Atiyah-Hitchin in Five Dimensional Einstein-Gauss-Bonnet Gravity

TL;DR

This paper constructs new exact solutions in five-dimensional Einstein-Gauss-Bonnet gravity using Atiyah-Hitchin geometry, revealing regular, physically constrained solutions with interesting extremal limit behaviors.

Contribution

It introduces a novel class of stationary solutions based on Atiyah-Hitchin geometry in five-dimensional Einstein-Gauss-Bonnet gravity, with analytical and numerical analysis.

Findings

Solutions are regular everywhere.

Extremal limits reduce to bolt and Taub-NUT geometries.

Asymptotic metrics are regular and well-behaved.

Abstract

We construct a new class of stationary exact solutions to five-dimensional Einstein-Gauss-Bonnet gravity. The solutions are based on four-dimensional self-dual Atiyah-Hitchin geometry. We find analytical solutions to the five-dimensional metric function that are regular everywhere. We find some constraints on the possible physical solutions by investigating the solutions numerically. We also study the behavior of the solutions in the extremal limits of the Atiyah-Hitchin geometry. In the extremal limits, the Atiyah-Hitchin metric reduces to a bolt structure and Euclidean Taub-NUT space, respectively. In these limits, the five-dimensional metric function approaches to a constant value and infinity, respectively. We find the asymptotic metrics are regular everywhere.