Equations of motion of compact binaries at the third post-Newtonian order

Details Equations of motion of compact binaries at the third post-Newtonian order Equations of motion of compact binaries at the third post-Newtonian order

2004-03-31

arxiv.org/abs/gr-qc/0403122v1

Pramana 53 (1999) 1-15

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, to appear in the Proceedings of the International Conference on Gravitation and Cosmology (ICGC-2004), ed. by B.R. I

Scientific paper

10.1007/BF02705192

The equations of motion of two point masses in harmonic coordinates are derived through the third post-Newtonian (3PN) approximation. The problem of self-field regularization (necessary for removing the divergent self-field of point particles) is dealt with in two separate steps. In a first step the extended Hadamard regularization is applied, resulting in equations of motion which are complete at the 3PN order, except for the occurence of one and only one unknown parameter. In a second step the dimensional regularization (in d dimensions) is used as a powerful argument for fixing the value of this parameter, thereby completing the 3-dimensional Hadamard-regularization result. The complete equations of motion and associated energy at the 3PN order are given in the case of circular orbits.

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