Charged binaries in gravitational tides

Next-generation low-frequency interferometers are expected to detect binary systems near supermassive black holes, where tidal effects can alter significantly the binary's motion. This motivates a broader investigation of how external gravitational fields influence the dynamics of physical systems. In this work, we consider a charged black hole binary system subject to a gravitational tide. We first construct a stationary gravitational tide acting on a dyonic Reissner-Nordström black hole and, focusing on the extreme mass-ratio limit, we analyze the motion of a test particle. By calculating the particle's secular Hamiltonian, we obtain the ISCO and light ring tidal shifts in terms of explicit functions of the binary's parameters. Our results show that tidal corrections are suppressed as the black hole's charge increases, but they persist in the extremal limit yielding a finite contribution. This work paves the way towards studying tidal effects on other charged systems, such as topological stars.