Generalisations of the Einstein-Straus model to cylindrically symmetric settings

TL;DR

This paper investigates the extension of Einstein-Straus models to cylindrically symmetric contexts, revealing significant restrictions that prevent embedding static objects into certain cosmological models.

Contribution

It introduces new limitations on cylindrically symmetric Einstein-Straus models, showing the impossibility of embedding static objects in some homogeneous cosmologies.

Findings

Models have severe restrictions, including constant metric coefficients.

Embedding static cylindrically symmetric objects in certain cosmologies is impossible.

The symmetry preservation leads to fundamental constraints on model construction.

Abstract

We study generalisations of the Einstein--Straus model in cylindrically symmetric settings by considering the matching of a static space-time to a non-static spatially homogeneous space-time, preserving the symmetry. We find that such models possess severe restrictions, such as constancy of one of the metric coefficients in the non-static part. A consequence of this is that it is impossible to embed static locally cylindrically symmetric objects in reasonable spatially homogeneous cosmologies.