Taub-NUT/bolt black holes in Gauss-Bonnet-Maxwell gravity

We present a class of higher-dimensional solutions to Gauss-Bonnet-Maxwell equations in 2k+2 dimensions with a U (1) fibration over a 2k-dimensional base space B. These solutions depend on two extra parameters, other than the mass and the Newman-Unti-Tamburino charge, which are the electric charge q and the electric potential at infinity V. We find that the form of metric is sensitive to geometry of the base space, while the form of electromagnetic field is independent of B. We investigate the existence of Taub-Newman-Unti-Tamburino/bolt solutions and find that in addition to the two conditions of uncharged Newman-Unti-Tamburino solutions, there exist two other conditions. These two extra conditions come from the regularity of vector potential at r=N and the fact that the horizon at r=N should be the outer horizon of the black hole. We find that for all nonextremal Newman-Unti-Tamburino solutions of Einstein gravity having no curvature singularity at r=N, there exist Newman-Unti-Tamburino solutions in Gauss-Bonnet-Maxwell gravity. Indeed, we have nonextreme Newman-Unti-Tamburino solutions in 2+2k dimensions only when the 2k-dimensional base space is chosen to be CP^2k. We also find that the Gauss-Bonnet-Maxwell gravity has extremal Newman-Unti-Tamburino solutions whenever the base space is a product of 2-torii with at most a 2-dimensional factor space of positive curvature, even though there a curvature singularity exists at r=N. We also find that one can have bolt solutions in Gauss-Bonnet-Maxwell gravity with any base space. The only case for which one does not have black hole solutions is in the absence of a cosmological term with zero curvature base space.