Particle creation in (2+1) circular dust collapse

TL;DR

This paper studies quantum particle creation during circular dust collapse in 2+1 dimensions, deriving a formula for quantum flux and showing no particles are created in naked singularity cases, but Hawking radiation occurs with BTZ black holes.

Contribution

It derives the Ford-Parker formula for 2+1 dimensions and analyzes particle creation in different collapse outcomes, highlighting differences from 3+1 cases.

Findings

No particle creation in naked singularity collapse

Hawking radiation observed in BTZ black hole formation

Derived a 2+1 dimensional quantum flux formula

Abstract

We investigate the quantum particle creation during the circularly symmetric collapse of a 2+1 dust cloud, for the cases when the cosmological constant is either zero or negative. We derive the Ford-Parker formula for the 2+1 case, which can be used to compute the radiated quantum flux in the geometric optics approximation. It is shown that no particles are created when the collapse ends in a naked singularity, unlike the 3+1 case. When the collapse ends in a BTZ black hole, we recover the expected Hawking radiation.