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

Abstract

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 Poincaré algebra is constructed with the aid of Dirac brackets. Uniqueness of the generators of the Poincaré 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 Poincaré 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.

42 pages, submitted to Phys. Rev. D

References in corpus (18)

• Dimensional regularization of the gravitational interaction of point masses
• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits
• Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms
• General relativistic dynamics of compact binaries at the third post-Newtonian order
• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem
• Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame
• Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries
• Hadamard Regularization
• New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity
• The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part
• On the equations of motion of point-particle binaries at the third post-Newtonian order
• Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order
• Lorentzian regularization and the problem of point-like particles in general relativity
• Post-Coulombian Dynamics at Order 1.5
• Reduction of the two-body dynamics to a one-body description in classical electrodynamics

Cited by in corpus (5)

• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Eccentric black hole mergers and zoom-whirl behavior from elliptic inspirals to hyperbolic encounters
• Radiation from low-momentum zoom-whirl orbits
• Covariant Equations of Motion of Extended Bodies with Arbitrary Mass and Spin Multipoles
• Covariant Equations of Motion Beyond the Spin-Dipole Particle Approximation