Analytical Derivation of Second-Order Deflection in Equatorial Plane of a Radially Moving Kerr-Newman Black Hole

TL;DR

This paper analytically derives the second-order gravitational deflection of relativistic particles in the equatorial plane of a moving Kerr-Newman black hole, extending previous first-order results and including kinematic corrections.

Contribution

It provides a novel analytical expression for second-order deflection in Kerr-Newman spacetime with a moving black hole, incorporating kinematic effects.

Findings

Second-order deflection formulas are compact and valid for both photons and massive particles.

Results reduce to known first-order deflection in the Schwarzschild limit when second-order terms are omitted.

Kinematic corrections significantly influence the deflection at second order.

Abstract

In this work, we base on the second-order post-Minkowskian equations of motion, and apply an iterative technique to analytically derive the gravitational deflection of the relativistic particles in the equatorial plane of Kerr-Newman black hole with a radial (or longitudinal) and constant velocity. We find that the kinematically correctional effects on the second-order contributions to the deflection can be expressed into a very compact form, which are valid for both the massive particle and photon. Our result reduces to the previous formulation for the first-order deflection caused by a moving Schwarzschild black hole when the second-order contributions are dropped.