全息引力作为研究强耦合体系与多体体系的理论，是引力物理的重要课题。近年黑洞阴影的拍摄使得利用黑洞阴影进行引力理论的验证成为了重要手段。本文回顾了全息对偶理论的发展历程，并在桥本幸士教授等人的工作基础上研究了全息带电反德西特黑洞的爱因斯坦环现象。我们在AdS边界的南极处输入无质量标量场的高斯波源作为探针，通过伪谱方法求解标量场，从而得到了边界各处的响应。利用光学设备对响应进行多普勒变换，我们得到了爱因斯坦环。若将观测点从无穷远边界的北极移动到低纬度处，屏幕上的爱因斯坦环将不再中心对称，在赤道观察时的屏幕成像将仅剩两个亮点。
我们关注了在北极观测时黑洞电荷参数对爱因斯坦环的影响，当黑洞电荷参数增大，爱因斯坦环的半径会随之增大，这与黑洞视界半径的效应相同。
随后通过研究光子路径，我们发现了经典引力时空中光子能量与动量的比值将决定光子轨道与光子到达边界时与径向方向的夹角，而光子球是光子轨道的特例。另一方面，我们利用CFT边界上的格林函数发现了粒子能量与角动量比值决定了它将在屏幕的何处成像。这为对比屏幕上的爱因斯坦环与光子球提供了重要途径。
因而我们利用WKB方法得到了准正模，从而得出在RN-AdS时空中的光子球对应能量与角动量的比值，并与同一时空观测得到的爱因斯坦环进行对比。我们发现，在标量粒子不带电时，带电AdS黑洞的爱因斯坦环主要由在光子球轨道上的光子提供。当粒子带电，由于电磁相互作用会干扰粒子轨道从而使得WKB中使用的大角动量近似失效，两者不再对应。因此我们在等效势中引入了电磁相互作用项，使准正模与爱因斯坦环观测结果获得了良好的对应，并发现爱因斯坦环随电荷的排斥或吸引而扩大或缩小，这意味着带电标量粒子不再沿光子球轨道运动。这为讨论全息爱因斯坦环与光子球的关系提供了新的论据。

The holography, as a powerful tool dealing with strong coupling systems and many-body systems, is a key theory in gravity. The physics community has treating black hole shadow as an important evidence to check gravity theory. We observe black hole shadow in the framework of holography. Using the holographic GKP-Witten relation and pseudo-spectral method, we obtain the response corresponding to the gaussian source setting on the south pole of AdS boundary. We observe the Einstein ring in RN-AdS spacetime by optical ``telescope'', which is equivalent to Fourier transformation. As the ``telescope'' move from north pole of boundary to equator, the ring will be broken and change to two spots finally. We investigate the effect of the charge parameter of black hole on the ring. Our result shows that as the charge increases, the radius of the ring enlarges, which is similar to the effect brought by radius of event horizon. 
We review the photon orbits in classical gravity and notice that the ratio of energy to momentum of photons are the key factor determining the orbits. We also use the Green function in CFT, whose poles correspond to the quasi-normal frequency in the gravity side. We recognize that the ring images on the screen are also determined by the same ratio of particles. These facts allow us to compare the Einstein ring and photon sphere.
We calculate the spectrum in spacetime by WKB method to obtain photon sphere. We have a comparison on Einstein ring and photon sphere in the same spacetime and conclude that the Einstein ring is produced by the photons on photon sphere if the particles have no charges. If the particles have charges, the large-$l$ approximation fails, so we consider the electromagnetic interaction in WKB process to have a better match if scalar field is charged. The radius of Einstein ring will scale if the charges change, which showing the shifting of orbits of charged scalar particles.