Reconstruction of Black Hole Metric Perturbations from Weyl Curvature II: The Regge-Wheeler gauge

Abstract. Perturbation theory of rotating black holes is described in terms of the Weyl scalars ψ4 and ψ0; each satisfying the Teukolsky’s complex master wave equation with spin s = ∓2, and respectively representing outgoing and ingoing radiation. We explicitly construct the metric perturbations out of these Weyl scalars in the ReggeWheeler gauge in the nonrotating limit. We propose a generalization of the ReggeWheeler gauge for Kerr background in the Newman-Penrose language, and discuss the approach for building up the perturbed spacetime of a rotating black hole. We also provide both-way relationships between waveforms defined in the metric and curvature approaches in the time domain, also known as the (inverse-) Chandrasekhar transformations, generalized to include matter.