标题： 带体电磁场的带电Rastall AdS黑洞全息爱因斯坦环 显示英文标题

标题： Holographic Einstein Ring of a Charged Rastall AdS Black Hole with Bulk Electromagnetic Field

摘要： 我们研究了带电Rastall AdS黑洞（BH）在AdS/CFT对应框架内的爱因斯坦图像。 考虑到全息设置，我们分析了不同模型参数值下的总响应函数的振幅。 随着参数$\lambda$和温度$T$的增加，响应函数的振幅减小，而随着电荷$e$和化学势$\mu$的增加，振幅则增大。 频率$\omega$的影响在体场中也起着重要作用，因为发现减少$\omega$会导致波的周期增加，这意味着响应函数的振幅也取决于波源。 The relation between $T$ to the inverse of the horizon $r_{h}$ for the parameter $\lambda$ is interpreted under fixed values of other involved parameters. These, in turn, affect the behavior of the response function and the Einstein ring, which may be used to differentiate the present work from previous studies. Via a special optical system, we construct the holographic images of the BH in bulk. The obtained results show that the Einstein ring always appears with concentric stripes at the position of the north pole, and this ring transforms into the luminosity-deformed ring or bright light spot when the distant observer lies away from the north pole. Moreover, from the brightness profiles, it is observed that as $\lambda$ grows, the shadow radius is significantly decreased, while the brightness of the ring is negligibly changed. We further investigate the influence of $T$ and $\mu$ on the ring radius. 这些结果表明，$T$的增加值导致阴影半径增加，而$\mu$的值增长时则会减少。 最后，我们通过讨论由几何光学得到的爱因斯坦环半径来结束这项工作，这与波动光学一致。 显示英文摘要

摘要： We study the Einstein images of a charged Rastall AdS black hole (BH) within the fabric of AdS/CFT correspondence. Considering the holographic setup, we analyze the amplitude of the total response function for various values of model parameters. With an increase in parameter $\lambda$ and temperature $T$, the amplitude of the response function is decreased, while it is increased with the increase of the electric charge $e$ and chemical potential $\mu$. The influence of frequency $\omega$ also plays an important role in the bulk field, as it is found that the decreasing $\omega$ leads to an increase in the periods of the waves, which means that the amplitude of the response function also depends on the wave source. The relation between $T$ to the inverse of the horizon $r_{h}$ for the parameter $\lambda$ is interpreted under fixed values of other involved parameters. These, in turn, affect the behavior of the response function and the Einstein ring, which may be used to differentiate the present work from previous studies. Via a special optical system, we construct the holographic images of the BH in bulk. The obtained results show that the Einstein ring always appears with concentric stripes at the position of the north pole, and this ring transforms into the luminosity-deformed ring or bright light spot when the distant observer lies away from the north pole. Moreover, from the brightness profiles, it is observed that as $\lambda$ grows, the shadow radius is significantly decreased, while the brightness of the ring is negligibly changed. We further investigate the influence of $T$ and $\mu$ on the ring radius. These results reveal that the increasing values of $T$ lead to an increase in the shadow radius and decrease as the values of $\mu$ grow. Finally, we finish this work with a discussion of the Einstein ring radius obtained by geometric optics, which is consistent with wave optics.