Abstract
We present the results of recent work on a gauge invariant approach to the gravitational perturbations of the Kerr space-time, using the modified Newman-Penrose formalism. The techniques used are a generalisation of those developed in the Schwarzschild case. The perturbed Bianchi identities are written in a form involving only certain tetrad and coordinate-gauge invariant field quantities. The integrability conditions for the perturbed Bianchi identities then provide a system of gauge invariant wave-like gravitational perturbation equations, and the transformations which relate them to one another. The analysis is coordinate-free, and provides a geometric and gauge invariant explanation of the transformations relating the Teukolsky equation and a Regge-Wheeler-like equation in the Kerr background. The electromagnetic and gravitational perturbations of the Reissner-Nordstrom space-time can also be investigated using this approach. We present a gauge invariant coupled wave-like electromagnetic-gravitational perturbation equation in this case, which may be decoupled.