# Black-hole scattering with general spin directions from minimal-coupling amplitudes

## TL;DR

This paper establishes a link between classical black-hole scattering with arbitrary spins and quantum amplitudes, deriving a spin-exponentiated amplitude structure from minimal coupling that captures spin effects at first post-Minkowskian order.

## Contribution

It derives a general amplitude framework for spinning black holes with arbitrary orientations from minimal coupling, including the complete series of spin-induced multipoles in the large spin limit.

## Key findings

- Re-derivation of the spin-exponentiated amplitude structure.
- Encoding of momentum and spin changes at first post-Minkowskian order.
- Connection to a rigorous amplitude-based framework for classical observables.

## 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.