A group-theoretic characterisation of Taub-Nut spacetime

TL;DR

This paper proves that all Ricci-flat spacetimes with $SU(2) imes U(1)$ symmetry and non-null orbits are locally isometric to a class of Taub-NUT spacetimes, providing a group-theoretic classification.

Contribution

It offers a group-theoretic characterization of Taub-NUT spacetimes, showing they encompass all Ricci-flat solutions with specified symmetry and orbit conditions.

Findings

All such symmetric Ricci-flat spacetimes are locally isometric to generalized Taub-NUT.

The result classifies these spacetimes using symmetry and orbit structure.

Provides a new perspective on the structure of Taub-NUT solutions.

Abstract

We prove that any $G=SU(2)\times U(1)$ symmetric spacetime that is Ricci flat (i.e. solves the matter-free $\Lambda=0$ Einstein equations) with non-null $G$-orbits is locally isometric to some maximally extended generalised Taub-NUT spacetime.