标题： 粒子的圆轨道和弱引力透镜效应 显示英文标题

标题： Circular orbit of a particle and weak gravitational lensing

摘要： 本文的目的有两方面。 首先，我们引入一种几何方法，基于Jacobi度量来研究静态和球对称时空中的粒子圆轨道。 其次，我们应用圆轨道来研究基于高斯-博内定理的零质量与类时粒子的弱引力偏转。 通过这种方式，我们得到一个偏转角的表达式，并将偏转角的研究扩展到渐近非平直的黑洞时空。 考虑了一些作为透镜的黑洞，例如共形Weyl引力中的静态球对称黑洞和bumblebee引力中的类施瓦茨希尔德黑洞。 我们的结果与之前的文献一致。 特别是，我们发现高斯曲率与圆轨道半径之间的联系大大简化了计算。 显示英文摘要

摘要： The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and time-like particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically non-flat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation.