Imprints of ModMax electrodynamics on particle dynamics and thermodynamic properties of Kalb–Ramond AdS black holes

We present a theoretical analysis of geodesic motion, thermodynamic properties, and field perturbations in anti-de Sitter black hole spacetimes within Kalb–Ramond gravity sourced by ModMax nonlinear electrodynamics. This framework incorporates both Lorentz-violating effects and nonlinear electromagnetic interactions, extending beyond classical black hole solutions. We examine the dynamics of neutral and charged test particles in this modified spacetime, demonstrating how ModMax nonlinearity, electric charge, cosmological constant, Lorentz-violating corrections, and black hole mass significantly alter particle trajectories compared to standard Schwarzschild and RN solutions. Through effective potential analysis, we show how these parameters shift the locations of innermost stable circular orbits and influence orbital stability. We investigate optical properties including photon trajectories, photon spheres, and black hole shadows, revealing parameter dependencies that offer potential observational constraints. Our thermodynamic analysis derives key quantities including Hawking temperature, Bekenstein–Hawking entropy, and explores Joule–Thomson expansion processes within the extended phase space framework. The analysis reveals rich phase structures with distinct cooling and heating regions influenced by all geometric parameters. We examine scalar and electromagnetic field perturbations through the Klein–Gordon and Maxwell equations, deriving perturbative potentials and computing greybody factors that quantify wave transmission probabilities.