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Vacuum-energy calculations with ideal reflecting boundaries are plagued byboundary divergences, which presumably correspond to real (but finite) physicaleffects occurring near the boundary. Our working hypothesis is that the stresstensor for idealized boundary conditions with some finite cutoff should be areasonable ad hoc model for the true situation. The theory will have a sensiblerenormalized limit when the cutoff is taken away; this requires making sense ofthe Einstein equation with a distributional source. Calculations with thestandard ultraviolet cutoff reveal an inconsistency between energy and pressuresimilar to the one that arises in noncovariant regularizations of cosmologicalvacuum energy. The problem disappears, however, if the cutoff is a spatialpoint separation in a "neutral" direction parallel to the boundary. Here wedemonstrate these claims in detail, first for a single flat reflecting wallintersected by a test boundary, then more rigorously for a region of finitecross section surrounded by four reflecting walls. We also show how themoment-expansion theorem can be applied to the distributional limits of thesource and the solution of the Einstein equation, resulting in a mathematicallyconsistent differential equation where cutoff-dependent coefficients have beenidentified as renormalizations of properties of the boundary. A number ofissues surrounding the interpretation of these results are aired.

Surface Vacuum Energy in Cutoff Models: Pressure Anomaly and Distributional Gravitational Limit