New solutions of Einstein equations in spherical symmetry: the Cosmic Censor to the court

TL;DR

This paper introduces new spherically symmetric solutions to Einstein's equations modeling gravitational collapse of anisotropic elastic materials, analyzing their singularities and implications for the Cosmic Censorship conjecture.

Contribution

It presents a novel class of solutions with separation of variables, satisfying physical conditions, and explores their singularity structures related to cosmic censorship.

Findings

Existence of solutions with non-vanishing stresses and kinematic properties.

Classification of collapse outcomes as black holes or naked singularities.

Insights into the conditions affecting the Cosmic Censorship conjecture.

Abstract

A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe the gravitational collapse of a class of anisotropic elastic materials. Standard requirements of physical acceptability are satisfied, in particular, existence of an equation of state in closed form, weak energy condition, and existence of a regular Cauchy surface at which the collapse begins. The matter properties are generic in the sense that both the radial and the tangential stresses are non vanishing, and the kinematical properties are generic as well, since shear, expansion, and acceleration are also non-vanishing. As a test-bed for cosmic censorship, the nature of the future singularity forming at the center is analyzed as an existence problem for o.d.e. at a singular point using techniques based on comparison theorems, and the spectrum of endstates - blackholes or naked singularities - is found in full generality. Consequences of these results on the Cosmic Censorship conjecture are discussed.