Naked Singularities in Higher Dimensional Gravitational Collapse

TL;DR

This paper investigates conditions under which naked singularities can form in higher-dimensional gravitational collapse, finding they do not appear beyond five dimensions in certain cases and analyzing the role of shear in five-dimensional collapse.

Contribution

It demonstrates that naked singularities do not occur in higher than five dimensions for marginally bound dust collapse and explores shear effects in five-dimensional non-marginally bound collapse.

Findings

Naked singularities are absent in space-times with more than five dimensions for marginally bound collapse.

Shear influences the formation of naked singularities in five-dimensional non-marginally bound collapse.

Exact solutions are obtained in five dimensions for detailed analysis.

Abstract

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space-time and the factors responsible for the appearance of a naked singularity are analyzed in the region close to the centre for the marginally bound case. It is clearly demonstrated that in the former case naked singularities do not appear in the space-time having more than five dimension, which appears to a strong result. The non-marginally bound collapse is also examined in five dimensions and the role of shear in developing naked singularities in this space-time is discussed in details. The five dimensional space-time is chosen in the later case because we have exact solution in closed form only in five dimension and not in any other case.