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

TL;DR

The paper derives the gravitational field of a two-body compact binary to the $2.5$PN order using a general fluid-based metric expressed in retarded potentials, and regularizes the point-particle self-field via Hadamard partie finie. From this metric, it reproduces the Damour–Deruelle $2.5$PN equations of motion for binary systems, including the leading radiation-reaction terms, and provides an explicit, algebraically closed-form expression for the metric coefficients of a binary in harmonic coordinates all over space-time up to $2.5$PN. The work offers a self-consistent PN framework suitable for generating initial data for numerical relativity and for modeling gravitational-wave emission from inspiralling binaries, with clear pathways toward extension to higher PN orders. The results are presented with careful treatment of non-compact, quadratic, and non-compact potentials, and include detailed regularization of distributions at the particle locations.

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.