Effective Energy-Momentum Tensor and Classical Magnetic Charge in Kaluza-Klein Gravity

We consider a version of Kaluza-Klein theory where the cylinder condition is not imposed. We replace this condition with the requirement that physics in four-dimensional spacetime should remain invariant under changes of coordinates in the five-dimensional bulk. This invariance does not eliminate physical effects from the extra dimension but separates them from spurious geometrical ones. We allow the metric and other quantities in the theory to have explicit dependence of the extra variable. We use the appropriate splitting technique to construct the most general induced energy-momentum tensor, compatible with the required invariance. It generalizes all previous results in the literature. There are two four-vectors, J m and J μ e , that separately satisfy the usual equation of continuity in 4D. These vectors appear as source-terms in equations that closely resemble the ones of electromagnetism. These are Maxwell-like equations for an antisymmetric tensor F̂μν that generalizes the usual electromagnetic one. This generalization is not an assumption, but follows naturally from the theory. Thus, if F̂μν can be identified with the electromagnetic tensor, then the theory predicts the existence of classical magnetic charge and current. The splitting formalism used allows us to construct 4D physical quantities from five-dimensional ones, in a way that is independent on how we choose our spacetime coordinates from those of the bulk. PACS: 04.50.+h; 04.20.Cv