Second Post-Minkowskian Metric for a Moving Kerr Black Hole

Abstract

The harmonic metric for a moving Kerr black hole is presented in the second post-Minkowskian approximation. It is further demonstrated that the obtained metric is consistent with the Liénard-Wiechert gravitational potential for a moving and spinning source with an arbitrary constant velocity. Based on the metric, we also give the post-Newtonian equations of motion for photon and massive test particle in the time-dependent gravitational field.