Gravitational collapse of scalar and vector fields

TL;DR

This paper investigates the gravitational collapse of homogeneous scalar and vector fields with various potentials, demonstrating conditions leading to black holes or naked singularities, and analyzing their strength and matching with Vaidya spacetime.

Contribution

It introduces classes of potentials for scalar and vector fields that determine collapse outcomes, and examines the strength of resulting singularities within homogeneous models.

Findings

Certain potentials lead to black hole formation.

Some potentials produce strong naked singularities.

Collapse outcomes depend on potential choice.

Abstract

We study here the unhindered gravitational collapse of spatially homogeneous (SH) scalar fields $\phi$ with a potential $V_{s}(\phi)$, as well as vector fields $\tilde{A}$ with a potential $V_{v}(B)$ where $B=g(\tilde{A},\tilde{A})$ and $g$ is the metric tensor. We show that in both cases, classes of potentials exist that give rise to black holes or naked singularities depending on the choice of the potential. The strength of the naked singularity is examined, and they are seen to be strong, in the sense of Tipler, for a wide class of respective potentials. We match the collapsing scalar/vector field with a generalized Vaidya spacetime outside. We highlight that full generality is maintained within the domain of SH scalar or vector field collapse.