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We consider here the gravitational collapse of a spherically symmetricinhomogeneous dust cloud described by the Tolman-Bondi models. By studying ageneral class of these models, we find that the end state of the collapse iseither a black hole or a naked singularity, depending on the parameters of theinitial density distribution, which are $\rho_{c}$, the initial central densityof the massive body, and $R_0$, the initial boundary. The collapse ends in ablack hole if the dimensionless quantity $\beta$ constructed out of thisinitial data is greater than 0.0113, and it ends in a naked singularity if$\beta$ is less than this number. A simple interpretation of this result can begiven in terms of the strength of the gravitational potential at the startingepoch of the collapse.Comment: Original title changed, numerical range of naked singularity  corrected. Plain Tex File. 14 pages. To appear in Physical Review

Role of initial data in the gravitational collapse of inhomogeneous dust