Self-dual cosmological Bianchi IX and VIII metrics

TL;DR

This paper links self-dual Bianchi IX and VIII cosmological models to the Nahm dynamical system, providing explicit solutions and metrics in both Euclidean and Minkowski signatures.

Contribution

It establishes a novel connection between self-dual cosmological models and the Nahm system, offering explicit solutions for diagonal reductions.

Findings

Explicit solutions for diagonal Nahm equations

Construction of self-dual metrics in Euclidean and Minkowski signatures

Demonstration of the Nahm system's applicability to Bianchi models

Abstract

We show that self-dual Bianchi IX and VIII cosmological models are described by the Nahm dynamical system for an appropriate type of matrices. We construct the general solutions in the case of the diagonal reductions of the corresponding Nahm equations and give the explicit expressions for the corresponding self-dual metrics in the Euclidean and in the Minkowski signature cases.