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Abstract No-hair theorem indicates that black holes cannot have their own magnetic dipole moment. They can be weakly magnetized in binary systems with a neutron star companion and an accretion disc of charged particles. A simple model suggested by Petterson states that a current loop accreting a Schwarzschild black hole generates dipole-like magnetic fields in the outer region of the loop that are uniform in the inner region. This study considers circular motion and collisions of charged test particles with magnetic dipole moments in the inner and outer regions. First, we derive the effective potential taking into account the magnetic interactions between external magnetic fields with electric charge and the magnetic dipole moment of the particle. We investigate the possible innermost stable circular orbits (ISCOs) of the charged and magnetized particles orbiting the magnetized Schwarzschild black hole inside and outside the current loop. Finally, we explore the collisional processes of these particles near the black hole horizons, examining the effects of magnetic interactions on the critical angular momentum of particles that may collide and the center of mass energy of the colliding particles. We discuss astrophysical relevant objects with magnetic dipole moment and electric charge: magnetized neutron stars, white dwarfs, rotating stellar-mass black holes, electrons, and protons, and also estimate the interaction parameters for them.
Khan et al. (Thu,) studied this question.