Charged black-hole binary evolution at second post-Newtonian order

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 next-to-next-to-leading-order conservative Lagrangian, leading-order dissipative effects in harmonic and Lorenz gauges, and provide the equations of motion, center-of-mass transformations, and the Lagrangian/ Hamiltonian in Arnowitt-Deser-Misner-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.