Gravitational Casimir energy in even dimensions

A method is described for calculating the one-loop gravitational effective potential (gravitational Casimir energy) in Kaluza-Klein theories with an even number of dimensions. The self-consistency condition that the effective potential vanish at its minimum is used to fix the subtraction point for a renormalization of the graviton wave function. The method avoids the use of a higher-dimensional cosmological constant. The calculation is performed for the background manifold (Minkowski space)x(N-sphere), in which case the potential is shown to be real and to possess a single stationary point, which turns out to be a maximum. A higher-dimensional cosmological constant appears to be necessary for global stability of the potential