Dynamics and epicyclic motions of particles around the Schwarzschild–de Sitter black hole in perfect fluid dark matter

In this paper, we investigate circular orbits for test particles around the Schwarzschild–de Sitter (dS) black hole surrounded by perfect fluid dark matter. We determine the region of circular orbits bounded by innermost and outermost stable circular orbits. We show that the impact of the perfect fluid dark matter shrinks the region where circular orbits can exist as the values of both innermost and outermost stable circular orbits decrease. We find that for specific lower and upper values of the dark matter parameter there exist double matching values for inner and outermost stable circular orbits. It turns out that the gravitational attraction due to the dark matter contribution dominates over cosmological repulsion. This gives rise to a remarkable result in the Schwarzschild–de Sitter black hole surrounded by dark matter field in contrast to the Schwarzschild–de Sitter metric. Finally, we study epicyclic motion and its frequencies with their applications to twin peak quasi-periodic oscillations (QPOs) for various models. We find the corresponding values of the black hole parameters which could best fit and explain the observed twin peak QPO object GRS 1915+109 from microquasars.