A generalization of the Einstein-Straus vacuole

The Einstein-Straus vacuole, which refers to a spherical Schwarzschild regi on immersed in a Friedmann universe, is generalized to the case in which th e exterior is an inhomogeneous Lemaitre-Tolman-Bondi model. This allows the average density in the vacuole to be chosen independently of the exterior density, but means that the redshift on the boundary is then determined. If the average density in the vacuole is large the boundary shows a blueshift . Evidence is presented that we may be living in a vacuole approximating to the local group of galaxies. This implies that the cosmic expansion has no effect on dynamics even on the scale of the Milky Way.