双点Padé近似在Schwarzschild黑洞度规中光线偏折中的应用
Two-Point Padé Approximants for the Deflection of Light in the Schwarzschild Black Hole Metric
AI总结：
本文提出双点[2,2]阶Padé近似，用于精确描述光线偏折角与临界冲击参数的关系，同时提供一个更简单的二次近似用于中间范围的计算。
摘要：
查尔斯·加勒特·达尔文于1959年用第一类椭圆积分计算了光子通过Schwarzschild黑洞的偏折角。此计算多次被重复，并以初等函数形式近似表示。本文提出双点[2,2]阶Padé近似，将临界冲击参数与实际冲击参数的比值与偏折角的指数负值联系起来，能准确覆盖所有大于临界冲击参数的范围，适用于所有保持在黑洞外的光子轨迹。还提供了一个更简单的二次近似，适用于中间范围但不适用于极值范围。
英文摘要：
The deflection angle of a light ray passing the Schwarzschild (spherically symmetric vacuum) black hole was calculated by Charles Galton Darwin in 1959 in terms of the elliptic integral of the first kind. This calculation has been repeated many times and has also been given approximately in terms of elementary functions for impact parameters that either are not too small or are close to the critical impact parameter. Here I present Padé 2-point approximants of order [2,2] (quadratic numerators and denominators), relating the critical impact parameter divided by the actual impact parameter to the exponential of the negative of the deflection angle, that fairly accurately cover the full range of impact parameters greater than the critical impact parameter, which is the case for all photon trajectories that remain outside the black hole. I also present a simpler quadratic approximation that works as well in the middle of the range but not so well at the extremes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
