Gravitational self-force on generic bound geodesics in Kerr spacetime

TL;DR

This paper presents the first calculation of the gravitational self-force on generic bound geodesics in Kerr spacetime, incorporating both dissipative and conservative effects, using a novel semi-analytical frequency domain approach.

Contribution

It extends existing methods to compute the gravitational self-force for generic orbits in Kerr spacetime, including new reconstruction and regularization techniques.

Findings

Validated the self-force calculations against known regularization parameters.

Confirmed consistency between local self-force effects and flux-based energy and momentum changes.

Achieved a semi-analytical method for generic orbit self-force computation in Kerr spacetime.

Abstract

In this work we present the first calculation of the gravitational self-force on generic bound geodesics in Kerr spacetime to first order in the mass-ratio. That is, the local correction to equations of motion for a compact object orbiting a larger rotating black hole due to its own impact on the gravitational field. This includes both dissipative and conservative effects. Our method builds on and extends earlier methods for calculating the gravitational self-force on equatorial orbits. In particular we reconstruct the local metric perturbation in the outgoing radiation gauge from the Weyl scalar $\psi_4$, which in turn is obtained by solving the Teukolsky equation using semi-analytical frequency domain methods. The gravitational self-force is subsequently obtained using (spherical) $l$-mode regularization. We test our implementation by comparing the large $l$-behaviour against the analytically known regularization parameters. In addition we validate our results be comparing the long-term average changes to the energy, angular momentum, and Carter constant to changes to these constants of motion inferred from the gravitational wave flux to infinity and down the horizon.