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Kerr-Schild Symmetries

B. Coll·S. R. Hildebrandt·J. M. M. Senovilla
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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.

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B. Coll, S. R. Hildebrandt, J. M. M. Senovilla. 2000-06-13. Kerr-Schild Symmetries. https://doi.org/10.1023/a%3A1010265830882

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