Collisions of particles in locally AdS spacetimes II Moduli of globally hyperbolic spaces

Abstract

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than $2\pi$ along a time-like graph $\Gamma$. To each such space we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.Comment: 29 pages, 3 figures. v2: 41 pages, improved exposition. To appear, Comm. Math. Phys. arXiv admin note: text overlap with arXiv:0905.182