Shell-crossings in Gravitational Collapse

TL;DR

This paper investigates shell-crossing singularities in spherically symmetric gravitational collapse, showing that near the center, such singularities can be avoided, simplifying the analysis of the collapse's final singularity.

Contribution

It proves that in spherically symmetric collapse, a finite neighborhood around the center is free of shell-crossings, enabling focused study of the genuine singularity without interference.

Findings

A finite neighborhood near the center has no shell-crossings.

Shell-crossings can be excluded when analyzing the final singularity.

Facilitates the study of genuine collapse singularities.

Abstract

While studying the continual gravitational collapse of a massive matter cloud in general relativity towards examining collapse final states, an important issue is that of whether shell-crossing singularities can develop as the collapse evolves. We examine this here to show that for any spherically symmetric collapse in general, there is always a finite neighborhood of the center in which there are no shell-crossings taking place. It follows that in order to study the final genuine shell-focusing singularity of collapse where the physical radius of the matter cloud shrinks to a vanishing value, we can always consider without any loss of generality a collapsing ball of a finite comoving radius in which there are no shell-crossings taking place. This clarifies an important point for gravitational collapse studies.