The universal phase space of AdS3 gravity

Details The universal phase space of AdS3 gravity The universal phase space of AdS3 gravity

2011-11-28

arxiv.org/abs/1111.6507v1

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, 2 figures

Scientific paper

We describe what can be called the "universal" phase space of AdS3 gravity, in which the moduli spaces of globally hyperbolic AdS spacetimes with compact spatial sections, as well as the moduli spaces of multi black hole spacetimes are realized as submanifolds. The universal phase space is parameterized by two copies of the universal Teichmuller space T(1). The parameterization is obtained from the correspondence between maximal surfaces in AdS3 and quasi-symmetric homeomorphisms of the unit circle. This yields a symplectic map from T^\starT(1) to T(1)xT(1) generalizing the well-known Mess map in the compact spatial surface setting. We also relate our parametrization to the Chern-Simons formulation of 2+1 gravity and, infinitesimally, to the holographic (Fefferman-Graham) description. In particular, we relate the charges arising in the holographic description (such as the mass and angular momentum of an AdS3 spacetime) to the periods of the quadratic differentials arising via the Bers embedding of T(1)xT(1).

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