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TitleReview on exact and perturbative deformations of the Einstein-Straus model : uniqueness and rigidity results
Author(s)Mena, Filipe C.
Mars, Marc
Vera, Raul
KeywordsEinstein-Straus model
Inhomogeneous cosmology
Influence of expansion in local systems
Matching of spacetimes
Static regions in FLRW
Stationary and axisymmetric regions in FLRW
Static regions in LRS
Perturbed matching theory
Perturbed Einstein-Straus model
Stationary and axisymmetric perturbations of Schwarzschild
FLRW perturbations
Issue date1-Oct-2013
PublisherSpringer Verlag
JournalGeneral Relativity and Gravitation
Abstract(s)The Einstein-Straus model consists of a Schwarzschild spherical vacuole in a Friedman-Lema^ tre-Robertson-Walker (FLRW) dust spacetime (with or without ). It constitutes the most widely accepted model to answer the question of the in uence of large scale (cosmological) dynamics on local systems. The conclusion drawn by the model is that there is no in uence from the cosmic background, since the spher- ical vacuole is static. Spherical generalizations to other interior matter models are commonly used in the construction of lumpy inhomogeneous cosmological models. On the other hand, the model has proven to be reluctant to admit non-spherical generalizations. In this review, we summarize the known uniqueness results for this model. These seem to indicate that the only reasonable and realistic non- spherical deformations of the Einstein-Straus model require perturbing the FLRW background. We review results about linear perturbations of the Einstein-Straus model, where the perturbations in the vacuole are assumed to be stationary and axially symmetric so as to describe regions (voids in particular) in which the matter has reached an equilibrium regime.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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