  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.
