Initial Data and the Final Fate of Inhomogeneous Dust Collapse

TL;DR

This paper investigates how the initial conditions of an inhomogeneous dust cloud influence whether it ends as a black hole or a naked singularity, highlighting the role of initial velocities in determining the final outcome.

Contribution

It demonstrates that initial velocities can be chosen to direct the collapse towards either a black hole or a naked singularity, and introduces a new family of black hole solutions with positive energy conditions.

Findings

Initial velocity choices determine collapse outcome.

Existence of a new family of black hole solutions.

Collapse can result in either a black hole or naked singularity.

Abstract

We examine here the relevance of the initial state of a collapsing dust cloud towards determining it's final fate in the course of a continuing gravitational collapse. It is shown that given any arbitrary matter distribution $M(r)$ for the cloud at the initial epoch, there is always a freedom to choose rest of the initial data, namely the initial velocities of the collapsing spherical shells, so that the collapse could result either in a black hole or a naked singularity depending on this choice. Thus, given the initial density profile, to achieve the desired end state of the gravitational collapse one has to give a suitable initial velocity to the cloud. We also characterize here a wide new family of black hole solutions resulting from inhomogeneous dust collapse. These configurations obey the usual energy conditions demanding the positivity of energy density.