Published in PRD, 2022
We compute the evolution of the action variables of an EMRI that is in resonance with a dynamic perturbation around a spinning black hole. We relate the Weyl invariant scalars that contain the emitted gravitational waveforms from the EMRI and perturbation to track the inspiral evolution. We compare our general/analytic technique with known results of static resonant cases (Keplerian and relativistic) and find a reasonably strong convergance with our dynamic cases and literature results.