A regular C^0 singularity is not necessarily weak

TL;DR

The paper presents examples of space-times with regular, continuous metrics that still exhibit strong scalar curvature singularities, challenging the assumption that such singularities are necessarily weak.

Contribution

It provides counterexamples showing that C^0 regularity does not imply weakness of singularities, and discusses unresolved issues regarding null Cauchy horizon singularities.

Findings

Some scalar curvature singularities are strong despite regular metrics

The assumption that C^0 singularities are weak is incomplete

The gravitational strength of null Cauchy horizon singularities remains unresolved

Abstract

Examples of space-times are given which contain scalar curvature singularities whereat the metric tensor is regular and continuous, but which are gravitationally strong. Thus the argument that such singularities are necessarily weak is incomplete; in particular the question of the gravitational strength of the null Cauchy horizon singularity which occurs in gravitational collapse remains open.