On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust

TL;DR

This paper analyzes how initial density parameters influence whether a collapsing dust cloud forms a black hole or a naked singularity, revealing a critical threshold in initial conditions.

Contribution

It identifies a specific initial data parameter threshold that determines the end state of gravitational collapse in inhomogeneous dust models.

Findings

Collapse results in black hole if parameter β > 0.0113

Collapse results in naked singularity if β < 0.0113

Initial gravitational potential strength predicts collapse outcome

Abstract

We consider here the gravitational collapse of a spherically symmetric inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a general class of these models, we find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of the initial density distribution, which are $\rho_{c}$, the initial central density of the massive body, and $R_0$, the initial boundary. The collapse ends in a black hole if the dimensionless quantity $\beta$ constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if $\beta$ is less than this number. A simple interpretation of this result can be given in terms of the strength of the gravitational potential at the starting epoch of the collapse.