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

الأصل · EN

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(r²) 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 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<∞ at r→0, there is a finite 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 final fate of collapse.