Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 19, Issue 9, Pages 2399-2424Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/19/9/306
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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.
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