Holographic Einstein Ring of Deformed AdS-Schwarzschild Black Holes

Abstract: In this work, the wave optics is employed to investigate the Einstein ring of a deformed AdS-Schwarzschild black hole (BH). When the source is fixed on the AdS boundary, one can obtain the corresponding response function generated on the antipodal side of the boundary. By utilizing a virtual optical system equipped with a convex lens, we are able to capture an image of the BH's holographic Einstein ring on the screen. The influence of the relevant physical parameters and the observer's position on the characteristics of the Einstein ring is also investigated, revealing that variations in the observer's position result in a transition of the displayed image from an axisymmetric ring to an arc, ultimately converging into a solitary point of luminosity. In addition, variations in the relevant physical parameters naturally exert influences on the Einstein ring. The photon ring of the BH was also investigated from a geometric optics perspective, and the numerical results indicate that the incident angle of the photon ring aligns with that of the Einstein ring. In the context of modified gravity theories, the investigation of Einstein rings formed by deformed AdS-Schwarzschild BH is expected to not only contribute to advancing the development of gravitational theories but also facilitate a more comprehensive understanding of spacetime geometry and the physical properties of BHs, thereby distinguishing them from Schwarzschild BH.