Effect of perfect fluid dark matter on particle motion around a static black hole immersed in an external magnetic field

We investigate particle and photon motion in the vicinity of a static and spherically symmetric black hole surrounded by perfect fluid dark matter in the presence of an external asymptotically uniform magnetic field. We determine the radius of the innermost stable circular orbit (ISCO) for charged test particles and the radius for unstable circular photon orbits and show that the effect of the presence of dark matter shrinks the values of ISCO and photon sphere radii. Based on the analysis of the ISCO radius we further show that the combined effects of dark matter and magnetic field can mimic the spin of a Kerr black hole up to $ a/M \approx 0.75-0.8$. Finally, we consider the effect of the presence of dark matter on the center of mass energy of colliding particles in the black hole vicinity. We show that the center of mass energy grows as the value of the dark matter parameter increases. This result, in conjunction with the fact that, in the presence of an external magnetic field, the ISCO radius can become arbitrarily close to the horizon leads to arbitrarily high energy that can be extracted by the collision process, similarly to what is observed in the super-spinning Kerr case.