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A two-mass expanding exact space-time solution

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Abstract

In order to understand how locally static configurations around gravitationally bound bodies can be embedded in an expanding universe, we investigate the solutions of general relativity describing a space–time whose spatial sections have the topology of a 3-sphere with two identical masses at the poles. We show that Israel junction conditions imply that two spherically symmetric static regions around the masses cannot be glued together. If one is interested in an exterior solution, this prevents the geometry around the masses to be of the Schwarzschild type and leads to the introduction of a cosmological constant. The study of the extension of the Kottler space–time shows that there exists a non-static solution consisting of two static regions surrounding the masses that match a Kantowski–Sachs expanding region on the cosmological horizon. The comparison with a Swiss-Cheese construction is also discussed.

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Authors and Affiliations

  1. Institut d’Astrophysique de Paris, UMR-7095 du CNRS, Université Paris-VI Pierre et Marie Curie, 98bis bd Arago, 75014, Paris, France

    Jean-Philippe Uzan

  2. Department of Mathematics and Applied Mathematics, Astrophysics Cosmology and Gravitation Center, University of Cape Town, Rondebosch, Cape Town, 7701, South Africa

    George F. R. Ellis & Julien Larena

Authors
  1. Jean-Philippe Uzan
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  2. George F. R. Ellis
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  3. Julien Larena
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Correspondence to Julien Larena.

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Uzan, JP., Ellis, G.F.R. & Larena, J. A two-mass expanding exact space-time solution. Gen Relativ Gravit 43, 191–205 (2011). https://doi.org/10.1007/s10714-010-1081-6

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