Occurrence of Naked Singularities in Higher Dimensional Dust Collapse

Abstract

We consider here the gravitational collapse of a inhomogeneous dust cloud described by Tolmanbondi models. We find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of initial density distribution. Collapse ends into a black hole if the dimensionless quantity ψ is greater than −22.18033 and ends into a naked singularity if ψ ≤ −22.18033. We find the occurrence of naked singularity in higher dimensional case. We proposed the concept of ‘trapped range’ of initial data in the different higher dimensional space-times. We show that ‘trapped range’ of initial data increases with the increase in dimensions of the space-times.