Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation

TL;DR

This paper develops a method to extract the regularized self force in a black hole binary system using orbital evolution data, applying it to determine conservative self force components in a post-Newtonian framework, and analyzing their impact on gravitational waveforms.

Contribution

It introduces a novel approach to indirectly determine the self force in black hole binaries within the post-Newtonian approximation, enhancing waveform modeling accuracy.

Findings

First- and second-order conservative self force determined

Self force contributions compared with spin-orbit effects

Improved gravitational waveform modeling

Abstract

Comparing the corrections to Kepler's law with orbital evolution under a self force, we extract the finite, already regularized part of the latter in a specific gauge. We apply this method to a quasi-circular orbit around a Schwarzschild black hole of an extreme mass ratio binary, and determine the first- and second-order conservative gravitational self force in a post Newtonian expansion. We use these results in the construction of the gravitational waveform, and revisit the question of the relative contribution of the self force and spin-orbit coupling.