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

TL;DR

The authors develop a 2.5PN spin-orbit framework for spinning compact binaries by modeling bodies as spinning point particles with a Bailey–Israel stress-energy tensor and applying Hadamard regularization. They formulate the PN expansion, compute the relevant PN potentials, and derive the complete 2.5PN spin-orbit contributions to the equations of motion, presenting both body-centered and center-of-mass forms and validating the results against the Kerr limit in the test-mass case. A key result is the explicit 2.5PN spin-orbit term in the relative acceleration, along with a thorough consistency set of checks, including Lorentz invariance. This work lays groundwork for future calculations of gravitational-wave luminosity and phase evolution, and provides a field suitable for constructing initial data for spinning binary black-hole mergers in numerical relativity.

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.