Influence of dark photon on magnetized and charged particle orbits around static spherically symmetric black hole

We elaborate on the problem of a magnetized particle motion in the spacetime of a static, spherically symmetric black hole influenced by weak magnetic fields stemming from visible and dark matter sectors. The Wald's procedure for obtaining the weakly magnetized solution, was generalized to the case of dark photon---Einstein-Maxwell gravity was implemented. The collision process analysis of two particles in the background of the black hole has been studied in order to find the signature of the presence of dark matter nearby to the object in question.