Role of initial data in the gravitational collapse of inhomogeneous dust

We consider here the gravitational collapse of a spherically symmetric inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a general class of these models, we find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of the initial density distribution, which are ${\mathrm{\rho }}_{\mathit{c}}$, the initial central density of the massive body, and ${\mathit{R}}_0$, the initial boundary. The collapse ends in a black hole if the dimensionless quantity β constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if β is less than this number. A simple interpretation of this result can be given in terms of the strength of the gravitational potential at the starting epoch of the collapse.