Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order

TL;DR

This paper derives the gravitational field and equations of motion for compact binary systems up to 2.5 post-Newtonian order, including radiation-reaction effects, using a regularization method for point particles.

Contribution

It extends the post-Newtonian approximation to 2.5PN order for binary systems and recovers known equations of motion using a systematic regularization approach.

Findings

Derived gravitational field up to 2.5PN order

Recovered Damour-Deruelle equations of motion

Provided a method for initial conditions in numerical simulations

Abstract

We derive the gravitational field and equations of motion of compact binary systems up to the 5/2 post-Newtonian approximation of general relativity (where radiation-reaction effects first appear). The approximate post-Newtonian gravitational field might be used in the problem of initial conditions for the numerical evolution of binary black-hole space-times. On the other hand we recover the Damour-Deruelle 2.5PN equations of motion of compact binary systems. Our method is based on an expression of the post-Newtonian metric valid for general (continuous) fluids. We substitute into the fluid metric the standard stress-energy tensor appropriate for a system of two point-like particles. We remove systematically the infinite self-field of each particle by means of the Hadamard partie finie regularization.