Self-force calculations with a spinning secondary

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

Automated summary

This article investigates the linear metric perturbation of a Schwarzschild black hole generated by a spinning compact object, with a focus on the effect of spin on the waveform phase. By deriving a two-timescale expansion of the field equations and a waveform-generation framework, all effects are taken into account through first postadiabatic order. The Regge-Wheeler-Zerilli formalism in the frequency domain is used to generate waveforms that include the complete effect of spin on the waveform phase. The calculations are performed using expansions at fixed orbital frequency, increasing computational efficiency and simplifying the procedure compared to previous approaches. Lastly, a fully relativistic, first-principles regularization procedure for gauge invariant self-force quantities to linear order in spin is provided, with Detweiler's redshift invariant being calculated as an example.