Roto-translational Effects on Deflection of Light and Particle by Moving Kerr Black Hole

TL;DR

This paper investigates how the combined rotation and translation of a Kerr black hole influence the deflection of light and particles, revealing a coupling effect that affects the total bending angle.

Contribution

It introduces the analysis of roto-translational effects on deflection by moving Kerr black holes, extending previous studies focused on static or purely translational scenarios.

Findings

Coupling between rotation and translation affects deflection angles.

Roto-translational deflection ratio varies with black hole velocity.

Post-Newtonian dynamics of photons and particles are analyzed.

Abstract

Velocity effects in first-order Schwarzschild deflection of light and particles have been explored in the previous literature. In this paper, we investigate the roto-translational-motion induced deflection by one moving Kerr black hole with an arbitrary but constant speed. It is shown that the coupling between the effects of the rotation and the translational motion always exists for both light and particles. The contribution of the roto-translational deflection to the total bending angle is discussed in detail. This ratio takes upper limit for light and it decreases monotonically with increasing translational velocity for a massive particle. For a given translational velocity of black hole, this ratio increases with the particle' velocity. In addition, the Post-Newtonian dynamics of the photon and particle is also presented.