Astrophysical signatures of AdS black holes with exotic matter: Cloud of strings, quintessence, and nonlinear electrodynamics

We investigate the optical properties and orbital dynamics of spherically symmetric Anti-de Sitter black holes in a modified gravity scenario incorporating nonlinear electrodynamics, cloud of strings, and quintessence dark energy. Building upon the exact black hole solutions derived by Nascimento et al. Universe 10(11) 2024 430, we analyze Einstein gravity coupled with nonlinear electromagnetic fields and exotic matter sources characterized by four fundamental parameters: the BH mass, nonlinear charge parameter, cloud of strings parameter, and quintessence field parameters. Through comprehensive geodesic analysis, we examine photon trajectories, effective potential behavior, and photon sphere formation in this modified spacetime. Shadow characteristics exhibit systematic dependencies on all parameters, with shadow radii varying as quintessence normalization changes, providing potentially observable signatures for Event Horizon Telescope measurements. We calculate Lyapunov exponents for circular photon orbits and derive complete trajectory equations that encode the collective effects of exotic matter sources. For neutral test particles, we analyze effective potentials, innermost stable circular orbits, and fundamental oscillation frequencies relevant to quasi-periodic oscillations in X-ray binaries. The innermost stable circular orbit radius increases systematically with cloud of strings and quintessence parameters while decreasing with nonlinear electromagnetic effects. Our frequency analysis reveals measurable modifications in radial, vertical, and azimuthal oscillation modes that could constrain exotic matter models through high-precision timing observations. Periastron precession calculations demonstrate radius-dependent frequency modulations with detectable deviations from general relativity predictions.