Black hole formation from point-like particles in three-dimensional anti-de Sitter space

TL;DR

This paper explores how collisions of multiple point-like particles in three-dimensional anti-de Sitter space can lead to black hole formation, providing exact solutions and analyzing the effects of inhomogeneity and symmetry breaking.

Contribution

It generalizes the two-particle collision results to many particles, including the construction of exact solutions and the analysis of inhomogeneous thin shell limits.

Findings

Exact solutions for black hole or conical singularity formation from multiple particles.

Inhomogeneous thin shell solutions when the number of particles approaches infinity.

Agreement of stress-energy tensor calculations with the point particle model.

Abstract

We study collisions of many point-like particles in three-dimensional anti-de Sitter space, generalizing the known result with two particles. We show how to construct exact solutions corresponding to the formation of either a black hole or a conical singularity from the collision of an arbitrary number of massless particles falling in radially from the boundary. We find that when going away from the case of equal energies and discrete rotational symmetry, this is not a trivial generalization of the two-particle case, but requires that the excised wedges corresponding to the particles must be chosen in a very precise way for a consistent solution. We also explicitly take the limit when the number of particles goes to infinity and obtain thin shell solutions that in general break rotational invariance, corresponding to an instantaneous and inhomogeneous perturbation at the boundary. We also compute the stress-energy tensor of the shell using the junction formalism for null shells and obtain agreement with the point particle picture.