Equivalence of Gibbons-Werner method to geodesics method in the study of gravitational lensing

Understand

The Gibbons-Werner method where the Gauss-Bonnet theorem is applied to study the gravitational deflection angle has received much attention recently.

• In this paper, we study the equivalence of the Gibbons-Werner method to the standard geodesics method, and it is shown that the geodesics method can be derived with the Gibbons-Werner method, for asymptotically flat case.
• In the geodesics method, the gravitational deflection angle of particle depends entirely on the geodesic curvature of the particle ray in the Euclidean space.
• The gravitational deflection of light in Kerr-Newman spacetime is calculated by different technologies under the Gibbons-Werner framework, as an intuitive example to show the equivalence.