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

Abstract

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–Nordström 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.