First Law of Mechanics for Compact Binaries on Eccentric Orbits

TL;DR

This paper establishes a first law of mechanics for eccentric binary systems using Hamiltonian formalism, validated within 3PN approximation, and explores applications to gravitational self-force and effective one-body models.

Contribution

It introduces a new first law of mechanics for eccentric binaries using Hamiltonian formalism, extending previous work to generic stable bound orbits.

Findings

The first law holds within the 3PN approximation.

Applications include informing post-Newtonian theory with self-force results.

Insights into effective one-body models for eccentric binaries.

Abstract

Using the canonical Arnowitt-Deser-Misner Hamiltonian formalism, a "first law of mechanics" is established for binary systems of point masses moving along generic stable bound (eccentric) orbits. This relationship is checked to hold within the post-Newtonian approximation to general relativity, up to third (3PN) order. Several applications are discussed, including the use of gravitational self-force results to inform post-Newtonian theory and the effective one-body model for eccentric-orbit compact binaries.