Quantum collapse of dust shells in 2+1 gravity

TL;DR

This paper investigates the quantum behavior of collapsing dust shells in 2+1 gravity, modeling the problem as a harmonic oscillator and exploring quantum indicators of horizon formation.

Contribution

It reduces the quantum collapse problem to a harmonic oscillator framework, providing new insights into quantum effects in 2+1 gravity dust shell collapse.

Findings

Quantum collapse modeled as harmonic oscillator

Wave packets exhibit quantum collapse behavior

Indications of horizon formation in quantum regime

Abstract

This paper considers the quantum collapse of infinitesimally thin dust shells in 2+1 gravity. In 2+1 gravity a shell is no longer a sphere but a ring of matter. The classical equation of motion has been considered by Peleg and Steif and Cristosomo and Olea. The minisuperspace quantum problem can be reduced to that of a harmonic oscillator in terms of the curvature radius of the shell, allowing the use of well-known methods to find the motion of coherent wave packets that give the quantum collapse of the shell. Classically, as the radius of the shell falls below a certain point, a horizon forms. In the quantum problem one can define various quantities that give "indications" of horizon formation. Without proper definitions of a "horizon" in quantum gravity, these can be nothing but indications.