Spherical Dust Collapse in Higher Dimensions

We consider here the question if it is possible to recover cosmic censorship when a transition is made to higher dimensional spacetimes, by studying the spherically symmetric dust collapse in an arbitrary higher spacetime dimension. It is pointed out that if only black holes are to result as end state of a continual gravitational collapse, several conditions must be imposed on the collapsing configuration, some of which may appear to be restrictive, and we need to study carefully if these can be suitably motivated physically in a realistic collapse scenario. It would appear that in a generic higher dimensional dust collapse, both black holes and naked singularities would develop as end states as indicated by the results here. The mathematical approach developed here generalizes and unifies the earlier available results on higher dimensional dust collapse as we point out. Further, the dependence of black hole or naked singularity end states as collapse outcomes, on the nature of the initial data from which the collapse develops, is brought out explicitly and in a transparent manner as we show here. Our method also allows us to consider here in some detail the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.