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

TL;DR

This paper analyzes the formation, structure, and physical significance of naked singularities in inhomogeneous Tolman-Bondi dust collapse models, exploring conditions for their visibility and implications for cosmic censorship.

Contribution

It extends previous studies by including a broad class of inhomogeneous collapse models, examining the nature and strength of naked singularities, and discussing conditions for their global visibility.

Findings

Naked singularities form at the center in many collapse models.

Families of non-spacelike trajectories can emerge from the singularity under certain conditions.

The curvature near the naked singularity can grow powerfully, indicating physical significance.

Abstract

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.