Black-hole scattering with general spin directions from minimal-coupling amplitudes
Alfredo Guevara, Alexander Ochirov, Justin Vines
TL;DR
This work establishes a gauge-invariant, on-shell route to the classical scattering of spinning black holes by using minimal-coupling amplitudes for massive spin-$s$ particles with arbitrary spin directions. By exploiting angular-momentum exponentiation and a Lorentz-boost framework, the authors derive a spin-dependent four-point amplitude that reproduces the full 1PM classical dynamics in the $s\to\infty$ limit, matching known results for momentum and spin transfers. The approach connects the holomorphic classical limit of on-shell amplitudes to the covariant multipole structure of Kerr black holes and yields a compact impact-parameter expression with a logarithmic kernel, demonstrating a unified path from quantum amplitudes to classical observables. The results pave the way for higher-loop, finite-size, and radiative corrections within the same on-shell, gauge-invariant framework, with potential extensions via double-copy methods and supersymmetric generalizations.
Abstract
We study the link between classical scattering of spinning black holes and quantum amplitudes for massive spin-$s$ particles. Generic spin orientations of the black holes are considered, allowing their spins to be deflected on par with their momenta. We rederive the spin-exponentiated structure of the relevant tree-level amplitude from minimal coupling to Einstein's gravity, which in the $s\to\infty$ limit generates the black holes' complete series of spin-induced multipoles. The resulting scattering function is seen to encode in a simple way the known net changes in the black-hole momenta and spins at first post-Minkowskian order. We connect our findings to a rigorous framework developed elsewhere for computing such observables from amplitudes.