On the structure of the post-Newtonian expansion in general relativity

Abstract

In the continuation of a preceding work, we derive a new expression for the metric in the near zone of an isolated matter system in post-Newtonian approximations of general relativity. The post-Newtonian metric, a solution of the field equations in harmonic coordinates, is formally valid up to any order, and is cast in the form of a particular solution of the wave equation, plus a specific homogeneous solution which ensures the asymptotic matching to the multipolar expansion of the gravitational field in the exterior of the system. The new form provides some insights on the structure of the post-Newtonian expansion in general relativity and the gravitational radiation reaction terms therein.

arXiv comment22 pages, to appear in Phys. Rev. D

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• Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order
• Multipole Expansion of Gravitational Waves: from Harmonic to Bondi coordinates
• The mass quadrupole moment of compact binary systems at the fourth post-Newtonian order
• Testing gravity at the Second post-Newtonian level through gravitational deflection of massive particles
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• Analyzing Gravitational Waves with General Relativity
• The Newtonian limit on cosmological scales
• Gravitational memory: new results from post-Newtonian and self-force theory
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order
• Extending Gibbons-Werner method to bound orbits of massive particles
• Analytic Approximations in GR and Gravitational Waves
• The Fourier transform of thick distributions
• Influence of cosmic expansion on gravitational waveforms
• Tidal effects in the total flux and waveform in massless scalar-tensor theories to, respectively, relative 2PN and 1.5PN orders
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates
• Report on GRG18, Session A3, Mathematical Studies of the Field Equations
• Reconstruction of the one-dimensional thick distribution theory