Circular orbit of a particle and weak gravitational lensing

TL;DR

This paper introduces a geometric approach using the Jacobi metric to analyze circular particle orbits and applies it to study weak gravitational lensing, extending results to non-flat black hole spacetimes and simplifying calculations.

Contribution

It presents a novel geometric method for analyzing particle orbits and gravitational lensing, extending the study to non-flat black hole spacetimes with simplified calculations.

Findings

Derived an expression for the deflection angle in various black hole spacetimes.

Extended gravitational lensing analysis to asymptotically non-flat black holes.

Confirmed consistency with previous literature on gravitational deflection.

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.