Vacuum gravitational fields with a null Killing vector
Abstract
Vacuum gravitational fields admitting a light-like Killing field were systematically studied starting around 1960. Besides the already known plane waves, a second class of gravitational wave fields was found. In contrast to plane waves, their wave surfaces were not flat, but had a negative Gaussian curvature. Recently, such solutions found attention again as "twisted gravitational waves". In the paper we review and extend the earlier results. In suitable coordinates, the metric assumes a simple shape. The waves are then determined by a single function that satisfies a Laplace equation in cylindrical coordinates. The "twisted waves" prove to be a special case.
Keywords
Cite
@article{arxiv.1910.00561,
title = {Vacuum gravitational fields with a null Killing vector},
author = {G. Dautcourt},
journal= {arXiv preprint arXiv:1910.00561},
year = {2020}
}
Comments
13 pages, v2: abstract extended, typos corrected, minor changes, v3: reviewer suggestions considered