Inspiraling binary charged black holes in an external magnetic field: Application of post-Newtonian dynamics in Einstein-Maxwell theory
We present a systematic post-Newtonian treatment of binary charged black holes immersed in external magnetic fields within the framework of Einstein-Maxwell theory. By incorporating a uniform external magnetic field into the two-body Lagrangian expanded to first post-Newtonian order, we derive the complete equations of motion that capture both gravitational and electromagnetic interactions. The magnetic Lorentz force fundamentally alters the orbital dynamics, breaking the conservation of linear and angular momentum and inducing transitions from planar to three-dimensional trajectories. {Through numerical integration of these equations, we compute the resulting gravitational waveforms and characterize the distinctive magnetic field signatures through time-domain and frequency-domain analysis.} Our results demonstrate that strong background magnetic fields can substantially modify the orbital evolution and leave distinctive signatures in the gravitational wave signals. These findings provide a promising avenue for detecting charged black holes and probing magnetic field environments through gravitational wave observations.