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Abstract

We develop the first model for extreme mass-ratio inspirals (EMRIs) into a
rotating massive black hole driven by the gravitational self-force. Our model
is based on an action angle formulation of the method of osculating geodesics
for eccentric, equatorial (i.e., spin-aligned) motion in Kerr spacetime. The
forcing terms are provided by an efficient spectral interpolation of the
first-order gravitational self-force 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 gravitational self-force at post-adiabatic order.
This implies that the model can be evolved without having to resolve all
$\mathcal{O}(10^6)$ orbit cycles of an EMRI, yielding an inspiral model that
can be evaluated in less than a second for any mass-ratio. In the case of a
non-rotating central black hole, we compare inspirals evolved using self-force
data computed in the Lorenz and radiation gauges. We find that the two gauges
generally produce differing inspirals with a deviation of comparable magnitude
to the conservative self-force correction. This emphasizes the need for
including the (currently unknown) dissipative second order self-force to obtain
gauge independent, post-adiabatic waveforms.