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 Psi. Here we construct Psi 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 psi(0) or Phi(0). Second, for perturbations produced by sources, we express Psi in terms of the mode functions of the source, i.e. the energy-momentum tensor T-alphabeta or the electromagnetic current vector J(alpha).