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Abstract

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 Friedman-Lemaitre-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 two-sphere at each instant of cosmic time. The motion of this two-sphere in spacetime is as follows: its would-be center (if there was 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 center must be at rest with respect to the cosmologic flow (thus giving a spherically symmetric model) when any of the standard energy-momentum tensors inside the static region is imposed.