标题： 强引力透镜效应由一个具有边缘不稳定光子球的Reissner-Nordström裸奇点引起 显示英文标题

标题： Strong gravitational lensing by a Reissner-Nordström naked singularity with a marginally unstable photon sphere

摘要： 我们研究了在Reissner-Nordström裸奇点时空中的边缘不稳定光子球的强引力透镜效应。 利用Picard-Fuchs方程，我们在各种情况下推导出偏转角的全阶幂级数表达式，包括来自光子球外部和内部的强偏转极限。 我们表明，在这两种情况下，偏转角都非对数发散，从而改进了现有的渐近公式。 将截断近似与数值结果进行比较，我们发现高阶修正对于达到与对数发散情况相当的精度是必不可少的。 使用这些改进的公式，我们还推导出不局限于几乎完美对齐情况的图像位置的精确近似。 显示英文摘要

摘要： We investigate strong gravitational lensing by a marginally unstable photon sphere in a Reissner-Nordstr\"{o}m naked singularity spacetime. Using the Picard-Fuchs equation, we derive full-order power series expressions for the deflection angle in various regimes, including the strong deflection limits from both outside and inside the photon sphere. We show that the deflection angle diverges non-logarithmically in both cases, refining existing asymptotic formulae. Comparing truncated approximations with numerical results, we find that higher-order corrections are essential to achieve comparable accuracy to logarithmic divergence cases. Using these improved formulae, we also derive precise approximations for image positions that are not restricted to the almost perfectly aligned cases.