Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures
General Relativity and Quantum Cosmology
2016-09-15 v1 High Energy Physics - Theory
Differential Geometry
Abstract
Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possibilities. In particular we construct new examples of neutral signature non--diagonal Bianchi type VIII Einstein metrics with self--dual Weyl tensor.
Keywords
Cite
@article{arxiv.1609.02747,
title = {Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures},
author = {Maciej Dunajski and Paul Tod},
journal= {arXiv preprint arXiv:1609.02747},
year = {2016}
}