NUT-Charged Black Holes in Gauss-Bonnet Gravity

TL;DR

This paper explores Taub-NUT/bolt solutions in Gauss-Bonnet gravity across various dimensions, revealing conditions under which these solutions exist, their relation to Einstein gravity solutions, and the influence of base space geometry.

Contribution

It provides the first comprehensive analysis of NUT and bolt solutions in Gauss-Bonnet gravity, detailing their existence criteria and relation to Einstein gravity solutions.

Findings

NUT solutions in Gauss-Bonnet gravity reduce to Einstein solutions as the Gauss-Bonnet parameter approaches zero.

Existence of extremal NUT solutions depends on the base space being a product of 2-torii with specific curvature properties.

Bolt solutions exist for base spaces with zero or positive constant curvature, except in the absence of a cosmological term with zero curvature base space.

Abstract

We investigate the existence of Taub-NUT/bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in $d$ dimensions. We find that for all non-extremal NUT solutions of Einstein gravity having no curvature singularity at $r=N$, there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter $\alpha$ goes to zero. Furthermore there are no NUT solutions in Gauss-Bonnet gravity that yield non-extremal NUT solutions to Einstein gravity having a curvature singularity at $r=N$ in the limit $% \alpha \to 0$. Indeed, we have non-extreme NUT solutions in $2+2k$ dimensions with non-trivial fibration only when the $2k$-dimensional base space is chosen to be $\mathbb{CP}^{2k}$. We also find that the Gauss-Bonnet gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a 2-dimensional factor space of positive curvature. Indeed, when the base space has at most one positively curved two dimensional space as one of its factor spaces, then Gauss-Bonnet gravity admits extreme NUT solutions, even though there a curvature singularity exists at $r=N$. We also find that one can have bolt solutions in Gauss-Bonnet gravity with any base space with factor spaces of zero or positive constant curvature. The only case for which one does not have bolt solutions is in the absence of a cosmological term with zero curvature base space.