Timelike geodesics of a modified gravity black hole immersed in an axially symmetric magnetic field

We investigate the dynamics of a neutral and a charged particle around a black hole in modified gravity immersed in a magnetic field. Our focus is on the scalar-tensor-vector theory as modified gravity. We are interested in exploring the conditions on the energy of the particle under which it can escape to infinity after collision with another neutral particle in the vicinity of the black hole. We calculate the escape velocity of particle orbiting in the innermost stable circular orbit (ISCO) after the collision. We study the effects of modified gravity on the dynamics of particles. Further, we discuss how the presence of a magnetic field in the vicinity of a black hole affects the motion of the orbiting particle. We show that the stability of ISCO increases due to the presence of a magnetic field. It is observed that a particle can go arbitrarily close to the black hole due to the presence of a magnetic field. Furthermore, ISCO for a black hole is more stable as compared with a Schwarzschild black hole. We also discuss the Lyapunov exponent and the effective force acting on the particle in the presence of a magnetic field.

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