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arXiv · 2006.13047

Circular orbit of a particle and weak gravitational lensing

Zonghai Li·Guodong Zhang·Ali Övgün
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Abstract

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.

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Zonghai Li, Guodong Zhang, Ali Övgün. 2020-06-21. Circular orbit of a particle and weak gravitational lensing. https://doi.org/10.1103/physrevd.101.124058

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