# Observables and amplitudes for spinning particles and black holes

## TL;DR

This paper introduces a formalism to compute classical scattering observables for spinning particles using on-shell amplitudes, applying it to Einstein gravity and reproducing recent black hole scattering results.

## Contribution

It develops a general on-shell amplitude-based method for classical observables involving spinning particles and applies it to black hole scattering in Einstein gravity.

## Key findings

- Reproduces recent first post-Minkowskian black hole scattering results.
- Provides a unified formalism for spinning particle scattering calculations.
- Connects amplitude methods with classical gravitational observables.

## Abstract

We develop a general formalism for computing classical observables for relativistic scattering of spinning particles, directly from on-shell amplitudes. We then apply this formalism to minimally coupled Einstein-gravity amplitudes for the scattering of massive spin 1/2 and spin 1 particles with a massive scalar, constructed using the double copy. In doing so we reproduce recent results at first post-Minkowskian order for the scattering of spinning black holes, through quadrupolar order in the spin-multipole expansion.