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      Geometric Finiteness, Holography and Quasinormal Modes for the Warped AdS_3 Black Hole

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          Abstract

          We show that there exists a precise kinematical notion of holography for the Euclidean warped \(AdS_3\) black hole. This follows from the fact that the Euclidean warped \(AdS_3\) black hole spacetime is a geometrically finite hyperbolic manifold. For such manifolds a theorem of Sullivan provides a one-to-one correspondence between the hyperbolic structure in the bulk and the conformal structure of its boundary. Using this theorem we obtain the holographic quasinormal modes for the warped \(AdS_3\) black hole.

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          Three-Dimensional Massive Gauge Theories

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            Geometry of the 2+1 Black Hole

            The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant and without couplings to matter, is analyzed in detail. It is shown that the black hole arises from identifications of points of anti-de Sitter space by a discrete subgroup of \(SO(2,2)\). The generic black hole is a smooth manifold in the metric sense. The surface \(r=0\) is not a curvature singularity but, rather, a singularity in the causal structure. Continuing past it would introduce closed timelike lines. However, simple examples show the regularity of the metric at \(r=0\) to be unstable: couplings to matter bring in a curvature singularity there. Kruskal coordinates and Penrose diagrams are exhibited. Special attention is given to the limiting cases of (i) the spinless hole of zero mass, which differs from anti-de Sitter space and plays the role of the vacuum, and (ii) the spinning hole of maximal angular momentum . A thorough classification of the elements of the Lie algebra of \(SO(2,2)\) is given in an Appendix.
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              Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes

              We obtain exact expressions for the quasi-normal modes of various spin for the BTZ black hole. These modes determine the relaxation time of black hole perturbations. Exact agreement is found between the quasi-normal frequencies and the location of the poles of the retarded correlation function of the corresponding perturbations in the dual conformal field theory. This then provides a new quantitative test of the AdS/CFT correspondence.
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                Author and article information

                Journal
                17 December 2009
                2010-06-05
                Article
                10.1088/0264-9381/27/16/165012
                0912.3584

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                SINP/TNP/2009/27
                Class.Quant.Grav.27:165012,2010
                Latex file, 7 pages. Journal version
                hep-th

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