Dyonic black holes in nonlinear electrodynamic from Kaluza-Klein theory with a Gauss-Bonnet term

TL;DR

This paper explores how five-dimensional Kaluza-Klein theory with a Gauss-Bonnet term modifies dyonic black hole solutions in four dimensions, revealing effects on electric fields and black hole metrics.

Contribution

It introduces new dyonic black hole solutions in a modified gravity framework incorporating nonlinear electrodynamics from higher dimensions.

Findings

Gauss-Bonnet corrections smooth electric fields at the origin for negative coupling.

Charged black hole solutions generalize Reissner-Nordström metrics.

Nonlinear electrodynamics effects are significant for dyonic configurations.

Abstract

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 negative values of the Gauss-Bonnet coupling constant. We investigate these solutions in flat space, and then extend them in the presence of gravity, obtaining charged black hole solutions that generalize the Reissner-Nordstr\"om metric.