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Collisions of Particles in Locally AdS Spacetimes II Moduli of Globally Hyperbolic Spaces |
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| Authors: | Thierry Barbot Francesco Bonsante Jean-Marc Schlenker |
| Affiliation: | 1. Laboratoire d’analyse non linéaire et géométrie, Université d’Avignon et des pays de Vaucluse, 33, Rue Louis Pasteur, 84 018, Avignon, France 2. Dipartimento di Matematica dell’Università degli Studi di Pavia, via Ferrata 1, 27100, Pavia, Italy 3. Mathematics Research Unit, University of Luxembourg, Campus Kirchberg, BLG, 6, rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg |
| Abstract: | We investigate globally hyperbolic 3-dimensional AdS manifolds containing “particles”, i.e., cone singularities of angles less than 2π along a time-like graph Γ. To each such space (equipped with a time-like vector field satisfying some additional properties) 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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