On the uniqueness of the Einstein-Straus model

Details On the uniqueness of the Einstein-Straus model On the uniqueness of the Einstein-Straus model

Sep 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001cqgra..18.3645m&link_type=abstract

Classical and Quantum Gravity, Volume 18, Issue 17, pp. 3645-3663 (2001).

Mathematics

Logic

7

Scientific paper

We show that the Einstein-Straus model does not give a robust answer to the problem of the influence of the cosmic expansion on the local physics. This is done by finding the most general static region embeddable in a Friedmann-Lemaître-Robertson-Walker expanding cosmology and showing that the model must be `almost spherically symmetric'. More precisely, we show that the boundary of the static region must be a 2-sphere at each instant of cosmic time. The motion of this 2-sphere in spacetime is as follows: its `would-be' centre (if there were no static region) moves along a path whose projection on any 3-space of constant cosmic time is a geodesic with respect to the induced 3-metric. The velocity of this geodesic is determined from the matching. In particular, this centre must be at rest with respect to the cosmological flow (thus giving a spherically symmetric model) when any of the standard energy-momentum tensors inside the static region is imposed.

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