Generalisations of the Einstein-Straus model to cylindrically symmetric settings

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.