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Generalisation of the Einstein-Straus model to anisotropic settings

Filipe C. Mena·Reza Tavakol·Raül Vera
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Abstract

We study the possibility of generalising the Einstein--Straus model to anisotropic settings, by considering the matching of locally cylindrically symmetric static regions to the set of $G_4$ on $S_3$ locally rotationally symmetric (LRS) spacetimes. We show that such matchings preserving the symmetry are only possible for a restricted subset of the LRS models in which there is no evolution in one spacelike direction. These results are applied to spatially homogeneous (Bianchi) exteriors where the static part represents a finite bounded interior region without holes. We find that it is impossible to embed finite static strings or other locally cylindrically symmetric static objects (such as bottle or coin-shaped objects) in reasonable Bianchi cosmological models, irrespective of the matter content. Furthermore, we find that if the exterior spacetime is assumed to have a perfect fluid source satisfying the dominant energy condition, then only a very particular family of LRS stiff fluid solutions are compatible with this model. Finally, given the interior/exterior duality in the matching procedure, our results have the interesting consequence that the Oppenheimer-Snyder model of collapse cannot be generalised to such anisotropic cases.

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Filipe C. Mena, Reza Tavakol, Raül Vera. 2002-05-03. Generalisation of the Einstein-Straus model to anisotropic settings. https://doi.org/10.1103/physrevd.66.044004

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