Singularities in gravitational collapse with radial pressure

TL;DR

This paper investigates how radial pressure influences gravitational collapse, revealing that visible, strong singularities can form from generic initial conditions, and pressure modifies possible endstates.

Contribution

It provides an analytical solution for spherical collapse with radial pressure and explores how pressure affects singularity formation and visibility.

Findings

Visible, Tipler strong singularities can develop from generic initial data.

Radial pressure changes the spectrum of collapse endstates.

Pressure can prevent singularities only at high energy densities.

Abstract

We analyze spherical dust collapse with non-vanishing radial pressure, $\Pi$, and vanishing tangential stresses. Considering a barotropic equation of state, $\Pi=\gamma\rho$, we obtain an analytical solution in closed form---which is exact for $\gamma=-1,0$, and approximate otherwise---near the center of symmetry (where the curvature singularity forms). We study the formation, visibility, and curvature strength of singularities in the resulting spacetime. We find that visible, Tipler strong singularities can develop from generic initial data. Radial pressure alters the spectrum of possible endstates for collapse, increasing the parameter space region that contains no visible singularities, but cannot by itself prevent the formation of visible singularities for sufficiently low values of the energy density. Known results from pressureless dust are recovered in the $\gamma=0$ limit.