Modiication of the Coulomb Potential from a Kaluza-klein Model with a Gauu-bonnet Term in the Action Typeset Using Revt E X

In four dimensions a Gauu-Bonnet term in the action corresponds to a total derivative, and it does therefore not contribute to the classical equations of motion. For higher-dimensional geometries this term has the interesting property (which it shares with other dimensionally continued Euler densities) that when the action is varied with respect to the metric, it gives rise to a symmetric, covariantly conserved tensor of rank two which is a function of the metric and its rst and second order derivatives. Here we review the uniication of General Relativity and electromagnetism in the classical ve-dimensional, restricted (with g 55 = 1) Kaluza-Klein model. Then we discuss the modiications of the Einstein-Maxwell theory that results from adding the Gauu-Bonnet term in the action. The resulting four-dimensional theory describes a non-linear U(1) gauge theory non-minimally coupled to gravity. For a point charge at rest we nd a perturbative solution for large distances which gives a mass-dependent correction to the Coulomb potential. Near the source we nd a power-law solution which seems to cure the short-distance divergency of the Coulomb potential. Possible ways to obtain an experimental upper limit to the coupling of the hypothetical Gauu-Bonnet term are also considered.