A characterization of the central shell-focusing singularity in spherical gravitational collapse

TL;DR

This paper characterizes the conditions under which a central shell-focusing singularity in spherical gravitational collapse is naked or covered, based on the behavior of the mass function near the singularity.

Contribution

It provides a new criterion for classifying singularities in gravitational collapse using the limiting behavior of the mass function relative to the area radius.

Findings

Naked singularity occurs if mass growth is slower than R.

Covered singularity occurs if mass growth is faster than R.

Singularity can be either naked or covered if mass growth equals R.

Abstract

We give a characterization of the central shell-focusing curvature singularity that can form in the spherical gravitational collapse of a bounded matter distribution obeying the dominant energy condition. This characterization is based on the limiting behaviour of the mass function in the neighbourhood of the singularity. Depending on the rate of growth of the mass as a function of the area radius R, the singularity may be either covered or naked. The singularity is naked if this growth rate is slower than R, covered if it is faster than R, and either naked or covered if the growth rate is same as R.