Generalized Strong Curvature Singularities and Cosmic Censorship

TL;DR

This paper introduces a broader definition of strong curvature singularities, classifies their causal geodesics, and proves a theorem indicating that only one class can be naked, supporting aspects of the cosmic censorship hypothesis.

Contribution

It proposes a more general definition of strong curvature singularities, classifies their geodesics, and proves a cosmic censorship theorem related to their visibility.

Findings

Only one class of generalized strong curvature singularities can be naked.

The new definition encompasses a wider range of singularities than previous definitions.

The theorem supports the cosmic censorship hypothesis by limiting the types of naked singularities.

Abstract

A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.