Motion of spinning particles around black hole in a dark matter halo

Abstract: The motion of a rapidly rotating object in curved spacetime is affected by the spin-curvature force, an effect captured in the motion of spinning test particles. Recently, Cardoso et al.~[Phys. Rev. D 105, L061501 (2022)] found an exact solution describing a black hole immersed in a Hernquist distribution of dark matter. In this work, we investigate the motion of spinning particles around this black hole. We use the Mathison-Papapetrou-Dixon equation and the Tulczyjew spin-supplementary condition to calculate the effective potential, four-momentum, and four-velocity of the spinning particle. The equatorial motion of spinning test particles and the properties of the innermost stable circular orbit are further studied. We find that the existence of dark matter halos can significantly change the orbital eccentricity, energy, and the innermost stable circular orbit parameters of spinning test particles. Compared to the Schwarzschild black hole, dark matter halos bring the innermost stable circular orbit of a spinning test particle closer to the event horizon. These results could help us understanding the properties of black holes in dark matter halos.