Initial data and the final fate of inhomogeneous dust collapse

We examine the relevance of the initial state of a collapsing dust cloud towards determining its final fate in the course of a continuing gravitational collapse. It is shown that given any arbitrary matter distribution M(r) for the cloud in the initial epoch, there is always the freedom to choose the rest of the initial data, namely the initial velocities of the collapsing spherical shells, so that the collapse could result either in a black hole or a naked singularity depending on this choice. Thus, given the initial density profile, to achieve the desired end state of the gravitational collapse one has to give a suitable initial velocity to the cloud. We also characterize a wide new family of solutions describing inhomogeneous dust collapse to a black hole. These configurations obey the usual energy conditions demanding the positivity of energy density.