Strengths of singularities in spherical symmetry

TL;DR

This paper develops covariant equations to characterize singularity strength in spherical symmetry, investigates different models, and proves the gravitational weakness of shell crossing singularities for timelike geodesics.

Contribution

It introduces covariant equations for singularity strength, distinguishes between types of singularities, and proves shell crossing singularities are gravitationally weak.

Findings

Covariant equations for singularity strength derived.

Difference between central and non-central singularities emphasized.

Shell crossing singularities are gravitationally weak for timelike geodesics.

Abstract

Covariant equations characterizing the strength of a singularity in spherical symmetry are derived and several models are investigated. The difference between central and non-central singularities is emphasised. A slight modification to the definition of singularity strength is suggested. The gravitational weakness of shell crossing singularities in collapsing spherical dust is proven for timelike geodesics, closing a gap in the proof.