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 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 < infinity at r --> 0, there is a finite region around the center that bounces and a naked singularity occurs. For 0 less than or equal to L/F < 4 at r --> 0, there is no such region. The results suggest that rotation may play a crucial role on the final fate of collapse.