Detweiler's gauge-invariant redshift variable: analytic determination of the nine and nine-and-a-half post-Newtonian self-force contributions

TL;DR

This paper analytically computes the ninth and ninth-and-a-half post-Newtonian terms of Detweiler's gauge-invariant redshift variable, advancing the precision of self-force calculations in gravitational physics.

Contribution

It provides the exact analytic expressions for higher-order post-Newtonian self-force contributions, extending previous computations.

Findings

Exact expressions for 9th and 9.5th post-Newtonian terms

Enhances precision of gravitational self-force models

Supports improved gravitational wave predictions

Abstract

Continuing our analytic computation of the first-order self-force contribution to Detweiler's redshift variable we provide the exact expressions of the ninth and ninth-and-a-half post-Newtonian terms.