Reissner-Nordstr\"om Black Holes at second post-Minkowskian order from Scattering Amplitudes

TL;DR

This paper calculates the classical Hamiltonian and scattering angle for charged binary systems at second post-Minkowskian order using scattering amplitudes, extending previous results to include electromagnetic interactions.

Contribution

It introduces a novel computation of the 2PM Hamiltonian for charged objects using scattering amplitudes, matching to effective field theory, and provides new insights into electromagnetic effects in gravitational scattering.

Findings

Hamiltonian valid to all velocities at 2PM order

Agreement with existing literature on scattering results

Comparison of scattering angle and binding energy with post-Newtonian results

Abstract

We employ one-loop scattering amplitudes in Einstein-Maxwell theory to compute the classical Hamiltonian of a binary system of two charged, non-spinning compact objects. The Hamiltonian is valid to all orders in velocity and up to second post-Minkowskian order (2PM), i.e. $\mathcal{O}(G^2)$. The classical interaction potential is extracted via matching to a non-relativistic classical effective field theory. We also provide the scattering angle at 2PM order. We perform several cross checks on our results and find full agreement with existing results in the literature. Finally, we also briefly discuss a comparison for the scattering angle, the binding energy and the periastron shift of a bound system up to the second post-Newtonian order.