Quantum mechanics

Theoretical physics

Gravitation

Perturbation theory (quantum mechanics)

Scattering amplitude

Scattering

Classical mechanics

Physics

Amplitude

Mathematics

Quantum electrodynamics

Binary number

Unitarity

General relativity

Arithmetic

Physical Review Letters

We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic expressions for the classical potential of a binary black hole system at second order in the gravitational constant and all orders in velocity. Our results exactly match all known results up to fourth post-Newtonian order, and offer a simple check of future higher order calculations. By design, these methods should extend to higher orders in perturbation theory.

From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion