A New Way to Derive the Taub-NUT Metric with Positive Cosmological Constant

TL;DR

This paper explores a new approach to deriving the Taub-NUT metric within biaxial Bianchi IX models with positive cosmological constant, highlighting the role of Killing tensors and discussing asymptotic behaviors.

Contribution

It introduces a novel method leveraging Killing tensors to derive the Taub-NUT metric in Lambda-Taub-NUT spacetime, expanding understanding of Bianchi IX models.

Findings

Identification of two non-trivial Killing tensors in the minisuperspace.

Derivation of the Taub-NUT metric using these tensors.

Discussion on the asymptotic behavior of Bianchi IX models.

Abstract

We investigate a biaxial Bianchi IX model with positive cosmological constant, which is sometimes called the Lambda-Taub-NUT spacetime, whose exact solution is well known. The minisuperspace of biaxial Bianchi IX models admits two non-trivial Killing tensors that play an important role for deriving the Taub-NUT metric. We also give a brief discussion about the asymptotic behaviour of Bianchi IX models.