标题： 由接近不稳定光子球的Reissner-Nordström裸奇点引起的强引力透镜效应 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对强引力透镜效应的影响。利用Picard-Fuchs方程，我们推导出各种情况下的偏折角全阶幂级数表达式，包括从光子球内外的强偏折极限。我们证明，在这两种情况下，偏折角都以非对数方式发散，改进了现有的渐近公式。通过比较截断近似与数值结果，我们发现高阶修正对于达到与对数发散情况相当的精度至关重要。利用这些改进后的公式，我们还推导出对图像位置的精确近似，这些近似不再局限于几乎完全对齐的情况。 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.