Astrophysical accretion processes near the black hole candidates, such as active galactic nuclei (AGN), X-ray binary (XRB), and other astrophysical sources, are associated with high-energetic emission of radiation of relativistic particles and outflows (winds and/or jets). It is widely believed that the magnetic field plays a very important role to explain such high energetic processes in the vicinity of those astrophysical sources. In the present research note, we propose that the black hole is embedded in an asymptotically uniform magnetic field. We investigate the dynamical motion of charged particles in the vicinity of a weakly magnetized black hole. We show that in the presence of the magnetic field, the radius of the innermost stable circular orbits (ISCO) for a charged particle is located close to the black hole’s horizon. The fundamental frequencies, such as Keplerian and epicyclic frequencies of the charged particle are split into two parts due to the magnetic field, as an analog of the Zeeman effect. The orbital velocity of the charged particle measured by a local observer has been computed in the presence of the external magnetic field. We also present an analytical expression for the four-acceleration of the charged particle orbiting around black holes. Finally, we determine the intensity of the radiating charged accelerating relativistic particle orbiting around the magnetized black hole.
The trajectory of a charged particle in the magnetic field of an infinite current carrying wire in the nonrelativistic limit