Dynamics of particles with electric charge and magnetic dipole moment near Schwarzschild-MOG black hole

Investigations of electromagnetic interactions between test-charged and magnetized particles are important in the dynamics of the particles in strong gravitational fields around black holes. Here, we study the dynamics of a particle having an electric charge and a magnetic dipole moment in the spacetime of a Schwarzschild black hole in modified gravity (MOG), called Schwarzschild-MOG black hole. First, we provide a solution of Maxwell equations for the angular component of electromagnetic four potentials in the Schwarzschild-MOG spacetime. Then, we derive equations of motion and effective potential for circular motion of such particles using a hybrid form of the Hamilton-Jacobi equation which includes both interactions of electric charge and magnetic dipole moment with the external magnetic field assumed as asymptotically uniform, and interaction between the particles and the MOG field. Also, we investigate the effects of the three types of interactions on the radius of innermost stable circular orbits (ISCOs) and the energy \& angular momentum of the particles at their corresponding ISCOs. Finally, we provide detailed analyses of the effects of the three interactions mentioned above on the center of mass energy in the collisions between neutral, electrically charged, and magnetized particles.