  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.
