Kerr-Schild Form of the Exact Metric for a Constantly Moving Kerr Black Hole and Null Gravitational Deflection

TL;DR

This paper derives an exact Kerr black hole metric moving at constant velocity in Kerr-Schild coordinates and calculates the null gravitational deflection of light, confirming previous results in the weak field limit.

Contribution

It provides a new exact metric for a moving Kerr black hole and applies it to compute light deflection, extending previous weak field analyses.

Findings

Derived the exact metric of a moving Kerr black hole in Kerr-Schild coordinates.

Calculated the null gravitational deflection up to second post-Minkowskian order.

Confirmed consistency with previous weak field deflection results.

Abstract

The exact metric of a moving Kerr black hole with an arbitrary constant velocity is derived in Kerr-Schild coordinates. We then calculate the null equatorial gravitational deflection caused by a radially moving Kerr source up to the second post-Minkowskian order, acting as an application of the weak field limit of the metric. The bending angle of light is found to be consistent with the result given in the previous works.