An invariant characterization of the quasi-spherical Szekeres dust models

TL;DR

This paper introduces a method to identify key features of quasi-spherical Szekeres dust models using Cartan invariants, aiding understanding of black hole formation in cosmology.

Contribution

It provides an invariant characterization of the models, linking geometric invariants to physical phenomena like shell-crossings and apparent horizons.

Findings

Apparent horizon detected by a Cartan invariant

Cartan invariants characterize shell-crossings and spacetime expansion

Invariant criteria for black hole formation in these models

Abstract

The quasi-spherical Szekeres dust solutions are a generalization of the spherically symmetric Lemaitre-Tolman-Bondi dust models where the spherical shells of constant mass are non-concentric. The quasi-spherical Szekeres dust solutions can be considered as cosmological models and are potentially models for the formation of primordial black holes in the early universe. Any collapsing quasi-spherical Szekeres dust solution where an apparent horizon covers all shell-crossings that will occur can be considered as a model for the formation of a black hole. In this paper we will show that the apparent horizon can be detected by a Cartan invariant. We will show that particular Cartan invariants characterize properties of these solutions which have a physical interpretation such as: the expansion or contraction of spacetime itself, the relative movement of matter shells, shell-crossings and the appearance of necks and bellies.