Resumming Spinning Black Hole Dynamics at Third Post-Minkowskian Order

TL;DR

This paper advances the understanding of spinning black hole interactions by computing high-order gravitational scattering amplitudes using amplitude methods and effective field theory, revealing features consistent with Kerr black holes.

Contribution

It introduces a third post-Minkowskian order calculation of spinning black hole scattering amplitudes with resummation techniques, extending previous lower-order results.

Findings

Computed gravitational amplitudes up to fifth order in spin

Resummed spin effects show Kerr-like ring singularities

Validated phase behavior with Kerr metric features

Abstract

We investigate the relativistic scattering of spinning black holes using modern amplitude methods within a heavy-mass effective field theory formalism at third post-Minkowskian order. Using a systematic self-force expansion up to first order in the mass ratio, the gravitational amplitude and the associated eikonal-like phase are computed for a spin-aligned binary system comprising a heavy and a light black hole up to fifth order in the total spin and up to quadratic order in the spin of the light black hole. We also consider the resummation of the heavy black hole's spin in both the probe limit and the radiation-reaction sector, and verify that the resulting phase displays the characteristic ring singularity features associated with the Kerr metric.