Black Hole Solution in Anti-de Sitter Space with a New Cloud of Strings Surrounded by Dark Matter Halo

This paper presents a comprehensive theoretical study of a Schwarzschild-like Anti-de Sitter (AdS) black hole (BH) influenced by a new cloud of strings (NCS) and a dark matter halo (DMH) characterized by a Dehnen-type density profile. We analyze the geodesic motion of both massless and massive test particles, highlighting how the NCS and DMH parameters affect the effective potentials, photon spheres, circular orbits, BH shadow, and the innermost stable circular orbit (ISCO) of test particles. Additionally, we investigate the thermodynamic behavior of the BH in an extended phase space by deriving key quantities, such as the Hawking temperature, the equation of state (EoS), Gibbs free energy, internal energy, and the specific heat capacity. Our results show that the presence of NCS and DMH induces significant modifications in both the dynamical and thermodynamical behavior of the BH, including shifts in the Hawking-Page transition and divergences in heat capacity, thereby reshaping the phase structure of the BH.