Primary Proca hair and the double-peak optics of black holes

The study investigates black holes with primary Proca hair, focusing on the unique double-peak structure in the effective potential caused by a massive vector field. This structure significantly alters the motion of photons and particles, resulting in new dynamical and observational effects. The research classifies geodesics and explores conditions for multiple circular orbits, emphasizing changes in the photon sphere, shadows, and lensing. Notably, the black-hole shadow may develop a two-boundary structure with inner rings, differing from the standard Schwarzschild black holes. These findings suggest observable effects in electromagnetic spectra, emphasizing the importance of double-barrier optical phenomena in strong-gravity observations.