Self-Force Calculations with a Spinning Secondary

TL;DR

This paper develops a comprehensive framework for calculating the self-force on a spinning secondary in a Schwarzschild spacetime, including waveform generation and a new regularisation method, advancing gravitational self-force modeling.

Contribution

It introduces a novel two-timescale expansion, a frequency domain waveform framework including spin effects, and the first regularisation procedure for gauge-invariant self-force quantities with a spinning secondary.

Findings

Waveforms including spin effects are generated using the Regge-Wheeler-Zerilli formalism.

A new regularisation method for gauge-invariant self-force quantities with spin is developed.

First strong-field self-force calculation with a spinning secondary, computing Detweiler's redshift invariant.

Abstract

We compute the linear metric perturbation to a Schwarzschild black hole generated by a spinning compact object, specialising to circular equatorial orbits with an (anti-)aligned spin vector. We derive a two-timescale expansion of the field equations, with an attendant waveform-generation framework, that includes all effects through first post-adiabatic 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 regularisation 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.