Null Geodesic Expansion in Spherical Gravitational Collapse

TL;DR

This paper derives formulas for null geodesic expansion during spherical gravitational collapse, analyzing stability of singularity solutions under small matter equation of state variations.

Contribution

It provides new expressions for null geodesic expansion in spherical collapse and demonstrates the stability of singularity solutions against small matter equation of state changes.

Findings

Derived explicit formulas for null geodesic expansion.

Showed stability of singularity solutions under small equation of state variations.

Analyzed both covered and naked singularity scenarios.

Abstract

We derive an expression for the expansion of outgoing null geodesics in spherical dust collapse and compute the limiting value of the expansion in the approach to singularity formation. An analogous expression is derived for the spherical collapse of a general form of matter. We argue on the basis of these results that the covered as well as the naked singularity solutions arising in spherical dust collapse are stable under small changes in the equation of state.