Vacuum energy, variational methods, and the Casimir energy

Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods the Schwarzschild and flat space energy difference. The one-loop approximation for TT tensors is considered here. An analogy between the computed energy difference in momentum space and the Casimir effect is illustrated. We find a singular behavior in the UV limit, due to the presence of the horizon when r=2m. When r>2m this singular behavior disappears, which is in agreement with various other models previously presented. [S0556-2821(99)02910-0].