Towards Metric Perturbations of Kerr Black Holes

Inspired by early work on perturbations of Kerr, we've developed a formulation of metric perturbation theory phrased in the spin coefficient formalsim of Newman and Penrose as modified by Geroch, Held and Penrose (GHP). In turn, this has driven the development of a Maple package, GHPTools, for performing the necessary calculations. In this talk I'll explain the basic ideas behind these tools and techniques and showcase some results obtained in the Schwarzschild geometry. Time permitting, I'll also discuss work in progress in the Kerr geometry.