Reconstruction of black hole metric perturbations from the Weyl curvature

Perturbation theory of rotating black holes is usually described in terms of Weyl scalars psi(4) and psi(0), which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials Psi in outgoing or ingoing radiation gauges. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e. psi(4) and psi(0). We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole.