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Generalization of the Einstein-Straus model to anisotropic settings

Filipe C. Mena, Reza Tavakol, and Raül Vera

  • School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom

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Phys. Rev. D 66, 044004 – Published 16 August, 2002

DOI: https://doi.org/10.1103/PhysRevD.66.044004

Abstract

We study the possibility of generalizing the Einstein-Straus model to anisotropic settings by considering the matching of locally cylindrically symmetric static regions to the set of G4 on S3 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 generalized to such anisotropic cases.

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Phys. Rev. D 66, 044004– Published 16 August, 2002
  • Received 18 April 2002

© 2002 American Physical Society

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