Schwarzschild-like AdS BH with a cloud of strings within LQG: Geodesic motions, Regge–Wheeler potential and thermodynamics

We conduct a comprehensive study of a Schwarzschild-AdS-like black hole (BH) surrounded by a cloud of strings (CoS) and loop quantum gravity (LQG) corrections, focusing on their geodesic dynamics, stability under perturbations, and thermodynamic properties. By analyzing null and time-like geodesics, we show how CoS and LQG effects significantly alter the effective potentials, modifying particle trajectories and orbital stability and other features. Our findings include analytical solutions for the photon sphere and numerical results for the innermost stable circular orbit (ISCO) radii, showing a significant increase in both radii with the presence of CoS. Additionally, a spin-dependent Regge–Wheeler potential analysis demonstrates that CoS and LQG influence the perturbative potentials for spin-0, 1, and 2 fields. Finally, we examine the BH’s thermal properties, noting substantial deviations in the Hawking temperature, entropy, and heat capacity from classical behavior, which have important implications for BH phase transitions, thermal stability, and the breakdown of the Bekenstein–Hawking entropy law.