Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime

TL;DR

This paper extends gravitational self-force calculations of gyroscope precession from Schwarzschild to Kerr spacetime, providing high-order post-Newtonian expansions, numerical data, and benchmarks for Kerr self-force computations.

Contribution

It generalizes previous results to Kerr spacetime, deriving high-order gauge-invariant precession functions and validating them with numerical data across various Kerr spins.

Findings

High-order post-Newtonian expansions for Kerr precession

Agreement between PN results and numerical data

Identification of lightring divergence behavior

Abstract

We generalize to Kerr spacetime previous gravitational self-force results on gyroscope precession along circular orbits in the Schwarzschild spacetime. In particular we present high order post- Newtonian expansions for the gauge invariant precession function along circular geodesics valid for arbitrary Kerr spin parameter and show agreement between these results and those derived from the full post-Newtonian conservative dynamics. Finally we present strong field numerical data for a range of the Kerr spin parameter, showing agreement with the GSF-PN results, and the expected lightring divergent behaviour. These results provide useful testing benchmarks for self- force calculations in Kerr spacetime, and provide an avenue for translating self-force data into the spin-spin coupling in effective-one-body models.