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

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 analyse the case of self-similar spacetimes and gain some insight into the role of stresses in deciding the nature of the singularities in this case.