标题： 黑洞在爱因斯坦-非线性电动力学理论中的引力透镜效应与多重光子球 显示英文标题

标题： Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres

摘要： 在本文中，我们研究非线性电动力学黑洞的引力透镜效应。 非线性电动力学黑洞是多事件视界黑洞的典型模型。 根据度规参数的选择，这些黑洞可以具有超过五个事件视界。 因此，在某些参数范围内，黑洞可以在事件视界之外具有多个不同大小的光子球。 具体而言，我们关注三重光子球附近的强引力透镜效应，特别是点源和天体球的高阶像的形成。 一个、两个或三个或更多光子球的存在显著增加了点源的高阶像的数量。 当黑洞被天体球照射时，三个光子球在黑洞图像中生成三个临界曲线，其中最小的临界曲线与阴影的边缘重合。 此外，由于非线性电动力学黑洞是多事件视界黑洞的模型，我们可以通过分析一个、两个和三个光子球的引力透镜效应之间的差异和模式，推断出具有超过三个光子球的黑洞的引力透镜效应和天体图像的变化。 显示英文摘要

摘要： In this paper, we study the gravitational lensing effects of non-linear electrodynamic black holes. Non-linear electrodynamic black holes serve as typical models for multi-event horizon black holes. Depending on the choice of metric parameters, these black holes can possess more than five event horizons. Consequently, within certain parameter ranges, black holes can have more than three photon spheres of varying sizes outside the event horizon. Specifically, we focus on the strong gravitational lensing effects near the triple photon spheres, particularly the formation of higher-order images of point sources and celestial spheres. The presence of one, two, or three or more photon spheres significantly increases the number of higher-order images of a point source. When a black hole is illuminated by a celestial sphere, the three photon spheres generate three critical curves in the black hole image, with the smallest critical curve coinciding with the shadow's edge. Additionally, since non-linear electrodynamic black holes are models of multi-event horizon black holes, we can infer the gravitational lensing effects and the changes in celestial images for black holes with more than three photon spheres by analyzing the distinctions and patterns between the gravitational lensing effects of one, two, and three photon spheres.