G3-homogeneous gravitational instantons

TL;DR

This paper classifies all self-dual gravitational instantons with three-dimensional homogeneous symmetry, revealing new solutions especially for Bianchi III, advancing understanding of Euclidean quantum gravity.

Contribution

It provides a comprehensive classification of homogeneous self-dual gravitational instantons and introduces new solutions for Bianchi III cases.

Findings

Complete classification of homogeneous self-dual instantons

New solutions discovered for Bianchi III

Framework based on algebra homomorphisms between Bianchi and SO(3) groups

Abstract

We provide an exhaustive classification of self-dual four-dimensional gravitational instantons foliated with three-dimensional homogeneous spaces, i.e. homogeneous self-dual metrics on four-dimensional Euclidean spaces admitting a Bianchi simply transitive isometry group. The classification pattern is based on the algebra homomorphisms relating the Bianchi group and the duality group SO(3). New and general solutions are found for Bianchi III.