Black holes vs. naked singularities formation in collapsing Einstein's clusters

TL;DR

This paper investigates how the initial density, velocity, and angular momentum profiles of Einstein's clusters influence whether their gravitational collapse results in a black hole or a naked singularity, extending previous research in the field.

Contribution

It introduces a detailed analysis of initial data parameters and their derivatives to determine collapse outcomes, expanding understanding of gravitational collapse in Einstein's clusters.

Findings

Collapse outcome depends on derivatives of initial profiles.

Black holes form under certain initial conditions.

Naked singularities can occur depending on initial data.

Abstract

Non-static, spherically symmetric clusters of counter-rotating particles, of the type first introduced by Einstein, are analysed here. The initial data space can be parameterized in terms of three arbitrary functions, namely; initial density, velocity and angular momentum profiles. The final state of collapse, black hole or naked singularity, turns out to depend on the order of the first non-vanishing derivatives of such functions at the centre. The work extends recent results by Harada, Iguchi and Nakao.