Transient Resonances in EMRIs: A Scalar Toy Model
We present calculations of the scalar self-force for a scalar point-charge following different $r\theta$-resonant geodesics in Kerr spacetime. Using this scalar model, we present two methods for constructing the self-force for resonant sources using two different phase parameterizations of the point-particle motion. We relate these two methods via a simple shifting relation that holds for both the scalar and gravitational self-forces. We discuss how this shifting relation allows us to compare self-force results both at and away from resonances. Finally, we provide new evidence that conservative scalar perturbations can drive the leading-order evolution of the orbital dynamics during resonances (i.e., the orbit-averaged rate of change of the Carter constant depends on contributions from the conservative self-force). This evidence conflicts with a commonly assumed conjecture that these integrated conservative contributions should vanish during both resonant and non-resonant motion.