Post-Newtonian methods: Analytic results on the binary problem

Abstract

A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field equations, the generalized isotropic ones of the canonical formalism of Arnowitt, Deser, and Misner and the harmonic ones of the Lorentz-covariant Fock-de Donder approach. Conserved quantities of isolated systems are identified and the Poincaré algebra is introduced. Post-Newtonian expansions are performed in the near and far (radiation) zones. The natural fitting of multipole expansions to post-Newtonian schemes is emphasized. The treated matter models are ideal fluids, pure point masses, and point masses with spin and mass-quadrupole moments modelling rotating black holes. Various Hamiltonians of spinning binaries are presented in explicit forms to higher post-Newtonian orders. The delicate use of black holes in post-Newtonian expansion calculations and of the Dirac delta function in general relativity find discussions.

44 pages, to appear in the book "Mass and Motion in General Relativity", proceedings of the CNRS School in Orleans/France, eds. L. Blanchet, A. Spallicci, and B. Whiting

References in corpus (2)

• Recoil velocity at 2PN order for spinning black hole binaries
• Comment on recent papers regarding next-to-leading order spin-spin effects in gravitational interaction

Cited by in corpus (6)

• Black-hole binaries, gravitational waves, and numerical relativity
• Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians
• Einstein's action and the harmonic gauge in terms of Newtonian fields
• Dressing the Post-Newtonian two-body problem and Classical Effective Field Theory
• Parametric instability in scalar gravitational fields
• The Fields of Ultra-Relativistic Gravitation