Trapped surfaces and spherical closed cosmologies

TL;DR

This paper establishes precise conditions under which trapped surfaces form in closed, spherically symmetric cosmological models, highlighting the roles of matter distribution, expansion, and matter flow.

Contribution

It provides necessary and sufficient criteria for trapped surface formation in closed cosmologies with localized inhomogeneities, directly in terms of physical variables.

Findings

Trapped surfaces form when excess matter is sufficiently concentrated.

Expansion and outward matter flow inhibit trapped surface formation.

Total excess mass must be limited to prevent trapped surfaces.

Abstract

This article gives necessary and sufficient conditions for the formation of trapped surfaces in spherically symmetric initial data defined on a closed manifold. Such trapped surfaces surround a region in which there occurs an enhancement of matter over the average. The conditions are posed directly in terms of physical variables and show that what one needs is a relatively large amount of excess matter confined to a small volume. The expansion of the universe and an outward flow of matter oppose the formation of trapped surfaces; an inward flow of matter helps. The model can be regarded as a Friedmann-Lema\^\i tre-Walker cosmology with localized spherical inhomogeneities. We show that the total excess mass cannot be too large.