Post-Newtonian Approximation for Spinning Particles

TL;DR

This paper develops a post-Newtonian approximation framework for spinning particles using Dixon and Bailey-Israel's energy-momentum tensor, deriving equations of motion and gravitational waveforms for such systems.

Contribution

It introduces a self-contained method to model spinning particles in post-Newtonian gravity, including waveform and luminosity calculations.

Findings

Derived equations of motion for spinning particles

Obtained gravitational waveforms and luminosity

Provided a new formalism for spinning particle dynamics

Abstract

Using an energy-momentum tensor for spinning particles due to Dixon and Bailey-Israel, we develop the post-Newtonian approximation for N spinning particles in a self-contained manner. The equations of motion are derived directly from this energy-momentum tensor. Following the formalism of Epstein- Wagoner, we also obtain the waveform and the luminosity of the gravitational wave generated by these particles.