Shell-crossings and shock formation during gravitational collapse in effective loop quantum gravity

TL;DR

This paper investigates gravitational collapse in loop quantum gravity, revealing that shell-crossing singularities and shock waves can occur during the bounce phase in inhomogeneous dust models.

Contribution

It demonstrates that shell-crossings are common in inhomogeneous collapse models within loop quantum gravity and discusses the necessity of weak solutions with shock waves.

Findings

Shell-crossings occur in inhomogeneous collapse models.

Weak solutions with shock waves are typically needed.

Shell-crossings are present even near the Oppenheimer-Snyder model.

Abstract

Effective models of gravitational collapse in loop quantum gravity for the Lema\^itre-Tolman-Bondi spacetime predict that collapsing matter reaches a maximum finite density, bounces, and then expands outwards. We show that in the marginally bound case, shell-crossing singularities commonly occur for inhomogeneous initial profiles of the dust energy density; this is the case in particular for all profiles that are continuous and of compact support, including configurations arbitrarily close to the Oppenheimer-Snyder model. When a shell-crossing singularity occurs, it is necessary to seek weak solutions to the dynamics; we argue that weak solutions typically contain shock waves.