Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Circular Orbit of a Particle and Weak Gravitational Lensing

Version 1 : Received: 26 March 2020 / Approved: 29 March 2020 / Online: 29 March 2020 (03:03:00 CEST)

A peer-reviewed article of this Preprint also exists.

Journal reference: Physical Review D 2020, 101
DOI: 10.1103/PhysRevD.101.124058


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.


relativity and gravitation; black hole; gravitational lensing; weak deflection angle; Gauss-Bonnet theorem; Weyl gravity; Bumblebee gravity


PHYSICAL SCIENCES, General & Theoretical Physics

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