Classical Hamiltonian of Reissner-Nordström black holes at second post-Minkowskian order from scattering amplitudes

We employ scattering amplitudes in Einstein-Maxwell theory to compute the classical Hamiltonian of a binary system of two charged, nonspinning compact objects. The effective Hamiltonian is valid to all orders in velocity and up to second post-Minkowskian (2PM) order, i.e., O ( G 2 ) . The classical interaction potential is extracted via matching the four-point tree and one-loop amplitudes to those of a suitably chosen classical effective field theory. We derive the 2PM scattering angle from the Hamiltonian and find complete agreement with known results. Using also the third-order result for the scattering angle computed by Wilson-Gerow, we expand the scattering angle at second post-Newtonian (2PN) order. Additionally, we provide expressions for the binding energy and periastron advance at 2PN order via the boundary-to-bound dictionary introduced by Kälin and Porto and find agreement with previous findings.