Perturbation dynamics and optical structure of black hole in cotton gravity coupled to nonlinear electrodynamics

We investigate black hole configurations within the theoretical framework of Cotton gravity coupled to nonlinear electrodynamics, with the aim of exploring how higher-derivative curvature terms and nonlinear electromagnetic interactions influence accretion behavior and optical characteristics. Restricting attention to static and spherically symmetric spacetimes, we examine scalar-field perturbations, test-particle dynamics, analytical bounds on greybody factors, and the optical appearance of the black hole under a static spherical accretion scenario. Our analysis demonstrates that the Cotton gravity contribution induces a genuine long-range deformation of the spacetime geometry, resulting in stronger wave confinement, an increased shadow radius, and outwardly displaced photon-ring structures when compared with the predictions of General Relativity. In contrast, nonlinear electrodynamics mainly affects the near-horizon region, giving rise to strong-field corrections that cannot be reproduced within standard Maxwell theory. We further show that the combined presence of Cotton gravity and nonlinear electrodynamics significantly modifies photon-sphere properties, orbital stability, and the location of the innermost stable circular orbit, thereby impacting accretion dynamics. Overall, these findings extend the Einstein–Maxwell paradigm and indicate that black hole imaging, accretion-related observables, and gravitational-wave measurements offer promising probes of Cotton gravity and nonlinear electrodynamics in the strong-gravity regime.