Particle motion around Schwarzschild-MOG black hole

In this paper, we present an analysis of the circular motion of test particles around a Schwarzschild-MOG black hole. Initially, our focus lies on studying the shadow cast by the spherically symmetric black hole within the framework of MOG gravity. Notably, we observe that the presence of MOG influences both the photon-sphere and the black hole’s shadow, causing them to increase in size. Furthermore, our research reveals that the characteristic radii of massive particles in circular orbits around the Schwarzschild-MOG black hole, specifically the innermost stable circular orbits (ISCO) and marginally bound orbits, are greater than those observed in the Schwarzschild metric alone. Additionally, we examine the electromagnetic field structure when a black hole is subjected to an external uniform magnetic field. Our findings demonstrate that in the vicinity of the Schwarzschild-MOG black hole, the magnetic field exhibits non-uniform behavior, with field lines becoming more densely distributed. Lastly, we delve into the motion of charged particles around the Schwarzschild-MOG black hole in the presence of an external magnetic field. Our investigation highlights that the ISCO position for charged particles is consistently less than that for neutral particles, indicating a significant distinction between the two scenarios.