Eccentric self-forced inspirals into a rotating black hole

We develop the first model for extreme mass-ratio inspirals (EMRIs) into a rotating massive black hole driven by the gravitational self-force (GSF).Our model is based on an action angle formulation of the method of osculating geodesics for eccentric, equatorial motion in Kerr spacetime.The forcing terms are provided by an efficient spectral interpolation of the first-order GSF in the outgoing radiation gauge. We apply a near-identity (averaging) transformation to eliminate all dependence of the orbital phases from the equations of motion, while maintaining all secular effects of the first-order GSF at post-adiabatic order. As such, the model can be evolved without having to resolve all ~10^6 orbit cycles of an EMRI, yielding an inspiral that can be evaluated in less than a second for any mass-ratio. In the case of a non-rotating black hole, we compare inspirals evolved using GSF data computed in the Lorenz and radiation gauges. We find that the two gauges produce differing inspirals with a deviation of comparable magnitude to the conservative GSF correction. This emphasizes the need for including the dissipative second order GSF to obtain gauge independent, post-adiabatic waveforms.