Initial data giving rise to naked singularities in spherically symmetric dust collapse

TL;DR

This paper investigates how different initial conditions in spherically symmetric dust collapse influence the formation of naked singularities, revealing that flat density profiles and high initial velocities make such singularities unlikely.

Contribution

It analyzes a four-parameter initial data family for dust collapse, identifying conditions that lead to naked singularities versus black hole formation.

Findings

Naked singularities occur in specific parameter limits.

Flat density profiles reduce the likelihood of naked singularities.

High initial velocities also decrease the probability of naked singularity formation.

Abstract

The phase space corresponding to a particular four-parameter family of initial data for the gravitational collapse of a spherically symmetric dust cloud is investigated. In a certain limit of the parameters, this family reproduces the case of homogenous mass density -constant mass distribution- and zero initial velocity, while in another limit, it generates a globally naked singularity. We show that for initial data characterizing flat density profiles, as well as large initial velocities, the probability of forming a globally naked singularity is low.