Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 22, Issue 15, Pages S569-S587Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/22/15/002
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Perturbation theory of rotating black holes is described in terms of the Weyl scalars psi(4) and psi(0), each satisfying 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 Regge-Wheeler gauge in the non-rotating limit. We propose a generalization of the Regge-Wheeler gauge for a Kerr background in Newman-Penrose language and discuss the approach for building up the perturbed spacetime of a rotating black hole. We also provide two-way relationships between waveforms defined in the metric and curvature approaches in the time domain, also known as (inverse) Chandrasekhar transformations, generalized to include matter.
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