Black holes versus naked singularities formation in collapsing Einstein clusters

Nonstatic, spherically symmetric clusters of counter-rotating particles, of the type first introduced by Einstein, are analyzed here. The initial data space can be parametrized in terms of three arbitrary functions: namely, initial density, velocity, and angular momentum profiles. The final state of collapse, black hole or naked singularity, turns out to depend on the order of the first nonvanishing derivatives of such functions at the center. The work extends recent results by Harada, Iguchi, and Nakao.