I will discuss what is the current state of the art for gravitational self-force waveforms and the ingredients that go into them. I will discuss how the second-order metric perturbation is used to calculate the amplitude, flux and phase of a gravitational wave and how the slowly-evolving first-order metric perturbation contributes to sourcing perturbations at second order. I will demonstrate...
I review how to compute the adiabatic radiation reaction to the
constants of motion including the Carter constant in Kerr spacetime.
I also talk about extending these ideas to post-adiabatic order, i.e.,
one order higher in the mass ratio, which would significantly simplifies
the construction of the gravitational wave waveform necessary for
the observation of extreme mass-ratio in-spirals.