Naked singularity formation in the collapse of a spherical cloud of counterrotating particles

TL;DR

This paper analyzes how counter-rotating particles in a spherical cloud influence gravitational collapse, revealing conditions under which naked singularities form or are avoided, highlighting the role of angular momentum.

Contribution

It provides explicit solutions for spherical collapse with counter-rotation, identifying how angular momentum profiles determine singularity formation or bounce behavior.

Findings

No central singularity if L(r)=O(r^2) at r→0

Naked singularity occurs in marginally bound collapse with L(r)=4F(r)

Rotation influences the final outcome of gravitational collapse

Abstract

We investigate collapse of a spherical cloud of counter-rotating particles. An explicit solution is given using an elliptic integral. If the specific angular momentum $L(r)=O(r^2)$ at $r\to 0$, no central singularity occurs. With $L(r)$ like that, there is a finite region around the center that bounces. On the other hand, if the order of $L(r)$ is higher than that, a central singularity occurs. In marginally bound collapse with $L(r)=4F(r)$, a naked singularity occurs, where $F(r)$ is the Misner-Sharp mass. The solution for this case is expressed by elementary functions. For $ 4 <L/F<\infty$ at $r\to0$, there is a finite region around the center that bounces and a naked singularity occurs. For $ 0 \le L/F< 4$ at $r\to0$, there is no such region. The results suggests that rotation may play a crucial role on the final fate of collapse.