Two-boundary problems in Euclidean quantum gravity

Recent work in the literature has studied a new set of local boundary condi tions for the quantized gravitational field, where the spatial components o f metric perturbations, and ghost modes, are subject to Robin boundary cond itions, whereas normal components of metric perturbations obey Dirichlet bo undary conditions. Such boundary conditions are here applied to evaluate th e one-loop divergence on a portion of flat Euclidean four-space bounded by two concentric three-spheres.