Naked singularities and the Weyl Curvature Hypothesis

TL;DR

This paper investigates the behavior of Weyl curvature near naked singularities in spherical gravitational collapse, highlighting divergence along null geodesics and discussing implications for the Weyl Curvature Hypothesis and thermodynamics.

Contribution

It provides a detailed analysis of Weyl curvature growth in naked singularity models and explores the potential physical constraints on their formation.

Findings

Weyl scalar diverges along outgoing null geodesics near naked singularities

Implications for the Weyl Curvature Hypothesis are discussed

Classical GR solutions with naked singularities may be thermodynamically forbidden

Abstract

We examine the growth of the Weyl curvature in two examples of naked singularity formation in spherical gravitational collapse - dust and the Vaidya spacetime. We find that the Weyl scalar diverges along outgoing radial null geodesics as they meet the naked singularity in the past. The implications of this result for the Weyl curvature hypothesis are discussed. We mention the possibility that although classical general relativity admits naked singularity solutions arising from gravitational collapse, the second law of thermodynamics could forbid their occurrence in nature. The method can also be used to compare the relative importance of initial data and that of the energy-momentum tensor in deciding the metric solution in any general case.