Slowly rotating voids in cosmology

We consider a spacetime consisting of an empty void separated from an almos t Friedmann-Lemaitre-wRobertson-Walker (FLRW) dust universe by a sphericall y symmetric, slowly rotating shell which is comoving with the cosmic dust. We treat in a unified manner all types of FLRW universes. The metric is exp ressed in terms of a constant characterizing the angular momentum of the sh ell, and parametrized by the comoving radius of the shell. Treating the rot ation as a first-order perturbation, we compute the dragging of inertial fr ames as well as the apparent motion of distant stars within the void. Final ly, we discuss, in terms of in principle measurable quantities, 'Machian' f eatures of the model.