Magnetic field screening process in a Kerr Black Hole

It has been shown that a rotating BH immersed in a test background magnetic field, of initial strength $B_0$ and aligned parallel to the BH rotation axis, generates an induced electric field, that is proportional to the magnetic field. In this system, an huge number of pairs can be emitted by vacuum polarization process and start to be accelerated to high energies, mean this electric field, emitting synchrotron photons. In this paper we study the screening effect of magnetic and electric field due to the magnetic pair production process (hereafter MPP) ($\gamma+B\rightarrow e^{+}+e^{-}$) made by the created pairs. The principal results of this study are that: these combined processes of synchrotron emission by accelerated electrons and MPP can decrease magnetic field of several order of magnitude on a small time scale; exist a lower limit for the magnetic field after that it cannot be screened anymore.