Gauge invariant perturbations of black holes .2. Kerr space-time

We cast the perturbed Bianchi identities into a form involving only tetrad and coordinate-gauge invariant field quantities. From the perturbed Blanch identities we then derive a system of gauge invariant wavelike gravitational perturbation equations. These are the Teukolsky equation, a gauge invariant analog of the Regge-Wheeler equation, and a new gravitational perturbation equation. The Bianchi identities also provide the transformations between the perturbation equations. In particular, the transformation between the Teukolsky equation and the analog of the Regge-Wheeler equation arises in this way. This work extends our previous analysis of the perturbations of the Schwarzschild black hole to the Kerr case. (C) 1997 American Institute of Physics.