Abstract
With the help of two new intrinsic tensor fields associated with the SL(2,R) quadratic Casimir of Killing fields, we uncover the SL(2,R) symmetry satisfied by the solutions to the equations of motion for various fields in the BTZ black hole in a uniform way by performing tensor and spinor analysis without resorting to any specific coordinate system. Then with the standard algebraic method developed recently, we determine the quasi-normal modes for various fields in the BTZ black hole. As a result, the quasi-normal modes are given by the infinite tower of descendants of the chiral highest weight mode, which is in good agreement with the previous analytic result obtained by exactly solving equations of motion instead.
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References
G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [SPIRES].
D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal field theory interpretation of black hole quasi-normal modes, Phys. Rev. Lett. 88 (2002) 151301 [hep-th/0112055] [SPIRES].
J.M. Maldacena and A. Strominger, AdS 3 black holes and a stringy exclusion principle, JHEP 12 (1998) 005 [hep-th/9804085] [SPIRES].
V. Balasubramanian, P. Kraus and A.E. Lawrence, Bulk vs. boundary dynamics in anti-de Sitter spacetime, Phys. Rev. D 59 (1999) 046003 [hep-th/9805171] [SPIRES].
I. Sachs and S.N. Solodukhin, Quasi-Normal Modes in Topologically Massive Gravity, JHEP 08 (2008) 003 [arXiv:0806.1788] [SPIRES].
B. Chen and J. Long, Hidden Conformal Symmetry and Quasi-normal Modes, Phys. Rev. D 82 (2010) 126013 [arXiv:1009.1010] [SPIRES].
B. Chen and J.-j. Zhang, Quasi-normal Modes of Extremal Black Holes from Hidden Conformal Symmetry, arXiv:1012.2219 [SPIRES].
R.M. Wald, General Relativity, University of Chicago Press, Chicago U.S.A. (1984).
Y. Choquet-Bruhat and C. DeWitt-Morette, Analysis, Manifolds and Physics, Part II: 92 A pplications, revised edition, North-Holland, Amsterdam The Netherlands (2000).
D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 Black Holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [SPIRES].
B. Chen, G. Moutsopoulos and B. Ning, Self-Dual Warped AdS 3 Black Holes, Phys. Rev. D 82 (2010) 124027 [arXiv:1005.4175] [SPIRES].
H. Zhang, work in progress.
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [SPIRES].
H. Zhang, work in progress.
A. Castro, A. Maloney and A. Strominger, Hidden Conformal Symmetry of the Kerr Black Hole, Phys. Rev. D 82 (2010) 024008 [arXiv:1004.0996] [SPIRES].
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Zhang, H. SL(2, R) symmetry and quasi-normal modes in the BTZ black hole. J. High Energ. Phys. 2011, 9 (2011). https://doi.org/10.1007/JHEP03(2011)009
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DOI: https://doi.org/10.1007/JHEP03(2011)009