Naked Singularities in Spherically Symmetric Inhomogeneous Tolman-Bondi Dust Cloud Collapse

We investigate the occurrence and nature of naked singularity for the inhomogeneous gravitational collapse of Tolman-Bondi dust clouds.It is shown that the naked singularities form at the center of the collapsing cloud in a wide class of collapse models which includes the earlier cases considered by Eardley and Smarr and Christodoulou. This class also contains self-similar as well as non-self-similar models. The structure and strength of this singularity is examined and the question is investigated as to when a non-zero measure set of non-spacelike trajectories could be emitted from the singularity as opposed to isolated trajectories coming out. It is seen that the weak energy condition and positivity of energy density ensures that the families of non-spacelike trajectories come out of the singularity. The curvature strength of the naked singularity is examined which provides an important test for its physical significance and powerful curvature growth near the naked singularity is pointed out for several subclasses considered. The conditions are discussed for the naked singularity to be globally naked. Implications for the basic issue of the final fate of gravitational collapse are considered once the inhomogeneities in the matter distribution are taken into account. It is argued that a physical formulation for the cosmic censorship may be evolved which avoids the features above. Possibilities in this direction are discussed while indicating that the analysis presented here should be useful for any possible rigorous formulation of the cosmic censorship hypothesis.