Kerr-Schild Symmetries

Details Kerr-Schild Symmetries Kerr-Schild Symmetries

2000-06-13

arxiv.org/abs/gr-qc/0006044v1

Gen.Rel.Grav. 33 (2001) 649-670

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, no figures, LaTeX

Scientific paper

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.

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