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We present a procedure that allows the construction of the metricperturbations and electromagnetic four-potential, for gravitational andelectromagnetic perturbations produced by sources in Kerr spacetime. This mayinclude, for example, the perturbations produced by a point particle or anextended object moving in orbit around a Kerr black hole. The construction iscarried out in the frequency domain. Previously, Chrzanowski derived the vacuummetric perturbations and electromagnetic four-potential by applying adifferential operator to a certain potential $\Psi $. Here we construct $\Psi $for inhomogeneous perturbations, thereby allowing the application ofChrzanowski's method. We address this problem in two stages: First, for vacuumperturbations (i.e. pure gravitational or electromagnetic waves), we constructthe potential from the modes of the Weyl scalars $\psi_{0}$ or $\phi_{0}$.Second, for perturbations produced by sources, we express $\Psi $ in terms ofthe mode functions of the source, i.e. the energy-momentum tensor $T_{\alpha\beta}$ or the electromagnetic current vector $J_{\alpha}$.Comment: 20 pages; few typos corrected and minor modifications made; accepted  to Phys. Rev.

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