Initial data and the end state of spherically symmetric gravitational collapse

Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a sphericall y symmetric matter cloud towards determining its end stare in the course of a continuing gravitational collapse. It is shown that given an arbitrary r egular distribution of matter at the initial epoch, there always exists an evolution from this initial data which would result either in a black hole or a naked singularity, depending on the allowed choice of free functions a vailable in the solution. It follows that given any initial density and pre ssure profiles for the cloud, there is a non-zero measure set of configurat ions leading either to black holes or naked singularities, subject to the u sual energy conditions ensuring the positivity of energy density. We also c haracterize here wide new families of black hole solutions resulting from s pherically symmetric collapse without requiring the cosmic censorship assum ption.