Year: 2012
Type: dissertation
Abstract: We describe what can be called the “universal” phase space of 2+1 AdS gravity, in which the moduli spaces of globally hyperbolic AdS spacetimes with compact Cauchy surface, as well as the moduli spaces of multi black hole spacetimes are realized as submanifolds. Importantly our phase space also includes all Brown-Henneaux excitations on the conformal boundary of asymptotically AdS spacetimes, with Diff+(S1)/SL(2,R)xDiff+(S1)/SL(2,R) contained as a submanifold.\n\nOur description of the universal phase space is obtained from results on the correspondence between maximal surfaces in AdS3 and quasi-symmetric homeomorphisms of the unit circle. We find that the phase space can be parametrized by two copies of the universal Teichmuller space T(D), or equivalently by the cotangent bundle over T(D). This yields a symplectic map from T*T(D) to T(D)xT(D) generalizing the well-known Mess map in the compact spatial surface setting.\nWe 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 asymptotically AdS spacetimes) to the periods of holomorphic quadratic differentials arising via the Bers embedding of T(D)xT(D).
Author: Carlos Scarinci
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2171770986