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arxiv: 1506.05648 · v2 · pith:CEAXKTV2new · submitted 2015-06-18 · 🌀 gr-qc

First Law of Mechanics for Compact Binaries on Eccentric Orbits

Alexandre Le Tiec This is my paper
classification 🌀 gr-qc
keywords binariescompacteccentricfirstmechanicsorbitspost-newtonianalong
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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.

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  1. Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order

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    Derives the 4PN conservative map between constants of motion and fundamental frequencies for eccentric orbits, resummed over eccentricity and validated against circular-orbit and self-force results.