Stationary axisymmetric electromagnetic fields around a rotating black hole

The form of stationary electromagnetic fields which are axisymmetric around a rotating black hole is derived, using Teukolsky's perturbation equation. The field of a circular equatorial charged current loop around the black hole is obtained, and it is shown that in a minimum-energy configuration the black hole and the current loop contain an equal but opposite net charge. The value of this equilibrium net charge is calculated.