# On Post-Minkowskian Hamiltonians in General Relativity

## TL;DR

This paper develops a method to derive post-Minkowskian Hamiltonians in General Relativity from scattering amplitudes, enabling precise modeling of binary black hole systems without spin.

## Contribution

It introduces a relativistic Lippmann-Schwinger framework to connect scattering amplitudes with classical Hamiltonians at any order in Newton's constant.

## Key findings

- Derived a 2nd order post-Minkowskian Hamiltonian for binary black holes without spin.
- Established equivalence with existing effective field theory methods.
- Demonstrated the approach's applicability to classical gravitational systems.

## Abstract

We describe the computation of post-Minkowskian Hamiltonians in General Relativity from scattering amplitudes. Using a relativistic Lippmann-Schwinger equation, we relate perturbative amplitudes of massive scalars coupled to gravity to the post-Minkowskian Hamiltonians of classical General Relativity to any order in Newton's constant. We illustrate this by deriving an Hamiltonian for binary black holes without spin up to 2nd order in the post-Minkowskian expansion and demonstrate explicitly the equivalence with the recently proposed method based on an effective field theory matching.