Harmonic Space Construction of the Quaternionic Taub-NUT metric

TL;DR

This paper details the harmonic space construction of a quaternionic extension of the Taub-NUT metric, providing an explicit form that incorporates isometry and parameter dependence, including special limiting cases.

Contribution

It introduces a harmonic space method to explicitly construct a quaternionic Taub-NUT metric with specific symmetries and parameters, expanding geometric understanding.

Findings

Explicit harmonic space form of the quaternionic Taub-NUT metric

Identification of isometry group as SU(2)×U(1)

Analysis of limiting cases with special parameter choices

Abstract

We present details of the harmonic space construction of a quaternionic extension of the four-dimensional Taub-NUT metric. As the main merit of the harmonic space approach, the metric is obtained in an explicit form following a generic set of rules. It exhibits $SU(2)\times U(1)$ isometry group and depends on two parameters, Taub-NUT `mass' and the cosmological constant. We consider several limiting cases of interest which correspond to special choices of the involved parameters.