Matching collapse and expansion across Matter Trapping surfaces in inhomogeneous $\Lambda$CDM models

TL;DR

This paper investigates the properties of matter trapping surfaces (MTS) in inhomogeneous $ ext{Lambda}$CDM models, revealing their role as characteristic surfaces that can separate independent solutions and presenting the first static, stable MTS in LTBdS models.

Contribution

It demonstrates that MTSs are characteristic surfaces of the Cauchy problem in spherical dust plus $ ext{Lambda}$ models and introduces the first static, stable MTS in LTBdS models.

Findings

MTSs are characteristic surfaces of the Cauchy problem.

MTSs can separate arbitrarily independent solutions.

First static, stable MTS found in LTBdS models.

Abstract

In the present work we examine the MTS, for the restriction to spherical dust plus $\Lambda$, proving that it actually is a characteristic surface of the Cauchy problem (generated by its characteristic curves), which opens the possibility for infinite solutions. This translate as the MTS being a boundary between arbitrarily independent solutions, reminiscent of the Birkhoff theorem effects. This property is illustrated with combinations of 3 examples containing MTSs and $\Lambda$ ($\Lambda$CDM, Schwarzschild-de\,Sitter, Lema\^itre-Tolman-Bondi-de\,Sitter: LTBdS -- i.e. the inhomogeneous, spherically symmetric $\Lambda$CDM). The LTBdS model presents a static, stable MTS for the first time.