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 (Formula presented) When (Formula presented) this singular behavior disappears, which is in agreement with various other models previously presented.