Physics

Scattering amplitude

Action (physics)

Mathematics

Scattering theory

Optics

Mathematical optimization

Hamiltonian (control theory)

Amplitude

Scattering

Quantum electrodynamics

Quantum mechanics

Classical mechanics

We review recent progress using amplitudes methods to obtain new results for the conservative classical scattering of two massive black holes at order O(G^4). We include contributions from both potential and radiation modes which effect the conservative dynamics through the tail effect. We compute the 2 → 2 scattering amplitudes and extract the radial action through the amplitude- action formula and derive the scattering angle. By matching we also obtain a Hamiltonian valid for arbitrary scattering trajectories.

Scattering amplitudes and conservative dynamics at the fourth post-Minkowskian order