Accelerating Taub-NUT and Eguchi-Hanson solitons in four dimensions

TL;DR

This paper develops a method to generate new four-dimensional vacuum Einstein solutions, including accelerating Taub-NUT and Eguchi-Hanson solitons, by exploiting SL(2,R) symmetry and applying it to known solutions.

Contribution

It introduces a solution-generating technique using SL(2,R) symmetry to produce accelerating versions of known Einstein solutions, including Taub-NUT and Eguchi-Hanson solitons.

Findings

New accelerating Taub-NUT solutions derived.

New accelerating Eguchi-Hanson solutions derived.

Charged versions of solutions also constructed.

Abstract

We construct new solutions of the vacuum Einstein field equations in four dimensions via a solution generating method utilizing the SL(2,R) symmetry of the reduced Lagrangian. We apply the method to an accelerating version of the Zipoy-Voorhees solution and generate new solutions which we interpret to be the accelerating versions of the Zipoy-Voorhees generalisation of the Taub-NUT solution (with Lorentzian signature) and the Zipoy-Voorhees generalisation of the Eguchi-Hanson solitons (with Euclidean signature). As an intermediary in the solution-generating process we obtain charged versions of the accelerated Zipoy-Voorhees-like families of solutions. Finally we present the accelerating version of the Taub-NUT solution and discuss its properties.