Initial data giving rise to naked singularities in spherically symmetric dust collapse

The phase space corresponding to a particular four-parameter family of initial data for the gravitational collapse of a spherically symmetric dust cloud is investigated. In a certain limit of the parameters, this family reproduces the case of homogenous mass density -constant mass distribution- and zero initial velocity, while in another limit, it generates a globally naked singularity. We show that for initial data characterizing flat density profiles, as well as large initial velocities, the probability of forming a globally naked singularity is low.