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

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.