We present a general procedure to calculate the equatorial circular test particle's constants of motion in the background of combined stationary and axisymmetric gravitational and electromagnetic fields. As an application, we analyze (using the magnetized Kerr metric) the accretion of a weakly coupled plasma onto an extreme supermassive black hole immersed in an external magnetic field. The case in which the black hole's angular momentum reduces to zero is also considered. It is shown that if the magnetic field is strong (∼${10}^{11}$ G), positive- and negative-charged test particles can have binding energies of approximately 100%. However, if the magnetic field is weak (∼${10}^{-6\mathrm{}}$ G), accreting electrons provide a more efficient mechanism (as compared to accreting protons) converting gravitational potential energy to radiation. Rayleigh-Taylor instabilities as well as regions in which the circular motion is forbidden could exist in the accretion plasma disk.

• Received 5 July 1989

DOI:https://doi.org/10.1103/PhysRevD.42.307