We investigate black hole solution within the framework of a generalized Chaplygin-Jacobi dark fluid background, focusing on perturbations and the greybody factor in this intriguing model. This model holds significance due to its characterization by two critical parameters \(\alpha \) and \(\beta \) which signify the deviation from the Schwarzschild black hole and the degree of anisotropy in the dark fluid respectively. We study the time evolution of the black hole by focusing on these key parameters, demonstrating that they significantly influence the damping and oscillation frequencies. Additionally, we evaluate the greybody factor bounds for the black hole under consideration. The key parameters \(\alpha \) and \(\beta \) significantly affect the bounds of the greybody factors, indicating that lower-frequency radiation can escape the black hole, while higher-frequency radiation is more effectively trapped. This highlights the substantial influence of \(\alpha \) and \(\beta \) on the characteristics of the black hole. Thus, we investigate the influence of these parameters on the optical properties of the black hole. By considering both static and infalling accretion models, we explore the impacts of \(\alpha \) and \(\beta \) on the black hole’s shadows and photon rings.
