Secular momentum transport by gravitational waves from spinning compact binaries

TL;DR

This paper derives a comprehensive set of equations describing how gravitational waves from spinning compact binaries cause a gradual loss of linear momentum, incorporating relativistic and spin effects.

Contribution

It introduces a closed system of coupled differential equations that unify dissipative and conservative dynamics for momentum loss in spinning binaries.

Findings

Derived equations include relativistic and spin-orbit effects.

Provides a framework for predicting momentum loss over time.

Bridges dissipative and conservative dynamics in binary systems.

Abstract

We present a closed system of coupled first order differential equations governing the secular linear momentum loss of a compact binary due to emitted gravitational waves, with the leading order relativistic and spin-orbit perturbations included. In order to close the system, the secular evolution equations of the linear momentum derived from the dissipative dynamics are supplemented with the secular evolutions of the coupled angular variables, as derived from the conservative dynamics.