Holographic Einstein Ring of Deformed AdS-Schwarzschild Black Holes

The Einstein ring of a deformed AdS-Schwarzschild black hole (BH) is investigated under the wave optics framework. When the source is fixed on the AdS boundary, we can obtain the corresponding response function generated on the opposite side of the boundary. Utilizing a specialized optical system equipped with a convex lens enables us to capture an image of the BH's holographic Einstein ring on the screen. The influence of the relevant physical parameters and the observed inclination on the characteristics of the Einstein ring can also be studied, which found that the alteration of the observer's position, the image displayed on the screen changes from an axisymmetric ring to an arc, ultimately becoming a solitary point of luminosity. Furthermore, variations in the relevant physical parameters naturally exert an influence on the Einstein ring, resulting in various changes to both its radius and brightness. We also discover the photon ring of the BH from the perspective of the geometric optics, and the numerical results demonstrate that the incident angle of the photon ring is consistent with that of the Einstein ring. It is found that the validity of studying the Einstein ring by wave optics. The investigation on the Einstein rings formed by the deformed AdS-Schwarzschild BHs is anticipated to yield more comprehensive insights into the spacetime geometry, enabling its distinction from Schwarzschild BH.