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

We investigate the collapse of a spherical cloud of counterrotating particles. An explicit solution for metric functions is given using an elliptic integral. If the specific angular momentum ${L(r)=O(r}^{2})$ at $\stackrel{\ensuremath{\rightarrow}}{r}0,$ 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 a 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 $4<L/F<\ensuremath{\infty}$ at $\stackrel{\ensuremath{\rightarrow}}{r}0,$ there is a finite region around the center that bounces and a naked singularity occurs. For $0<~L/F<4$ at $\stackrel{\ensuremath{\rightarrow}}{r}0,$ there is no such region. The results suggest that rotation may play a crucial role on the final fate of collapse.

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