Naked singularities in Tolman-Bondi-de Sitter collapse

TL;DR

This paper investigates the formation of naked singularities during spherical dust collapse with a cosmological constant, revealing their local nakedness, strength, and generic nature, with divergence in curvature scalars indicating a non-local origin.

Contribution

It demonstrates the conditions under which naked singularities form in Tolman-Bondi-de Sitter collapse, highlighting their generic and strong nature with divergence in curvature scalars.

Findings

Central naked singularity is locally naked and Tipler strong.

Singularity forms from a non-zero measure set of initial data.

Weyl curvature dominates Ricci curvature at the singularity.

Abstract

We study the formation of central naked singularities in spherical dust collapse with a cosmological constant. We find that the central curvature singularity is locally naked, Tipler strong, and generic, in the sense that it forms from a non-zero-measure set of regular initial data. We also find that the Weyl and Ricci curvature scalars diverge at the singularity, with the former dominating over the latter, thereby signaling the non-local origin of the singularity.