Holographic Einstein ring of charged phantom AdS black hole

Within the framework of AdS/CFT correspondence, this paper studies the holographic shadow images of charged Phantom AdS black holes. Using a Gaussian oscillator source on the AdS boundary, the test waves generated by this source propagate through the black hole spacetime are detected by the response function on the other side of the boundary. The results show that the amplitude of the response function differs for different wave sources and gravitational parameters. From an optical system with a convex lens, we successfully constructed the shadow image of the black hole. When the wave source is located at the South Pole and the observation inclination is zero, a series of axially symmetric concentric circular patterns are always displayed on the screen. As the observation inclination increases, the brightest ring transforms into a ring with distorted brightness, Eventually collapsing to a bright spot. Additionally, the research finds that the shadow image depends not only on the black hole’s temperature and chemical potential but also on the frequency of the wave source. Based on the geometric optics, the incidence angle of the photon ring is also discussed, and finds that it Matches the angular distance of the Einstein ring obtained by the holographic framework, which validates the effectiveness of studying Einstein rings through AdS/CFT correspondence.