Kerr-Schild Symmetries
Abstract
We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.
Cite
@article{arxiv.gr-qc/0006044,
title = {Kerr-Schild Symmetries},
author = {B. Coll and S. R. Hildebrandt and J. M. M. Senovilla},
journal= {arXiv preprint arXiv:gr-qc/0006044},
year = {2015}
}
Comments
15 pages, no figures, LaTeX