Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession

TL;DR

This paper analytically computes high-order post-Newtonian self-force contributions to gravitational spin precession, providing exact expressions up to the tenth order and introducing a novel WKB-based regularization method.

Contribution

It presents the first exact expressions for the tenth and tenth-and-a-half post-Newtonian terms and introduces a new WKB approach for computing self-force regularization parameters.

Findings

Exact expressions for 10th and 10.5th post-Newtonian terms

New WKB-based method for self-force regularization

Enhanced precision in gravitational spin precession calculations

Abstract

Continuing our analytic computation of the first-order self-force contribution to the "geodetic" spin precession frequency of a small spinning body orbiting a large (non-spinning) body we provide the exact expressions of the tenth and tenth-and-a-half post-Newtonian terms. We also introduce a new approach to the analytic computation of self-force regularization parameters based on a WKB analysis of the radial and angular equations satisfied by the metric perturbations.