Abstract
We extend previous work (2020 Class. Quantum Grav. 37 075001) to the case of Maxwell’s equations with a source. Our work shows how to construct a vector potential for the Maxwell field on the Kerr–Newman background in a radiation gauge. 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.
Highlights
We extend previous work [14] to the case of Maxwell’s equations with a source
While the electromagnetic self-force F abJb does not require the knowledge of the vector potential but only of Fab, the determination of the vector potential is of interest as a simpler toy model for the case of gravitational perturbations, and would in particular be relevant for calculating higher order selfforce corrections in theories wherein charged fields couple to the vector potential1
The equation for the spin 1 potential has to be solved in effect anyway – even in the case of gravitational perturbations alone – when converting the spin 2 metric perturbation hab obtained in a singular gauge to the Lorenz gauge
Summary
The Maxwell scalar φ0 can be viewed as defining an operator T , given in GHP form by: OΦ = [(þ − ρ − 2ρ) (þ − ρ ) − (ð − τ − 2τ ) (ð − τ )] Φ,. As observed by [4, 20], if O†Φ = 0, Aa ≡ Re(S†Φ)a is a real-valued solution to the Maxwell’s equations with vanishing source. Such a Φ {−2, 0} is called a “Hertz potential”. Such a gauge is referred to traditionally as “(ingoing) radiation gauge.”
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