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

TL;DR

This paper develops a method to construct a retarded vector potential for Maxwell's equations with sources in Kerr-Newman spacetime using a radiation gauge, extending previous work to include sources and analyzing singularities.

Contribution

It introduces a new approach to construct the vector potential with sources in Kerr-Newman spacetime, combining Hertz potential reconstruction and null ray integration.

Findings

Constructed retarded vector potential with sources in Kerr-Newman

Analyzed singularity structure for point particle sources

Extended previous source-free work to include sources

Abstract

We extend previous work [arXiv:1908.09095] to the case of Maxwell's equations with a source. Our work shows how to construct a retarded vector potential for the Maxwell field on the Kerr-Newman background in a radiation gauge. As in our previous work, 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.