Initial data and the end state of spherically symmetric gravitational collapse

TL;DR

This paper investigates how the initial conditions of a spherically symmetric matter cloud influence whether gravitational collapse results in a black hole or a naked singularity, showing both outcomes are possible from generic initial data.

Contribution

It demonstrates that for any initial density and pressure profiles, there exist evolution paths leading to either black holes or naked singularities, without assuming cosmic censorship.

Findings

Existence of evolution paths to black holes or naked singularities from generic initial data

Characterization of new black hole solutions without cosmic censorship

Non-zero measure set of initial configurations leading to different end states

Abstract

Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing gravitational collapse. It is shown that given an arbitrary regular distribution of matter at the initial epoch, there always exists an evolution from this initial data which would result either in a black hole or a naked singularity depending on the allowed choice of free functions available in the solution. It follows that given any initial density and pressure profiles for the cloud, there is a non-zero measure set of configurations leading either to black holes or naked singularities, subject to the usual energy conditions ensuring the positivity of energy density. We also characterize here wide new families of black hole solutions resulting from spherically symmetric collapse without requiring the cosmic censorship assumption.