Accretion disk luminosity for black holes surrounded by dark matter with tangential pressure

We study the motion of test particles in the gravitational field of a Schwarzschild black hole surrounded by a spherical dark matter cloud with non-zero tangential pressure and compute the luminosity of the accretion disk. The presence of non vanishing tangential pressures allows to mimic the dark matter's angular momentum while still considering a static model, which simplifies the mathematical framework. We compare the numerical results about the influence of dark matter on the luminosity of accretion disks around static supermassive black holes with the previously studied cases of isotropic and anisotropic pressures. We show that the flux and luminosity of the accretion disk in the presence of dark matter are different from the case of a Schwarzschild black hole in vacuum and highlight the impact of the presence of tangential pressures.