The Universal Phase Space of AdS3 Gravity

TL;DR

This paper introduces a comprehensive phase space framework for AdS3 gravity, linking moduli spaces of spacetimes with universal Teichmüller space, and relates it to Chern-Simons theory and holography.

Contribution

It constructs a universal phase space parametrized by two copies of the Universal Teichmüller space, connecting geometric, Chern-Simons, and holographic descriptions of AdS3 gravity.

Findings

Parametrization of AdS3 spacetimes via T(1) and quasisymmetric homeomorphisms.

Relation between holographic charges and Bers embedding periods.

A symplectic map generalizing the Mess map for non-compact surfaces.

Abstract

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 parametrized by two copies of the Universal Teichm\"uller space T(1) and is obtained from the correspondence between maximal surfaces in AdS3 and quasisymmetric homeomorphisms of the unit circle. 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 obtain a relation between the generators of quasiconformal deformations in each T(1) sector and the chiral Brown-Henneaux vector fields. We also 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). Our construction also yields a symplectic map from T*T(1) to T(1)xT(1) generalizing the well-known Mess map in the compact spatial surface setting.