Vacuum Energy, Variational Methods and the Casimir Energy

TL;DR

This paper uses variational methods to compute the energy difference between Schwarzschild and flat space, revealing a singular UV behavior near the horizon and drawing an analogy to the Casimir effect.

Contribution

It introduces a variational approach to calculate gravitational energy differences and explores their relation to the Casimir effect, including the behavior near horizons.

Findings

Singular UV behavior at the horizon ($r=2m$)

Disappearance of singularity for $r>2m$

Analogy established between energy difference and Casimir effect

Abstract

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 behaviour in the UV-limit, due to the presence of the horizon when $r=2m.$ When $r>2m$ this singular behaviour disappears, which is in agreement with various other models previously presented.