Singularity resolution in gravitational collapse

TL;DR

This paper studies the gravitational collapse of a scalar field with a Higgs-like potential, showing that under certain conditions, the collapse avoids forming trapped surfaces and a singularity, resulting in a globally visible ultra high density region.

Contribution

It demonstrates that scalar field collapse can avoid singularity formation and trapped surfaces, providing new insights into gravitational collapse scenarios with Higgs-like potentials.

Findings

Collapse can reach ultra high densities without forming trapped surfaces.

Singularity can be avoided, leading to a globally visible high-density region.

Collapse evolution depends on transcendental density functions.

Abstract

We investigate the unhindered gravitational collapse of a homogeneous scalar field with nonzero potential, a two-dimensional analog of the Mexican hat-shaped Higgs field potential. The collapsing scalar field is surrounded by an exterior retarded (outgoing) generalized Vaidya spacetime. We prove that the density dependence on the scale factor cannot be expressed as an algebraic function in such a scenario. For a certain transcendental expression of the density of such field as a function of scale factor, we then show that the collapse evolves to a singularity at an infinite comoving time, which is equivalent to saying that the singularity is avoided altogether. An ultra high density region of the order of Planck length can, however, be reached in a finite comoving time. The absence of the formation of trapped surfaces makes this ultra high density region globally visible.