Collisions of Particles in Locally AdS Spacetimes I. Local Description and Global Examples

Abstract

We investigate 3-dimensional globally hyperbolic AdS manifolds (or more generally constant curvature Lorentz manifolds) containing “particles”, i.e., cone singularities along a graph Γ. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than 2π 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 Γ). 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.