Gravitational deflection of light in polar-axis plane of a moving Kerr-Newman black hole

TL;DR

This paper investigates the gravitational deflection of light by a moving Kerr-Newman black hole in the polar-axis plane, deriving exact metrics and deflection angles up to second post-Minkowskian order, highlighting the effects of black hole motion.

Contribution

It introduces the first exact metric for a moving Kerr-Newman black hole using Lorentz boosting and derives the null deflection angle considering the black hole's motion and spin effects.

Findings

Deflection angle is independent of black hole spin.

Motion of the black hole affects the gravitational lensing.

Derived equations can aid future astronomical observations.

Abstract

The gravitational deflection of light signals restricted in the polar-axis plane of a moving Kerr-Newman (KN) black hole with a constant velocity along the polar axis is studied within the second post-Minkowskian (PM) approximation. For this purpose, the Lorentz boosting technique is adopted to obtain the exact metric of a moving KN black hole with an arbitrary constant velocity in Kerr-Schild coordinates for the first time. Based on the weak field limit of the exact metric, we then derive the equations of motion of test particles constrained in the polar-axis plane of a moving KN source whose velocity is along the polar axis and collinear with its angular momentum. An iterative technique is utilized subsequently in the calculations of the null deflection angle up to the 2PM order caused by the moving lens, and this deflection angle is found to be spin-independent. Finally, we discuss the influence of the motion of the lens on the gravitational deflection and estimate the possibility to detect this kinematical effect. Our work might be helpful for future astronomical observations.