Post-Newtonian light propagation in Kerr-Newman spacetime

TL;DR

This paper derives a second-order post-Newtonian solution for light propagation and deflection in Kerr-Newman spacetime, providing a comprehensive formula applicable to any incident direction.

Contribution

It presents the first second-order post-Newtonian solution for light in Kerr-Newman spacetime, including a unified deflection formula for arbitrary incident directions.

Findings

Second-order post-Newtonian light deflection formula derived.

Unified expression valid for any incident light direction.

Results expressed in a coordinate system based on initial light direction and impact vector.

Abstract

The second-order post-Newtonian solution for the light propagation in the field of Kerr-Newman black hole is achieved via an iterative method. Based on this result, we further obtain the second-order post-Newtonian light deflection in Kerr-Newman spacetime, which is formulated in an united form for any arbitrarily incident directions. All results are exhibited in the coordinate system constituted by the initial light-direction vector, the impact vector, and their cross-product.