Horizons in 2+1-dimensional collapse of particles

TL;DR

This paper presents a geometric method to analyze the formation of horizons during head-on collisions of particles in 2+1-dimensional anti-de Sitter spacetimes, revealing how black hole horizons develop and evolve.

Contribution

It introduces a simple geometric construction for modeling particle collisions and horizon formation in 2+1-dimensional spacetimes with negative cosmological constant, including horizon dynamics.

Findings

Horizon typically begins at a point and expands into a closed curve with corners.

Horizon propagates along spacelike caustics.

Horizon disappears after passing the particles.

Abstract

A simple, geometrical construction is given for three-dimensional spacetimes with negative cosmological constant that contain two particles colliding head-on. Depending on parameters like particle masses and distance, the combined geometry will the that of a particle, or of a black hole. In the black hole case the horizon is calculated. It is found that that the horizon typically starts at a point and spreads into a closed curve with corners, which propagate along spacelike caustics and disappear as the horizon passes the particles.