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

Abstract

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 ${\varphi }_0$. Second, for perturbations produced by sources, we express $\Psi$ in terms of the mode functions of the source, i.e. the energy-momentum tensor $T_{\alpha \beta }$ or the electromagnetic current vector $J_{\alpha }$.

20 pages; few typos corrected and minor modifications made; accepted to Phys. Rev. D

References in corpus (3)

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• Gravitational self force and gauge transformations
• Reconstruction of Black Hole Metric Perturbations from Weyl Curvature

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