Magnetic fluxes across black holes in a strong magnetic field regime

The magnetic flux across a magnetized Kerr-Newman black hole is examined. I t is shown by employing the Ernst-Wild spacetime how the flux across an axi ally symmetric cap located on the horizon depends on the magnetic field str ength and vanishes for certain values of parameters, analogously to the cas e of an external asymptotically uniform and aligned test magnetic field acr oss extreme black holes. Discussion in terms of intuitive graphs is present ed.