Geodesics and thermodynamics of Einstein-Power-Yang–Mills AdS black holes

In this paper, we investigate the geodesic equations in the spacetime of Einstein-Power–Yang–Mills anti-de Sitter (AdS) black holes. We obtain analytical solutions to the geodesic equations using Weierstrass elliptic and Kleinian sigma hyperelliptic functions. We classify possible orbits such as flyby, bound, terminating bound, and terminating escape orbits based on the analytical solutions and effective potential. We also briefly study the thermodynamics of these black holes, plotting the horizon radius versus mass to demonstrate the possibility of having one or three horizons. We derive expressions for temperature, entropy, pressure, and volume, and interpret the results. We find that there is a possibility of van der Waals-like behavior for the holographic dual fluid corresponding to these Einstein-Power-Yang–Mills AdS black holes.