Estimation of gravitational bending of light in the weak deflection limit

TL;DR

This paper derives a simple, general expression for the gravitational bending angle of light in the weak deflection limit for static, spherically symmetric spacetimes, including second-order corrections for Schwarzschild geometry.

Contribution

It provides a new, straightforward formula for light deflection that accounts for second-order effects without assuming infinite source or observer distances.

Findings

Derived a general expression for light bending in weak deflection limit.

Obtained explicit second-order correction for Schwarzschild spacetime.

Highlighted the importance of polar axis choice in calculations.

Abstract

After discussing some subtle issues concerning the computation of deflection angle, a general but simple expression of bending angle of light rays in weak deflection limit has been presented for a general static and spherically symmetric space-time. In this context the importance of proper choice of polar axis has been highlighted. Applying the prescribed method the explicit expression of bending angle up to an accuracy of second order in mass is obtained for the Schwarzschild geometry without restricting the source and the observer to be at infinite distance away from the lens.