Second Post-Minkowskian Metric for a Moving Kerr Black Hole
Guansheng He, Chunhua Jiang, and Wenbin Lin
TL;DR
This paper derives a second post-Minkowskian harmonic metric for a moving Kerr black hole, demonstrating its consistency with known gravitational potentials and providing equations of motion for particles in this dynamic spacetime.
Contribution
It presents the second post-Minkowskian harmonic metric for a moving Kerr black hole and derives related equations of motion, extending previous static or linear models.
Findings
The metric is consistent with Liénard-Wiechert gravitational potential.
Derived post-Newtonian equations of motion for particles.
Validated the harmonic metric for a moving, spinning 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 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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