Spherical gravitational collapse: tangential pressure and related equations of state

TL;DR

This paper derives equations governing spherical gravitational collapse with tangential pressure, revealing conditions for singularity formation and naked singularities, and provides an exact series solution for collapse with a linear equation of state.

Contribution

It introduces a new exact series solution for collapse with tangential pressure and compares singularity conditions to dust collapse models.

Findings

Singular and non-singular solutions can arise from collapse with tangential pressure.

Conditions for naked singularities are identical to dust collapse models.

An exact series solution for collapse with linear equation of state is obtained.

Abstract

We derive an equation for the acceleration of a fluid element in the spherical gravitational collapse of a bounded compact object made up of an imperfect fluid. We show that non-singular as well as singular solutions arise in the collapse of a fluid initially at rest and having only a tangential pressure. We obtain an exact solution of Einstein equations, in the form of an infinite series, for collapse under tangential pressure with a linear equation of state. We show that if a singularity forms in the tangential pressure model, the conditions for the singularity to be naked are exactly the same as in the model of dust collapse.