Magnetic fluxes across black holes

By using solutions of Maxwell's equations on the Kerr background it is shown that the flux of the magnetic fields, generated by stationary axially symmetric sources, across one half of the surface of the horizon decreases as the angular momentum of the hole increases, and becomes zero when the hole is an extreme Kerr black hole. The flux can, however, be large if the field is not axially symmetric. This is demonstrated explicitly in the case of a field which is asymptotically uniform, but is not aligned with the hole's rotation axis. The fluxes calculated for hemispheres in various locations on the horizon reveal how the field is dragged along by the rotating geometry. Starting out from an exact solution of Einstein's equations representing a Schwarzschild black hole in a magnetic universe, it is found that there exists a finite upper boundary on the magnetic field strength for which the flux across the horizon has a maximum value. The results might be relevant in those models of quasars and radio galaxies in which the magnetic field anchored in the center black hole is used to extract rotational energy from the hole.