A two-mass expanding exact space-time solution

Details A two-mass expanding exact space-time solution A two-mass expanding exact space-time solution

2010-05-11

arxiv.org/abs/1005.1809v2

Gen.Rel.Grav.43:191-205,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 5 figures. Replaced to match the published version

Scientific paper

10.1007/s10714-010-1081-6

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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