0 D ec 1 99 6 INITIAL DATA AND THE FINAL FATE OF INHOMOGENEOUS DUST COLLAPSE

We examine here the relevance of the initial state of a collapsing dust cloud towards determining it's final fate in the course of a continuing gravitational collapse. It is shown that given any arbitrary matter distribution M (r) for the cloud at the initial epoch, there is always a freedom to choose 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 here a wide new family of black hole solutions resulting from inhomogeneous dust collapse. These configurations obey the usual energy conditions demanding the positivity of energy density.