Constants of motion in gravitational self-force theory

TL;DR

This paper explores how constants of motion in gravitational self-force theory can improve the analysis and modeling of binary systems, providing both numerical and analytical insights up to high post-Newtonian orders.

Contribution

It introduces a method to use constants of motion directly in self-force theory for better comparison, hybridization, and waveform generation, with detailed calculations up to 9PN order.

Findings

Computed constants of motion and frequency corrections numerically and analytically.

Established consistency with 4PN results from post-Newtonian theory.

Identified perturbed locations of key orbital curves such as the separatrix.

Abstract

Synergies between self-force theory and other approaches to the gravitational two-body problem have traditionally relied on calculations of gauge-invariant observables as functions of orbital frequencies. However, in self-force theory one can also define a complete set of constants of motion: energy, azimuthal angular momentum, and radial and polar actions. Here we outline how directly utilizing these constants allows for more straightforward comparisons and hybridizations across the parameter space, as well as more streamlined waveform generation through flux-balance laws. Restricting to the case of nonspinning binaries and first order in self-force, we compute the constants of motion and the corrections to fundamental frequencies numerically as well as analytically (to 9PN in a post-Newtonian expansion), establishing consistency with the highest-order (4PN) results available from post-Newtonian theory. We also apply the results to identify the perturbed locations of special curves in the parameter space: circular orbits and the separatrix between bound and plunging orbits.