Gravitational collapse with non-vanishing tangential stresses II: a laboratory for cosmic censorship experiments

TL;DR

This paper develops a framework using exact solutions and root equations to explore how tangential stresses influence the formation and nature of singularities during gravitational collapse, providing insights into cosmic censorship.

Contribution

It introduces a new explicit construction of the root equation for anisotropic elastic spheres with tangential stresses, advancing understanding of singularity nature and cosmic censorship.

Findings

Tangential stresses do not expose covered dust singularities.

The root equation helps analyze singularity types in self-similar spacetimes.

A conjecture on singularity nature based on initial data and stresses is proposed.

Abstract

The general exact solution describing the dynamics of anisotropic elastic spheres supported only by tangential stresses is reduced to a quadrature using Ori's mass-area coordinates. This leads to the explicit construction of the root equation governing the nature of the central singularity. Using this equation, we formulate and motivate on physical grounds a conjecture on the nature of this singularity. The conjecture covers a large sector of the space of initial data; roughly speaking, it asserts that addition of a tangential stress cannot undress a covered dust singularity. The root equation also allows us to analyze the case of self-similar spacetimes and to get some insight on the role of stresses in deciding the nature of the singularities in this case.