On the Role of Initial Data in 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 ρc, the initial central density of the massive body, and R0, 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. PACS Nos: 04.20. Cv, 97.60. Lf, 95.30. Sf