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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

List of Tables

Table 1:
Numerically determined value of the 3PN coefficient for the SF part of the redshift observable defined by Eq. (292). The analytic post-Newtonian computation [68] is confirmed with many significant digits.

Table 2:
Numerically determined values of higher-order PN coefficients for the SF part of the redshift observable defined by Eq. (292). The uncertainty in the last digit (or two last digits) is indicated in parentheses. The 4PN numerical value agrees with the analytical expression (293 *).

Table 3:
Post-Newtonian contributions to the accumulated number of gravitational-wave cycles $𝒩 cycle$ for compact binaries detectable in the bandwidth of LIGO-VIRGO detectors. The entry frequency is $fseismic = 10 Hz$ and the terminal frequency is $c3 fISCO = 63∕2πGm-$ . The main origin of the approximation (instantaneous vs. tail) is indicated. See also Table 4 in Section 11 below for the contributions of spin-orbit effects.

Table 4:
Spin-orbit contributions to the number of gravitational-wave cycles $𝒩cycle$ [defined by Eq. (319 *)] for binaries detectable by ground-based detectors LIGO-VIRGO. The entry frequency is $fseismic = 10 Hz$ and the terminal frequency is $---c3-- fISCO = 63∕2πGm$ . For each compact object the magnitude $χa$ and the orientation $κa$ of the spin are defined by $Sa = Gm2a χaSˆa$ and $κa = Sˆa ⋅ ℓ$ ; remind Eq. (366 *). The spin-spin (SS) terms are neglected.