CASIMIR ENERGY IN A CURVED BACKGROUND WITH A SPHERICAL BOUNDARY - AN EXACTLY SOLVABLE CASE

We reconsider the Casimir effect for the massless conformal scalar field in a ''half Einstein universe.'' This case is interesting in that it could be solved analytically by several different methods. Thus, it allows us to compare and understand effects of different approaches. We first calculate the renormalized vacuum energy by using the mode sum method and study the effects of different cutoff functions. Next, we calculate the renormalized vacuum energy-momentum tensor by using the covariant point-splitting method. We construct the Green's functions by using the eigenfunctions, which are obtained by solving the wave equation with the appropriate boundary conditions (Dirichlet and Neumann). We discuss further properties of this case as well as its relation to previous calculations.