Enhanced plateau effect at resonance in realistic non-integrable EMRIs

When an EMRI in a perturbed integrable gravitational field, such as a deformed Kerr black hole, undergoes a prolonged resonance, the frequencies that engage in resonance retain a fixed rational ratio, despite experiencing adiabatic changes due to radiation reaction. In the past this plateau effect in the evolution of the ratio of frequencies has been investigated by studying the orbital evolution through kludge models, which provide approximate average losses of energy and angular momentum experienced by a test particle in this field. By employing a Newtonian gravitational field that closely resembles a pure Kerr or a perturbed Kerr relativistic field, we demonstrate that the actual adiabatic evolution of an orbit driven by an artificial ``self-force'' results in more prolonged periods of resonance crossings compared to those obtained by imposing a predetermined rate of energy and angular momentum change throughout the orbital progression.