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General Relativity and Quantum Cosmology, gr-qc
Abstract:
In this paper, we complete our preceding work on the Fokker Lagrangian
describing the dynamics of compact binary systems at the fourth post-Newtonian
(4PN) order in harmonic coordinates. We clarify the impact of the non-local
character of the Fokker Lagrangian or the associated Hamiltonian on both the
conserved energy and the relativistic periastron precession for circular
orbits. We show that the non-locality of the action, due to the presence of the
tail effect at the 4PN order, gives rise to an extra contribution to the
conserved integral of energy with respect to the Hamiltonian computed on shell,
which was not taken into account in our previous work. We also provide a direct
derivation of the periastron advance by taking carefully into account this
non-locality. We then argue that the infra-red (IR) divergences in the
calculation of the gravitational part of the action are problematic, which
motivates us to introduce a second ambiguity parameter, in addition to the one
already assumed previously. After fixing these two ambiguity parameters by
requiring that the conserved energy and the relativistic periastron precession
for circular orbits are in agreement with numerical and analytical
gravitational self-force calculations, valid in the limiting case of small mass
ratio, we find that our resulting Lagrangian is physically equivalent to the
one obtained in the ADM Hamiltonian approach.
