Collisions of massive particles, timelike thin shells and formation of black holes in three dimensions

TL;DR

This paper constructs exact solutions for black hole and conical singularity formation from collisions of massive particles in three-dimensional anti-de Sitter space, including thin shell spacetimes with arbitrary mass distributions.

Contribution

It generalizes previous work by allowing arbitrary masses and positions, and introduces novel timelike thin shell solutions with complex embeddings.

Findings

Exact solutions for black hole formation from particle collisions

Construction of timelike thin shell spacetimes with arbitrary mass and embedding

Consistency with earlier massless particle results and dual CFT analysis

Abstract

We study collisions of massive pointlike particles in three dimensional anti-de Sitter space, generalizing the work on massless particles in [1]. 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 massive particles that fall in radially and collide at the origin of AdS. No restrictions on the masses or the angular and radial positions from where the particles are released, are imposed. We also consider the limit of an infinite number of particles, obtaining novel timelike thin shell spacetimes. These thin shells have an arbitrary mass distribution as well as a non-trivial embedding where the radial location of the shell depends on the angular coordinate, and we analyze these shells using the junction formalism of general relativity. We also consider the massless limit and find consistency with earlier results, as well as comment on the stress-energy tensor modes of the dual CFT.