# Electromagnetic fields on Kerr spacetime, Hertz potentials and Lorenz gauge

## TL;DR

This paper compares two methods for constructing electromagnetic potentials on Kerr spacetime, showing their gauge relation and deriving a new separable Hertz potential linking to the Lorenz gauge.

## Contribution

It demonstrates the gauge relation between two existing methods and introduces a novel separable Hertz potential for the Lorenz gauge.

## Key findings

- The vector potentials are related by explicit gauge transformations.
- A new separable Hertz potential for the Lorenz gauge is derived.
- The methods are applicable to electromagnetic field analysis on Kerr spacetime.

## Abstract

We review two procedures for constructing the vector potential of the electromagnetic field on Kerr spacetime, namely, the classic method of Cohen & Kegeles, yielding $A^\mu$ in a radiation gauge, and the newer method of Frolov et al., yielding $A^\mu$ in Lorenz gauge. We demonstrate that the vector potentials are related by straightforward gauge transformations, which we give in closed form. We obtain a new result for a separable Hertz potential $H^{\mu \nu}$ such that $A_{\text{lor}}^\mu = \nabla_\nu H^{\mu \nu}$.