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

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 $r\to 0$, there is a finite region around the center that bounces and a naked singularity occurs. For $0\le L/F<4$ at $r\to 0$, there is no such region. The results suggests that rotation may play a crucial role on the final fate of collapse.

6 pages, Accepted for Publication as a Rapid Communication in Physical Review D, Some Minor Corrections

References in corpus (1)

• Cosmic censorship and spherical gravitational collapse with tangential pressure

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