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We identify a set of Hertz potentials for solutions to the vector waveequation on black hole spacetimes. The Hertz potentials yield Lorenz gaugeelectromagnetic vector potentials that represent physical solutions to theMaxwell equations, satisfy the Teukolsky equation, and are related to theMaxwell scalars by straightforward and separable inversion relations. Ourconstruction, based on the GHP formalism, avoids the need for a mode ansatz andleads to potentials that represent both static and non-static solutions. As anexplicit example, we specialise the procedure to mode-decomposed perturbationsof Kerr spacetime and in the process make connections with previous results.

Separable electromagnetic perturbations of rotating black holes