Singular shell embedded into a cosmological model

TL;DR

This paper extends Israel's formalism to describe the dynamics of singular shells within non-vacuum cosmological models, deriving equations of motion and analyzing embeddings in Schwarzschild and FLRW spacetimes.

Contribution

It generalizes the formalism for singular shells to non-vacuum universes and provides new solutions for shell embeddings in cosmological models.

Findings

Derived relativistic equations of motion for shells in non-vacuum spacetimes.

Presented solutions for shell embeddings with and without embedded masses.

Reviewed the embedding of Schwarzschild mass into cosmological models.

Abstract

We generalize Israel's formalism to cover singular shells embedded in a non-vacuum Universe. That is, we deduce the relativistic equation of motion for a thin shell embedded in a Schwarzschild/Friedmann-Lemaitre-Robertson-Walker spacetime. Also, we review the embedding of a Schwarzschild mass into a cosmological model using "curvature" coordinates and give solutions with (Sch/FLRW) and without the embedded mass (FLRW).