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Variations on Birkhoff’s theorem

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Abstract

The relation between the expanding universe and local vacuum solutions, such as that for the Solar System, is crucially mediated by Birkhoff’s theorem. Here we consider how that relation works, and give generalizations of Birkhoff’s theorem when there are geometric and matter and perturbations. The issue of to what degree dark matter might influence the solar system emerges as a significant question.

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Notes

  1. This is of academic interest only, as charged stars do not exist in reality. If they did, astronomy would be governed by electric forces rather than gravity, because gravity is such a weak force.

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Acknowledgments

We thank Chris Clarkson for helpful comments, and the NRF and UCT Research Committee for financial support.

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Authors and Affiliations

  1. Mathematics Department and ACGC, University of Cape Town, Cape Town, 7700, South Africa

    George F. R. Ellis

  2. Astrophysics and Cosmology Research Unit, School of Mathematics Statistics and Computer Science, University of KwaZulu-Natal, Durban, 4000, South Africa

    Rituparno Goswami

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  1. George F. R. Ellis
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  2. Rituparno Goswami
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Correspondence to Rituparno Goswami.

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This article belongs to the Topical Collection: Progress in Mathematical Relativity with Applications to Astrophysics and Cosmology.

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Ellis, G.F.R., Goswami, R. Variations on Birkhoff’s theorem. Gen Relativ Gravit 45, 2123–2142 (2013). https://doi.org/10.1007/s10714-013-1568-z

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