Gravitational lensing and observational features of a dynamic black hole

In this work, we investigate the gravitational lensing effects and the dynamic evolution of the shadow of Vaidya black holes by employing backward ray-tracing techniques. Within the celestial sphere framework, the black hole shadow exhibits a complete evolutionary sequence, transitioning from an initial stable configuration through continuous expansion to a final static state. Notably, during and after the active accretion phase, a distinct lensing ring emerges outside the shadow. Extending this analysis to the thin accretion disk model reveals richer observational signatures. A bright ring, formed by the superposition of the photon ring and lensing ring, appears outside the shadow but persists only during the initial and final stages of accretion, vanishing entirely when accretion becomes active. Interestingly, as the accretion process progresses, an additional ring-like structure, which is caused by the dynamical redshift effect, emerges in the image. This ring-like structure not only contracts inward but also brightens continuously as accretion proceeds. Under varying observational inclinations, the Doppler effect and the dynamical redshift effect jointly modulate the brightness distribution of the image, resulting in significant asymmetry in the inner shadow, bright ring, and additional ring. Our findings uncover dynamical redshift as a novel observable phenomenon intrinsic to evolving spacetimes, offering a potential discriminant for identifying accreting black holes and providing observational access to the imprints of temporal spacetime evolution on black hole images.