KUNS 1500 Naked singularity formation in the collapse of a spherical cloud of counterrotating particles

We investigate collapse of a spherical cloud of counter-rotating particles. An explicit solution is given using an elliptic integral. If the speci c angular momentum L(r) = O(r) at r! 0, no central singularity occurs. With L(r) like that, there is a nite 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 <1 at r ! 0, there is a nite region around the center that bounces and a naked singularity occurs. For 0 L=F < 4 at r ! 0, there is no such region. The results suggests that rotation may play a crucial role on the nal fate of collapse.