Classification of Petrov Type D Generalized Kerr-Schild Transformations

We study the Petrov type D Generalized Kerr-Schild vacuum space-times. If the background is a Minkowski space-time the resulting Kerr-Schild metrics are classified, while if we start from a Petrov type D background we first put restrictions on the possible perturbation null directions. It is then shown that the GKS metrics are different from the background if the null direction has nonvanishing expansion or twist, otherwise the transformation is merely a change of coordinates.