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  Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order

Bernard, L., Blanchet, L., Bohe, A., Faye, G., & Marsat, S. (2017). Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order. Physical Review D, 95(4): 044026. doi:10.1103/PhysRevD.95.044026.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002C-3F1A-4 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002E-2BE3-B
Genre: Journal Article

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 Creators:
Bernard, Laura, Author
Blanchet, Luc, Author
Bohe, Alejandro1, Author              
Faye, Guillaume, Author
Marsat, Sylvain1, Author              
Affiliations:
1Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:1933290              

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Free keywords: 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.

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 Dates: 2016-10-252017-01-062017
 Publication Status: Published in print
 Pages: 30 pages, 1 figure
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1610.07934
URI: http://arxiv.org/abs/1610.07934
DOI: 10.1103/PhysRevD.95.044026
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : American Physical Society
Pages: - Volume / Issue: 95 (4) Sequence Number: 044026 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/111088197762258