Collisions of particles in locally AdS spacetimes I. Local description and global examples

Details Collisions of particles in locally AdS spacetimes I. Local description and global examples Collisions of particles in locally AdS spacetimes I. Local description and global examples

2010-10-18

arxiv.org/abs/1010.3602v1

Communications in Mathematical Physics 308(2011):1, 147-200

Mathematics

Differential Geometry

This is a rewritten version of the first part of arxiv:0905.1823. That preprint was too long and contained two types of result

Scientific paper

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph $\Gamma$. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than $2\pi$ on time-like singular segments). We construct examples of such manifolds, describe the cone singularities that can arise and the way they can interact (the local geometry near the vertices of $\Gamma$). We then adapt to this setting some notions like global hyperbolicity which are natural for Lorentz manifolds, and construct some examples of globally hyperbolic AdS manifolds with interacting particles.

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