Separable electromagnetic perturbations of rotating black holes

TL;DR

This paper develops a method to generate separable electromagnetic perturbations of rotating black holes using Hertz potentials, simplifying the analysis of Maxwell solutions in Kerr spacetime.

Contribution

It introduces a new Hertz potential construction for electromagnetic perturbations on black hole backgrounds, avoiding mode ansatz and enabling static and dynamic solutions.

Findings

Hertz potentials satisfy the Teukolsky equation and are related to Maxwell scalars via separable relations.

The method applies to Kerr spacetime perturbations, connecting with previous results.

The approach simplifies the analysis of electromagnetic perturbations in rotating black hole spacetimes.

Abstract

We identify a set of Hertz potentials for solutions to the vector wave equation on black hole spacetimes. The Hertz potentials yield Lorenz gauge electromagnetic vector potentials that represent physical solutions to the Maxwell equations, satisfy the Teukolsky equation, and are related to the Maxwell scalars by straightforward and separable inversion relations. Our construction, based on the GHP formalism, avoids the need for a mode ansatz and leads to potentials that represent both static and non-static solutions. As an explicit example, we specialise the procedure to mode-decomposed perturbations of Kerr spacetime and in the process make connections with previous results.