Geometric Properties and QPOs of Reissner-Nordstrom-AdS Black Hole with a Cloud of Strings Surrounded by Quintessence in Rastall Gravity

In this work, we performed a comprehensive theoretical investigation of the optical and dynamical properties of static, charged anti-de Sitter (AdS) black holes surrounded by a cloud of strings and a quintessence-like fluid, within the framework of Rastall gravity. We derive the effective potential for null geodesics and analyze key optical features such as the effective radial force experienced by photons, photon trajectories, circular photon orbits (photon spheres), and the resulting BH shadows. Furthermore, we explored the topological structure of the photon ring (PR), examining how both geometric and physical parameters influence these features of photon sphere. In addition, we studied the dynamics of neutral test particles using the Hamilton–Jacobi formalism, with particular focus on the innermost stable circular orbit (ISCO). Using the effective potential governing massive particle motion, we investigated quasi-periodic oscillations (QPOs) and computed the fundamental oscillation frequencies. Our results demonstrate how the presence of a string cloud, quintessence-like fluid, and deviations from general relativity significantly affect both the optical and dynamical properties of the BH spacetime.