All ASD complex and real 4-dimensional Einstein spaces with $\Lambda \ne 0$ admitting a nonnull Killing vector
Mathematical Physics
2016-02-10 v2 math.MP
Abstract
Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant equipped with a nonnul Killing vector are considered. It is shown, that any conformally nonflat metric of such spaces can be always brought to a special form and the Einstein field equations can be reduced to the Boyer-Finley-Pleba\'nski equation (Toda field equation). Some alternative form of the metric are discussed. All possible real slices (neutral, Euclidean and Lorentzian) of ASD complex spaces admitting a nonnull Killing vector are found.
Cite
@article{arxiv.1312.4284,
title = {All ASD complex and real 4-dimensional Einstein spaces with $\Lambda \ne 0$ admitting a nonnull Killing vector},
author = {Adam Chudecki},
journal= {arXiv preprint arXiv:1312.4284},
year = {2016}
}