Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order

TL;DR

This paper derives the 2.5 post-Newtonian order spin-orbit coupling effects on the gravitational field and equations of motion for compact binaries, advancing the understanding of spin effects in gravitational wave modeling.

Contribution

It introduces a new method for calculating spin effects at 2.5PN order using a modified stress-energy tensor, extending previous work to include higher-order spin contributions.

Findings

Derived 2.5PN spin-orbit coupling effects

Regularized divergent terms with Hadamard finite part

Set groundwork for gravitational-wave phase evolution analysis

Abstract

We derive spin-orbit coupling effects on the gravitational field and equations of motion of compact binaries in the 2.5 post-Newtonian approximation to general relativity, one PN order beyond where spin effects first appear. Our method is based on that of Blanchet, Faye, and Ponsot, who use a post-Newtonian metric valid for general (continuous) fluids and represent pointlike compact objects with a delta-function stress-energy tensor, regularizing divergent terms by taking the Hadamard finite part. To obtain post-Newtonian spin effects, we use a different delta-function stress-energy tensor introduced by Bailey and Israel. In a future paper we will use the 2.5PN equations of motion for spinning bodies to derive the gravitational-wave luminosity and phase evolution of binary inspirals, which will be useful in constructing matched filters for signal analysis. The gravitational field derived here may help in posing initial data for numerical evolutions of binary black hole mergers.