On the radiation gauge for spin-1 perturbations in Kerr–Newman spacetime

Abstract

We extend previous work (2020 Class. Quantum Grav. 37 075001) to the case of Maxwell’s equations with a source. Our work shows how to construct a vector potential for the Maxwell field on the Kerr–Newman background in a radiation gauge. The vector potential has a ‘reconstructed’ term obtained from a Hertz potential solving Teukolsky’s equation with a source, and a ‘correction’ term which is obtainable by a simple integration along outgoing principal null rays. The singularity structure of our vector potential is discussed in the case of a point particle source.

Black hole perturbation theory and gravitational self-force

“…In the case of metric perturbations, Teukolsky's results yield solutions for the spin-weight ±2 components of the perturbed Weyl tensor, but do not give a method for obtaining a corresponding metric perturbation. Subsequent results (and their equivalents for electromagnetic perturbations) [36,104,199,207,162,183,81,90] derived a method for reconstructing a metric perturbation from a Hertz potential, which in turn can be obtained from the spin-weight ±2 components of the Weyl tensor.…”

“…The interested reader may refer to [199,104,36] for the original derivations of the reconstruction procedure, to [8] for an analysis of the sourced equation satisfied by the Hertz potential, to [124,42] for details of metric completion, and to [81,90] for a thorough explanation of the corrector tensor approach.…”