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

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

2012-02-26

arxiv.org/abs/1202.5753v1

Mathematics

Differential Geometry

29 pages, 3 figures

Scientific paper

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.

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