Non-vanishing Magnetic Flux through the Slightly-charged Kerr Black Hole

In association with the Blanford-Znajek mechanism for rotational energy extraction from Kerr black holes, it is of some interest to explore how much of magnetic flux can actually penetrate the horizon at least in idealized situations. For completely uncharged Kerr hole case, it has been known for some time that the magnetic flux gets entirely expelled when the hole is maximally-rotating. In the mean time, it is known that when the rotating hole is immersed in an originally uniform magnetic field surrounded by an ionized interstellar medium (plasma), which is a more realistic situation, the hole accretes certain amount of electric charge. In the present work, it is demonstrated that as a result of this accretion charge small enough not to disturb the geometry, the magnetic flux through this slightly charged Kerr hole depends not only on the hole's angular momentum but on the hole's charge as well such that it never vanishes for any value of the hole's angular momentum.