Cosmic censorship and spherical gravitational collapse with tangential pressure

TL;DR

This paper investigates spherical gravitational collapse with tangential pressure, demonstrating that positive pressure leads to horizon-covered singularities while negative pressure results in non-naked singularities, differing significantly from dust collapse behavior.

Contribution

It provides an exact solution framework for collapse with tangential pressure and analyzes the conditions for horizon formation and singularity visibility.

Findings

Positive pressure causes an outward expanding region near the center.

Collapse always results in covered singularities, not naked.

The evolution differs markedly from dust collapse even with small pressure ratios.

Abstract

We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state. It turns out that the Einstein equations can be reduced to the solution of an integral for the evolution of the area radius. We show that for positive pressure there is a finite region near the center which necessarily expands outwards, if collapse begins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity - any such singularity will necessarily be covered by a horizon. For negative pressure the entire object collapses inwards, but any singularities that could arise are not naked. Thus the nature of the evolution is very different from that of dust, even when the ratio of pressure to density is infinitesimally small.