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

TL;DR

This paper studies 3D AdS spacetimes with cone singularities representing particles, constructing examples, analyzing local and global geometry, and exploring interactions under physically relevant conditions.

Contribution

It introduces a framework for analyzing particles in AdS spacetimes, constructs explicit examples, and extends notions like global hyperbolicity to include interacting cone singularities.

Findings

Constructed examples of globally hyperbolic AdS manifolds with particles.

Described possible cone singularities and their interactions.

Extended geometric notions to include singularities and interactions.

Abstract

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.