Kerr-Schild symmetries

We study continuous groups of generalized Kerr-Schild transformations and t he vector fields that generate them in any n-dimensional manifold with a Lo rentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformati on direction is fixed. The properties of these Lie algebras are briefly ana lyzed and we show that they are generically finite-dimensional but that the y may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the followi ng cases: any two-dimensional metric, the general spherically symmetric met ric and deformation direction, and the flat metric with parallel or cylindr ical deformation directions.