Abstract
The Einstein–Straus model results from the embedding of a Schwarzs- child spherically symmetric region on a FLRW dust spacetime. It constituted the first, and most widely accepted, model to answer the question of the influence of large scale (cosmological) dynamics on local systems. The conclusion drawn by the model was that there is no influence from the cosmic background, since the spherical vacuole is static. However, apart from being highly inflexible, the model has been proved to be remarkably reluctant to admit non-spherical generalizations. This led us to consider the problem of the linearised perturbations of the Einstein–Straus model, first from a purely geometrical point of view. We now concentrate on imposing the Einstein field equations and in understanding the mixing between vector and tensor modes in the FLRW side, which arises as a consequence of the existence of an inner boundary. In particular, we analyse the relationship between exterior gravitational waves and the stationary and axial vacuum perturbations inside.
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Acknowledgements
MM acknowledges support from the projects FIS2009-07238, FIS2012-30926 (MICINN) and P09-FQM-4496 (Junta de Andalucía and FEDER funds). RV thanks support from project IT-221-07 of the Basque Government, and FIS2010-15492 from the MICINN. FM thanks CMAT, University of Minho, for support through FEDER Funds—“Programa COMPETE” and FCT Projects Est-C/MAT/UI0013/2011, PTDC/MAT/108921/2008 and CERN/FP/116377/2010.
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Mars, M., Mena, F.C., Vera, R. (2014). Cosmological Gravitational Waves and Einstein–Straus Voids. In: García-Parrado, A., Mena, F., Moura, F., Vaz, E. (eds) Progress in Mathematical Relativity, Gravitation and Cosmology. Springer Proceedings in Mathematics & Statistics, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40157-2_6
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DOI: https://doi.org/10.1007/978-3-642-40157-2_6
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