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General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
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.
