Self-force calculations with a spinning secondary

We compute the linear metric perturbation to a Schwarzschild black hole generated by spinning compact object, specializing circular equatorial orbits with an (anti-)aligned spin vector. derive two-timescale expansion of field equations, attendant waveform-generation framework, that includes all effects through first postadiabatic order, and we use Regge-Wheeler-Zerilli formalism in frequency domain generate waveforms include complete effect on waveform phase. perform calculations using expansions at fixed orbital frequency, increasing computational efficiency, simplifying procedure compared previous approaches. Finally, provide fully relativistic, first-principles regularization for gauge invariant self-force quantities order spin. this produce strong-field, conservative calculation including secondary---computing Detweiler's redshift invariant.