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