Lambda<0 Quantum Gravity in 2+1 Dimensions II: Black Hole Creation by Point Particles

TL;DR

This paper investigates black hole formation in 2+1 dimensional Lambda<0 quantum gravity, showing that while individual processes are exponentially suppressed, the total probability of black hole creation is not, due to contributions from multiple topologies.

Contribution

It introduces a formalism linking black hole creation probability to Liouville theory and analyzes the total production rate considering all internal topologies.

Findings

Individual black hole creation probability is exponentially small.

Total black hole production probability is of order unity.

Semi-classical limit dominated by classical Liouville action.

Abstract

Using the recently proposed formalism for Lambda<0 quantum gravity in 2+1 dimensions we study the process of black hole production in a collision of two point particles. The creation probability for a BH with a simplest topology inside the horizon is given by the Liouville theory 4-point function projected on an intermediate state. We analyze in detail the semi-classical limit of small AdS curvatures, in which the probability is dominated by the exponential of the classical Liouville action. The probability is found to be exponentially small. We then argue that the total probability of creating a horizon given by the sum of probabilities of all possible internal topologies is of order unity, so that there is no exponential suppression of the total production rate.