Nonsingular electrodynamics of a rotating black hole boosted in an asymptotically uniform magnetic test field

We extend the Wald solution to a black hole that is also boosted. More specifically, we derive analytic solutions for the Maxwell equations for a rotating black hole moving at constant speed in an asymptotically uniform magnetic test field. By adopting Kerr-Schild coordinates we avoid singular behaviours at the horizon and obtain a complete description of the charge and current distributions in terms of the black-hole spin and boost. Using this solution, we compute the energy losses expected when charged particles are accelerated along the magnetic field lines, improving previous estimates that had to cope with singular electromagnetic fields on the horizon. When used to approximate the emission from binary black holes in a uniform magnetic field, our estimates match reasonably well those from numerical-relativity calculations in the force-free approximation.