A unified 1PM formula gives the gravitational time delay of relativistic massive and massless particles by a radially moving Schwarzschild lens, matching known light and static limits.
Second Post-Minkowskian Metric for a Moving Kerr Black Hole
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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 Li\'{e}nard-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.
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Leading-order gravitational time delay of massive particles by a moving Schwarzschild lens
A unified 1PM formula gives the gravitational time delay of relativistic massive and massless particles by a radially moving Schwarzschild lens, matching known light and static limits.