Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-08-29
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Revtex 3.0, preprint, 20 pages, new references included. Some Comments on the reparametrisation invariance added in the introd
Scientific paper
We calculate, in a class of Gauge invariant functionals, by variational methods, the difference of vacuum energy between two different backgrounds: Schwarzschild and Flat Space. We perform this evaluation in an Hamiltonian formulation of Quantum Gravity by standard ''$3+1$'' decomposition. After the decomposition the scalar curvature is expanded to second order with respect to the Schwarzschild metric. We evaluate this energy difference in momentum space, in the lowest possible state (regardless of any negative mode). 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 presented in the literature.
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