First law of mechanics for compact binaries on eccentric orbits
First law of mechanics for compact binaries on eccentric orbits
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 …