We study the dynamics of electrically charged black-hole binaries and their gravitational-wave emission during the inspiral phase. Within the post-Newtonian framework, we derive the conservative and dissipative dynamics up to second order (2PN), combining Effective Field Theory and classical methods. We compute the NNLO conservative Lagrangian, LO dissipative effects in harmonic and Lorenz gauges, and provide the equations of motion, center-of-mass transformations, and the Lagrangian/Hamiltonian in ADM-type coordinates. We also obtain gauge-invariant expressions for the binding energy, periastron advance in quasi-circular orbits, and the scattering angle in unbound orbits. Our results extend previous analyses and are fully consistent with recent post-Minkowskian findings.
@article{arxiv.2509.20432,
title = {Charged Black-Hole Binary Evolution at Second Post-Newtonian Order},
author = {Andrea Placidi and Elisa Grilli and Marta Orselli and Matteo Pegorin and Nicola Bartolo and Pierpaolo Mastrolia},
journal= {arXiv preprint arXiv:2509.20432},
year = {2026}
}