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 nonzero tangential pressure, and compute the luminosity of the accretion disk. The presence of nonvanishing tangential pressure allows us to mimic the dark matter's angular momentum, while still considering a static model, which simplifies the mathematical framework. We compare the numerical results of the influence of dark matter on the luminosity of the 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 a vacuum, and highlight the impact of the presence of tangential pressures.