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

Amos Ori
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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 $Ψ$. Here we construct $Ψ$ 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 $ψ_{0}$ or $ϕ_{0}$. Second, for perturbations produced by sources, we express $Ψ$ in terms of the mode functions of the source, i.e. the energy-momentum tensor $T_{αβ}$ or the electromagnetic current vector $J_α$.

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Amos Ori. 2002-12-29. Reconstruction of inhomogeneous metric perturbations and electromagnetic four-potential in Kerr spacetime. https://doi.org/10.1103/physrevd.67.124010

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