Black Hole Creation in 2+1 Dimensions

TL;DR

In 2+1 dimensional gravity with a negative cosmological constant, the paper shows that two point particles colliding in $AdS_3$ can form a BTZ black hole. It uses a cutting-gluing construction based on holonomies in $SL(2)$ to build the spacetime and analyzes the threshold energy that separates massive outcomes from black hole formation, with the horizon length fixed by the holonomy as $2\mu$ (the black hole mass). The approach yields an explicit solution describing the collapse into a non-rotating BTZ black hole and discusses extremal and rotating generalizations, including the global causal structure of black hole formation in AdS$_3$. The work provides a concrete, exact framework for black hole formation in a toy model of quantum gravity and clarifies the role of holonomies and geodesics in 3D AdS gravity.

Abstract

When two point particles, coupled to three dimensional gravity with a negative cosmological constant, approach each other with a sufficiently large center of mass energy, then a BTZ black hole is created. An explicit solution to the Einstein equations is presented, describing the collapse of two massless particles into a non-rotating black hole. Some general arguments imply that massive particles can be used as well, and the creation of a rotating black hole is also possible.

Figures (8)

• Figure 1: Construction of a geodesic on the Poincaré disc
• Figure 2: A particle cutting out a wedge from Minkowski space.
• Figure 3: A massless particle passing through anti-de-Sitter space
• Figure 4: Two particles colliding and joining.
• Figure 5: Two massless particles joining and forming a massive particle.