The Central Singularity in Spherical Collapse

TL;DR

This paper investigates the nature of the central singularity in spherical gravitational collapse, showing that under broad conditions, it is a strong curvature singularity, especially for geodesics with angular momentum.

Contribution

It derives necessary conditions for a weak singularity and demonstrates these are generally violated, establishing the singularity as strong for most geodesics.

Findings

Central singularity is generally a strong curvature singularity.

Conditions for a weak singularity are rarely satisfied.

Geodesics with angular momentum end in strong singularities.

Abstract

The gravitational strength of the central singularity in spherically symmetric space-times is investigated. Necessary conditions for the singularity to be gravitationally weak are derived and it is shown that these are violated in a wide variety of circumstances. These conditions allow conclusions to be drawn about the nature of the singularity without having to integrate the geodesic equations. In particular, any geodesic with a non-zero amount of angular momentum which impinges on the singularity terminates in a strong curvature singularity.