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Analytic Continuation for Asymptotically AdS 3D Gravity | | Kirill Krasnov
; | | Date: |
16 Nov 2001 | | Journal: | Class.Quant.Grav. 19 (2002) 2399-2424 | | Subject: | General Relativity and Quantum Cosmology; Complex Variables | gr-qc hep-th math.CV | | Abstract: | We have previously proposed that asymptotically AdS 3D wormholes and black holes can be analytically continued to the Euclidean signature. The analytic continuation procedure was described for non-rotating spacetimes, for which a plane t=0 of time symmetry exists. The resulting Euclidean manifolds turned out to be handlebodies whose boundary is the Schottky double of the geometry of the t=0 plane. In the present paper we generalize this analytic continuation map to the case of rotating wormholes. The Euclidean manifolds we obtain are quotients of the hyperbolic space by a certain quasi-Fuchsian group. The group is the Fenchel-Nielsen deformation of the group of the non-rotating spacetime. The angular velocity of an asymptotic region is shown to be related to the Fenchel-Nielsen twist. This solves the problem of classification of rotating black holes and wormholes in 2+1 dimensions: the spacetimes are parametrized by the moduli of the boundary of the corresponding Euclidean spaces. We also comment on the thermodynamics of the wormhole spacetimes. | | Source: | arXiv, gr-qc/0111049 | | Services: | Forum | Review | PDF | Favorites | |
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