. B 461 (1996) 581 [gr-qc/9412019] [INSPIRE].
H.K. Kunduri and J. Lucietti, Classification of near-horizon geometries of extremal black holes, Living Rev. Rel. 16 (2013) 8 [arXiv:1306.2517] [INSPIRE].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
G. Compere, The Kerr/CFT correspondence and its extensions: a comprehensive review, Living Rev. Rel. 15 (2012) 11 [arXiv:1203.3561] [INSPIRE].
K. Hajian, A. Seraj and M.M. Sheikh-Jabbari, NHEG mechanics: laws of near horizon extremal geometry (thermo)dynamics, JHEP 03 (2014) 014 [arXiv:1310.3727] [INSPIRE].
W. Magnus and S. Winkler, Hill’s Equation, Dover publications, New York U.S.A. (2004).
H.P. McKean and P. van Moerbeke, The Spectrum of Hill’s Equation, Invent. Math. 30 (1975) 217.
F. Gesztesy, G.M. Graf and B. Simon, The ground state energy of Schrödinger operators, Commun. Math. Phys. 150 (1992) 375.
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Sheikh-Jabbari, M.M., Yavartanoo, H. On quantization of AdS3 gravity I: semi-classical analysis. J. High Energ. Phys. 2014, 104 (2014). https://doi.org/10.1007/JHEP07(2014)104
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DOI: https://doi.org/10.1007/JHEP07(2014)104