Curvature conditions for the occurrence of a class of spacetime singularities

TL;DR

This paper explores the relationship between curvature conditions and the formation of certain spacetime singularities, extending previous results on cosmic censorship and the inextendibility condition beyond strong curvature singularities.

Contribution

It proves a theorem linking the inextendibility condition to Ricci curvature growth, broadening the class of singularities considered in cosmic censorship.

Findings

Inextendibility condition can apply to more general singularities.

Theorem relates inextendibility to Ricci curvature growth.

Results extend cosmic censorship to broader singularity classes.

Abstract

It has previously been shown [W. Rudnicki, Phys. Lett. A 224, 45 (1996)] that a generic gravitational collapse cannot result in a naked singularity accompanied by closed timelike curves. An important role in this result plays the so-called inextendibility condition, which is required to hold for certain incomplete null geodesics. In this paper, a theorem is proved that establishes some relations between the inextendibility condition and the rate of growth of the Ricci curvature along incomplete null geodesics. This theorem shows that the inextendibility condition may hold for a much more general class of singularities than only those of the strong curvature type. It is also argued that some earlier cosmic censorship results obtained for strong curvature singularities can be extended to singularities corresponding to the inextendibility condition.