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

2004/11/11 by Raoul-Martin Memmesheimer, Gerhard Schäfer
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Pulsars and Gravitational Waves Research #gr-qc

paper · pdf · doi:10.1103/physrevd.71.044021

published as Phys.Rev.D71:044021,2005 · 42 pages, submitted to Phys. Rev. D

arxiv created 2004/11/11 · openalex publication_date 2005/02/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The conservative dynamics of two point masses given in harmonic coordinates up to the third post-Newtonian 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 or 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.

Citations

• Quantization of Gauge Systems
• Generalized Hamiltonian Dynamics
• Constraints in Covariant Field Theories
• Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits
• Binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part