Non-marginally bound inhomogeneous dust collapse in higher dimensional space-time

TL;DR

This paper studies the formation of naked singularities in higher-dimensional inhomogeneous dust collapse, analyzing various bound states and the inhomogeneity conditions needed for such singularities to occur.

Contribution

It provides a detailed analysis of naked singularity formation in self-similar higher-dimensional dust collapse, including conditions on inhomogeneity and bound states.

Findings

Naked singularities can form in higher-dimensional dust collapse.

The degree of inhomogeneity influences singularity visibility.

Bound, marginally bound, and unbound cases are analyzed.

Abstract

We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by a self-similar higher dimensional Tolman-Bondi space-time. Bound, marginally bound and unbound space-times are analyzed. The degree of inhomogeneity of the collapsing matter necessary to form a naked singularity is given.