A Novel Method for Calculating Deflection Angle

Abstract

In this paper, we introduce a method for calculating the deflection angle in the weak-field approximation, applicable to both null and timelike rays. By combining the trajectory equation $\mathcal{Z}(u)=(du/d\ddot{I}•{)}^2$ and the `straight line' $u(\ddot{I}†)=\sin \ddot{I}†/b$, we introduce a new function $\hat{I}¦(\ddot{I}†)$. The deflection angle can then be expressed as $\hat{I}´=\hat{I}¦(0)+\hat{I}¦(\ddot{I}€)-\ddot{I}€$, which directly depends on the impact parameter rather than the closest approach distance. This method offers a convenient and straightforward approach to calculations, avoiding the complexities of integration or iterative procedures. As an illustrative application, we compute the deflection angle for charged particle in the Kerr-Newman spacetime.

5 pages