Dyonic black holes in nonlinear electrodynamics from Kaluza–Klein theory with a Gauss–Bonnet term

Five-dimensional Kaluza-Klein theory with an Einstein-Gauss-Bonnet Lagrangian induces nonlinear corrections to the four-dimensional Maxwell equations, which however remain second-order. Although these corrections do not have effect on the purely electric or magnetic monopole solutions for pointlike charges, they affect the dyonic solutions, smoothing the electric field at the origin for positive values of the Gauss-Bonnet coupling constant. We investigate these solutions in flat space, and then extend them in the presence of a minimal coupling to gravity, obtaining exact charged black hole solutions that generalize the Reissner-Nordström metric.