Superradiance, geodesics and shadows of black holes in dark photon with higher-order correction

The exploration of black holes in the presence of dark photon fields offers a compelling pathway to investigate hidden sector interactions and their gravitational impacts. We analyze static, spherically symmetric black hole solutions within dark photon models featuring Yukawa-type interactions and higher-order magnetic dipole corrections. These modifications are introduced via a generalized energy-momentum tensor sourced by the dark photon field, resulting in a nontrivial deformation of the spacetime geometry. We investigate the dynamics of massless and massive particles, emphasizing the influence of dark sector parameters on effective potentials, photon spheres, and circular geodesics. Notably, the innermost stable circular orbit radius, particle energy, and angular momentum exhibit sensitive dependence on mA′ and gD, suggesting observable deviations in accretion disk behavior and gravitational wave emissions. Through numerical analysis, we compute the shadow radius Rs and demonstrate that dark photon corrections either compress or enlarge the black hole shadow, depending on the interplay between Yukawa screening and gauge coupling. The geodetic precession frequency ΘGPF is also shown to vary significantly from classical expectations, pointing to dark-sector-induced frame-dragging effects. Additionally, we explore the superradiance phenomenon by solving the Klein-Gordon equation for charged scalar perturbations in the modified background. Our results identify conditions for wave amplification and highlight how dark photon interactions can enhance or suppress the superradiant scattering regime. Overall, this study presents a unified framework that connects dark photon physics with black hole thermodynamics, geodesic motion, optical properties, and stability.