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"Gravitational Radiation from Post-Newtonian Sources
and Inspiralling Compact Binaries"
Luc Blanchet 
Abstract
1 Introduction
1.1 Analytic approximations and wave generation formalism
1.2 The quadrupole moment formalism
1.3 Problem posed by compact binary systems
1.4 Post-Newtonian equations of motion
1.5 Post-Newtonian gravitational radiation
A Post-Newtonian Sources
2 Non-linear Iteration of the Vacuum Field Equations
2.1 Einstein’s field equations
2.2 Linearized vacuum equations
2.3 The multipolar post-Minkowskian solution
2.4 Generality of the MPM solution
2.5 Near-zone and far-zone structures
3 Asymptotic Gravitational Waveform
3.1 The radiative multipole moments
3.2 Gravitational-wave tails and tails-of-tails
3.3 Radiative versus source moments
4 Matching to a Post-Newtonian Source
4.1 The matching equation
4.2 General expression of the multipole expansion
4.3 Equivalence with the Will–Wiseman formalism
4.4 The source multipole moments
5 Interior Field of a Post-Newtonian Source
5.1 Post-Newtonian iteration in the near zone
5.2 Post-Newtonian metric and radiation reaction effects
5.3 The 3.5PN metric for general matter systems
5.4 Radiation reaction potentials to 4PN order
B Compact Binary Systems
6 Regularization of the Field of Point Particles
6.1 Hadamard self-field regularization
6.2 Hadamard regularization ambiguities
6.3 Dimensional regularization of the equations of motion
6.4 Dimensional regularization of the radiation field
7 Newtonian-like Equations of Motion
7.1 The 3PN acceleration and energy for particles
7.2 Lagrangian and Hamiltonian formulations
7.3 Equations of motion in the center-of-mass frame
7.4 Equations of motion and energy for quasi-circular orbits
7.5 The 2.5PN metric in the near zone
8 Conservative Dynamics of Compact Binaries
8.1 Concept of innermost circular orbit
8.2 Dynamical stability of circular orbits
8.3 The first law of binary point-particle mechanics
8.4 Post-Newtonian approximation versus gravitational self-force
9 Gravitational Waves from Compact Binaries
9.1 The binary’s multipole moments
9.2 Gravitational wave energy flux
9.3 Orbital phase evolution
9.4 Polarization waveforms for data analysis
9.5 Spherical harmonic modes for numerical relativity
10 Eccentric Compact Binaries
10.1 Doubly periodic structure of the motion of eccentric binaries
10.2 Quasi-Keplerian representation of the motion
10.3 Averaged energy and angular momentum fluxes
11 Spinning Compact Binaries
11.1 Lagrangian formalism for spinning point particles
11.2 Equations of motion and precession for spin-orbit effects
11.3 Spin-orbit effects in the gravitational wave flux and orbital phase
Acknowledgments
References
Footnotes
Updates
Figures
Tables

Gravitational Radiation from Post-Newtonian Sources
and Inspiralling Compact Binaries

Luc Blanchet 
Institut d’Astrophysique de Paris
bis Boulevard Arago
75014 Paris, France

'External link'http://www2.iap.fr/users/blanchet
Major update of lrr-2006-4 (see article history and change log for details).

Abstract

To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries – binary star systems composed of neutron stars and/or black holes in their late stage of evolution – require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary’s orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries – moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.

Keywords: Gravitational radiation, Post-Newtonian approximations, Multipolar expansion, Inspiralling compact binary

Go to first Section
Luc Blanchet, "Gravitational Radiation from Post-Newtonian Sources
and Inspiralling Compact Binaries",
Living Rev. Relativity, 17 (2014), 2, doi:10.12942/lrr-2014-2, URL (accessed <date>): http://www.livingreviews.org/lrr-2014-2.
© The author(s), except where otherwise noted. This work is licensed under a Creative Commons Attribution 4.0 International License.