Dyonic Black Holes in Kaluza-Klein Theory with a Gauss-Bonnet Action

Kaluza-Klein theory attempts a unification of gravity and electromagnetism through the hypothesis that spacetime has five dimensions, of which only four are observed. The original model gives rise to the standard Einstein-Maxwell theory after dimensional reduction. However, in five dimensions, the Einstein-Hilbert action is not unique, and one can add to it a Gauss-Bonnet term, giving rise to nonlinear corrections in the dimensionally reduced action. We consider such a model, which reduces to Einstein gravity nonminimally coupled to nonlinear electrodynamics. The black hole solutions of the four-dimensional model modify the Reissner-Nordstrom solutions of general relativity. We show that in the modified solutions, the gravitational field presents the standard singularity at r=0, while the electric field can be regular everywhere if the magnetic charge vanishes.