Casimir energy in a curved background with a spherical boundary and arbitrary radius: An exact solution via the point splitting method

We calculate the renormalized quantum vacuum energy-momentum tensor inside a spherical boundary, where the background geometry inside the boundary is represented by the closed static Friedmann metric. The renormalized energy density has two terms, one of which comes from the local curvature and the other one is due to the presence of the boundary. The renormalized energy density has a nonintegrable divergence as the boundary is approached