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We investigate 3-dimensional globally hyperbolic AdS manifolds containing"particles", i.e., cone singularities of angles less than $2\pi$ along atime-like graph $\Gamma$. To each such space we associate a graph and a finitefamily of pairs of hyperbolic surfaces with cone singularities. We show thatthis data is sufficient to recover the space locally (i.e., in the neighborhoodof a fixed metric). This is a partial extension of a result of Mess fornon-singular globally hyperbolic AdS manifolds.

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