Quantum dust collapse in 2+1 dimensions

TL;DR

This paper explores quantum dust collapse in 2+1 dimensions, revealing that collapse halts at the apparent horizon without forming an event horizon, supported by internal Unruh radiation.

Contribution

It provides a quantum mechanical analysis of dust collapse in 2+1 dimensions, showing collapse termination at the apparent horizon and the role of Unruh radiation in supporting the static solution.

Findings

Collapse halts at the apparent horizon

No event horizon is formed in the quantum model

Radial pressure from Unruh radiation sustains the static ball

Abstract

In this paper we will examine the consequence of a canonical theory of quantum dust collapse in 2+1 dimensions. The solution of the WDW equation describing the collapse indicates that collapsing shells outside the apparent horizon are accompanied by outgoing shells within the apparent horizon during their collapse phase and stop collapsing once they reach the apparent horizon. Taking this picture of quantum collapse seriously, we determine a static solution with energy density corresponding to a dust ball whose collapse has terminated at the apparent horizon. We show that the boundary radius of the ball is larger than the BTZ radius confirming that no event horizon is formed. The ball is sustained by radial pressure which we determine and which we attribute to the Unruh radiation within it.