Atiyah-Hitchin in Five Dimensional Einstein-Maxwell Theory

TL;DR

This paper constructs and analyzes new five-dimensional Einstein-Maxwell solutions based on Atiyah-Hitchin space, revealing their geometric properties and asymptotic behavior through numerical methods.

Contribution

It introduces exact five-dimensional Einstein-Maxwell solutions using Atiyah-Hitchin space, exploring their properties despite the lack of explicit closed-form expressions.

Findings

Solutions are regular except at the bolt location.

Metrics asymptotically approach Euclidean Taub-NUT space.

Properties are investigated numerically due to the lack of explicit forms.

Abstract

We construct exact solutions to five-dimensional Einstein-Maxwell theory based on Atiyah-Hitchin space. The solutions cannot be written explicitly in a closed form, so their properties are investigated numerically. The five-dimensional metric is regular everywhere except on the location of original bolt in four-dimensional Atiyah-Hitchin base space. On each time-fixed slices, the metric, asymptotically approaches an Euclidean Taub-NUT space.