用新的refractive index和加速度公式研究引力透镜的运动学方法
A kinematical approach to gravitational lensing using new formulae for refractive index and acceleration
摘要：
本文使用史瓦西度规推导出一个有效的折射率和加速度矢量，占相对论偏转的光线，否则经典的运动学框架。新的折射率和已知的路径方程进行整合，分别给出精确的结果的旅行时间和偏转角。本文导出了一个新的坐标加速度公式，它描述了无质量试验粒子在球对称质量密度分布附近的运动轨迹。一个标准的射线拍摄技术是用来比较的偏转角和时间延迟预测这个新的公式与以前计算的值，并与标准的一阶近似。最后，射线射击法用于强透镜和弱透镜的理论例子，再现已知的多个质量的双平面焦散图案。
英文摘要：
This paper uses the Schwarzschild metric to derive an effective refractive index and acceleration vector that account for relativistic deflection of light rays, in an otherwise classical kinematic framework. The new refractive index and the known path equation are integrated to give accurate results for travel time and deflection angle, respectively. A new formula for coordinate acceleration is derived which describes the path of a massless test particle in the vicinity of a spherically symmetric mass density distribution. A standard ray-shooting technique is used to compare the deflection angle and time delay predicted by this new formula with the previously calculated values, and with standard first order approximations. Finally, the ray shooting method is used in theoretical examples of strong and weak lensing, reproducing known observer-plane caustic patterns for multiple masses.
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