English

Vacuum gravitational fields with a null Killing vector

General Relativity and Quantum Cosmology 2020-02-06 v3

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

R2 v1 2026-06-23T11:31:57.251Z