An invariant characterization of the quasi-spherical Szekeres dust models

• Published in: General relativity and gravitation 2019-12, Vol.51 (12), Article 164
• Main Authors: Coley, A. A., Layden, N., McNutt, D. D.
• Format: Article
• Language: English
• Subjects: Astronomical models; Astronomy; Astrophysics and Cosmology; Classical and Quantum Gravitation; Cosmology; Differential Geometry; Dust; Gravity; Horizon; Invariants; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Research Article; Spherical shells; Theoretical
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-019-2647-6

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.