Gravitational collapse of thin shell of dust in shape dynamics

TL;DR

This paper investigates the gravitational collapse of a dust shell within shape dynamics, revealing static and oscillatory solutions and conditions under which the shell avoids singularity formation.

Contribution

It introduces a novel analysis of dust shell collapse in shape dynamics, highlighting behaviors in large momentum regimes and limitations of current approximations.

Findings

Shell never reaches singularity at high momentum

Shell does not reach the origin in finite time

Large momentum approximation breaks down near certain conditions

Abstract

We studied the gravitational collapse of a shell of dust in shape dynamics. We found out static and oscillatory solutions. In the large momentum limit we found out that the shell never reaches the singularity when the momentum of the shell is much larger than the mass of the shell in magnitude. The shell does not reach to the origin in a finite amount of time however when the momentum of the shell becomes comparable to minus the mass of shell, the large momentum approximation breaks down. Therefore more detailed future works hopefully may be able to answer the question of singularity formation in this setup.