Tidal effects of a dark matter halo around a galactic black hole* *Supported by the National Natural Science Foundation of China (11875026, 11875025, 12035005, 2020YFC2201400)

Abstract

We investigate tidal forces and geodesic deviation motion in the spacetime of a black hole in a galaxy with a dark matter halo. Our results show that tidal forces and geodesic deviation motion depend on the mass of the dark matter halo and the typical lengthscale of the galaxy. The effect of the typical lengthscale of the galaxy on the tidal force is opposite to that of dark matter mass. With increasing dark matter mass, the radial tidal force increases in the region far from the black hole but decreases in the region near the black hole. Furthermore, the absolute value of angular tidal force monotonously increases with the dark matter halo mass. The angular tidal force also depends on the particle energy, and the effects of dark matter become more distinct for the test particle at higher energies, which differs from the behavior observed in typical static black hole spacetimes. We also present the change in the geodesic deviation vector with dark matter halo mass and the typical lengthscale of a galaxy under two types of initial conditions.