Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates

Details Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates

2004-11-11

arxiv.org/abs/gr-qc/0411057v1

Phys.Rev.D71:044021,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

42 pages, submitted to Phys. Rev. D

Scientific paper

10.1103/PhysRevD.71.044021

The conservative dynamics of two point masses given in harmonic coordinates up to the third post-Newtonian (3pN) order is treated within the framework of constrained canonical dynamics. A representation of the approximate Poincar\'e algebra is constructed with the aid of Dirac brackets. Uniqueness of the generators of the Poincar\'e group resp. the integrals of motion is achieved by imposing their action on the point mass coordinates to be identical with that of the usual infinitesimal Poincar\'e transformations. The second post-Coulombian approximation to the dynamics of two point charges as predicted by Feynman-Wheeler electrodynamics in Lorentz gauge is treated similarly.

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