Gravitational collapse of an isentropic perfect fluid with a linear equation of state

TL;DR

This paper studies how the initial conditions and the equation of state influence whether a collapsing perfect fluid forms a black hole or a naked singularity, clarifying the roles of initial data and dynamics in gravitational collapse outcomes.

Contribution

It demonstrates that the final outcome of gravitational collapse depends on initial data and free functions, highlighting the influence of the equation of state and initial conditions.

Findings

Collapse outcomes depend on initial density and pressure profiles.

Choice of free functions affects whether a black hole or naked singularity forms.

The role of the equation of state in collapse dynamics is clarified.

Abstract

We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state $p=k\rho$. It is shown that given a regular initial data in terms of the density and pressure profiles at the initial epoch from which the collapse develops, the black hole or naked singularity outcomes depend on the choice of rest of the free functions available, such as the velocities of the collapsing shells, and the dynamical evolutions as allowed by Einstein equations. This clarifies the role that equation of state and initial data play towards determining the final fate of gravitational collapse.