Reconstruction of inhomogeneous metric perturbations and electromagnetic four-potential in Kerr spacetime

We present a procedure that allows the construction of the metric perturbations and electromagnetic four-potential, for gravitational and electromagnetic perturbations produced by sources in Kerr spacetime. This may include, for example, the perturbations produced by a point particle or an extended object moving in orbit around a Kerr black hole. The construction is carried out in the frequency domain. Previously, Chrzanowski derived the vacuum metric perturbations and electromagnetic four-potential by applying a differential operator to a certain potential. Here we construct for inhomogeneous perturbations, thereby allowing the application of Chrzanowski's method. We address this problem in two stages: First, for vacuum perturbations (i. e. pure gravitational or electromagnetic waves), we construct the potential from the modes of the Weyl scalars ₀ or ₀. Second, for perturbations produced by sources, we express in terms of the mode functions of the source, i. e. the energy-momentum tensor T_ or the electromagnetic current vector J_.