Invariant characterization of Szekeres models with positive cosmological constant

Abstract

We present an invariant characterization of black holes in the Szekeres spacetime with positive cosmological constant. In the formation of the black holes, we locate geometric horizons, and show that they coincide with the more traditional apparent horizons in the Szekeres models. We also define an invariant approach for detecting shell crossings. It is shown that shell crossing regions in the Szekeres models can be contained within the geometric horizons for situations where no naked singularities form, allowing for the study of astrophysical models that are inhomogeneous and with a cosmological constant. A measure of inhomogeneity through the dipole functions in the Szekeres models is used to compute shell crossing surfaces along particular directions in the spacetime. An example of the method applied to the axially symmetric collapse of a quasispherical dust is given, motivated by previous work on primordial black hole formation. Future extensions and generalizations of this work are also discussed.