Letelier-AdS Black Hole Surrounded by a Perfect Fluid Dark Matter in the presence of Quintessence

Abstract: This study investigates a Schwarzschild-anti de Sitter black hole coupled to a cloud of strings featuring only the electric-like component of the string bivector, embedded in a perfect fluid dark matter and a quintessence field. We examine the dynamics of photons and massive particles, focusing on trajectories, photon spheres, BH shadows, their topological characteristics, and innermost stable circular orbits (ISCOs), and emphasizing the influence of string cloud, perfect-fluid dark matter, and quintessence-like field parameters. Additionally, we explore the black hole's thermodynamics, deriving the Hawking temperature, Gibbs free energy, and specific heat, and discuss the modified first law of thermodynamics and thermodynamic topology under external matter fields. We demonstrate that the presence of a string cloud, perfect-fluid dark matter, and a quintessence-like field together modifies the geodesic structure and thermodynamic properties, thereby shifting the results relative to the standard Schwarzschild BH solution.