Negative Pressure and Naked Singularities in Spherical Gravitational Collapse

TL;DR

This paper investigates how the sign and magnitude of radial pressure influence the formation of black holes or naked singularities during spherical gravitational collapse, revealing conditions under which singularities are visible or hidden.

Contribution

It provides a detailed analysis of the role of radial pressure in determining the nature of singularities in classical spherical collapse, highlighting conditions for naked singularity formation.

Findings

Positive radial pressure leads to covered singularities.

Negative radial pressure can result in naked singularities if pressure-to-density ratio ≤ -1/3.

Threshold ratio of pressure to density determines horizon formation.

Abstract

Assuming the weak energy condition, we study the nature of the non-central shell-focussing singularity which can form in the gravitational collapse of a spherical compact object in classical general relativity. We show that if the radial pressure is positive, the singularity is covered by a horizon. For negative radial pressures, the singularity will be covered if the ratio of pressure to the density is greater than -1/3 and naked if this ratio is $\leq -1/3$.