In flat (3+1)-dimensional spacetime, the vacuum energy induced by an impenetrable magnetic flux tube with Robin boundary conditions depends on the curvature coupling ξ; only Dirichlet and Neumann boundary conditions make the ξ-term vanish.
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Effects of Curvature-Scalar Coupling on Vacuum Energy in Flat (3+1)-Dimensional Space-Time
In flat (3+1)-dimensional spacetime, the vacuum energy induced by an impenetrable magnetic flux tube with Robin boundary conditions depends on the curvature coupling ξ; only Dirichlet and Neumann boundary conditions make the ξ-term vanish.