Casimir effect in a 'half Einstein universe': an exactly solvable case in curved background and with a spherical boundary

The authors reconsider the Casimir problem for the massless conformal scalar field in a 'half Einstein universe'. They first calculate the renormalized vacuum energy by using the mode sum method. Next, they calculate the renormalized vacuum energy-momentum tensor by using the point-splitting method. They construct the Green function by using the eigenfunctions, which are obtained by solving the wave equation with the appropriate boundary conditions. They discuss the importance of this case as well as its relation to previous calculations.