Post-Newtonian Theory for Gravitational Waves

Luc Blanchet

Post-Newtonian Theory for Gravitational Waves

T0 review · 0 major / 3 minor · reviewed 2026-05-13 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The MPM-PN formalism yields equations of motion for compact binaries at 4PN and gravitational waveforms at 4.5PN order.

desk verdict This is a competent review consolidating the MPM-PN formalism and its results up to 4PN/4.5PN for binary gravitational waves, with no new calculations. read the letter →

arxiv 1310.1528 v6 pith:XEXURS7X submitted 2013-10-06 gr-qc

Luc Blanchet This is my paper · ORCID

classification gr-qc

keywords post-Newtoniantheorygravitationalwavescompactbinariesmultipolarpost-Minkowskianequationsofmotionwaveformradiationreaction

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This review presents the multipolar-post-Minkowskian scheme merged with the post-Newtonian expansion as a single formalism for the orbital dynamics and gravitational radiation of isolated matter systems. The approach has been applied to inspiraling compact binaries to derive high-order predictions needed for interpreting signals from ground-based and space-borne detectors. It incorporates dimensional regularization to handle divergences and details landmark results including multipole moments, radiation reaction, conservative dynamics of circular orbits, and non-linear wave propagation effects such as tails and memory. The formalism also extends to eccentric orbits and spin interactions.

What carries the argument

The MPM-PN formalism, a merger of the multipolar-post-Minkowskian expansion for the exterior gravitational field with the post-Newtonian expansion for the near-zone dynamics.

What would settle it

A direct numerical comparison between the 4PN equations of motion and 4.5PN waveforms predicted by the formalism and full numerical relativity simulations during the late inspiral phase would test whether the expansion converges as claimed.

Watch

Extended reading notes

Core claim

The MPM-PN formalism, which combines the multipolar-post-Minkowskian approximation with the standard post-Newtonian expansion, has been successfully applied to compact binary systems. This produces equations of motion up to the fourth post-Newtonian level and gravitational waveforms and fluxes to 4.5PN order beyond the Einstein quadrupole formula. The scheme remains valid for general isolated matter systems and incorporates techniques for curing ultra-violet and infra-red divergences through dimensional regularization.

Load-bearing premise

The merged approximation scheme remains valid and convergent when applied to the strong-field, highly relativistic regime of inspiraling compact binaries near merger.

Editorial extensions

If this is right

Precise templates for analyzing data from LIGO, Virgo, KAGRA, and future detectors such as LISA become available for neutron-star and black-hole binaries.
Non-linear effects in wave propagation, including tails and non-linear memory, can be included consistently in the waveform models.
Spin-orbit and spin-spin contributions to the dynamics and flux can be calculated to the same high post-Newtonian orders.
The formalism extends to eccentric orbits while retaining the same regularization methods for divergences.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

These high-order analytic results can serve as benchmarks for numerical codes that simulate the final merger and ringdown phases.
The same regularization techniques may prove useful when extending the expansion to other strong-field systems such as black-hole binaries with extreme mass ratios.
The first law of compact binary mechanics derived within the formalism links conservative dynamics to the gravitational wave flux in a manner that could guide further analytic work on energy balance.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Request a human review

A listed scientist reviews the paper for a fee and the review publishes here regardless of verdict. See the reviewers or get listed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

read the letter

This paper is a review of the multipolar-post-Minkowskian post-Newtonian (MPM-PN) scheme for modeling gravitational waves from isolated systems, with emphasis on compact binaries. It summarizes how the approach has reached equations of motion at 4PN and waveforms plus fluxes at 4.5PN beyond the quadrupole formula. The text covers dimensional regularization for both ultraviolet and infrared divergences, then walks through several established results: multipole moment definitions, radiation reaction, conservative dynamics of circular orbits, the first law of compact binary mechanics, tail effects, iterated tails, and nonlinear memory. It also treats eccentric orbits and spin-orbit plus spin-spin contributions to the motion and flux. The writing is direct and the citations point back to the original derivations, which is appropriate for a review. The abstract and structure match the content, and the scope stays within what the cited literature has already delivered. No new derivations or numerical checks appear here. One limitation is that readers who want to reproduce or extend the high-order terms will still need the earlier papers for the detailed algebra; this summary is not self-contained for that purpose. The paper assumes the MPM-PN expansion remains useful near merger without providing fresh evidence on convergence in the strong-field regime, which is standard for reviews but leaves the practical cutoff for detectors as an external question. The work is aimed at gravitational-wave data analysts and theorists who need a single reference for the current PN accuracy level when building templates for LIGO, Virgo, or LISA. It would be worth sending to peer review as a review article because it organizes the landmark results coherently and flags the remaining open directions without overclaiming novelty.

Referee Report

0 major / 3 minor

Summary. This review article presents the multipolar-post-Minkowskian (MPM) approximation scheme merged with the standard post-Newtonian (PN) expansion into a single formalism (MPM-PN) valid for general isolated matter systems. It summarizes the successful application of this formalism to compact binary systems, yielding equations of motion to 4PN order and gravitational waveforms/fluxes to 4.5PN order beyond the Einstein quadrupole formula, while detailing dimensional regularization for UV/IR divergences, multipole moments, radiation reaction, conservative dynamics of circular orbits, the first law of compact binary mechanics, non-linear propagation effects (tails, iterated tails, memory), eccentric orbits, and spin effects (spin-orbit and spin-spin).

Significance. If the summarized results hold, the review consolidates landmark high-order PN calculations essential for modeling inspiraling compact binaries observable by LIGO/Virgo/KAGRA and future detectors (Einstein Telescope, LISA). It provides a coherent reference for the MPM-PN framework, including its handling of divergences and non-linear effects, thereby supporting accurate waveform templates and parameter estimation in gravitational-wave astronomy.

minor comments (3)

Abstract: the phrasing '4.5PN order beyond the Einstein quadrupole formula' is standard but could briefly note that this refers to the total PN order in the flux/waveform (i.e., 4.5PN relative to leading quadrupole) to avoid potential ambiguity for readers new to the field.
The manuscript would benefit from an explicit statement in the introduction or conclusion clarifying the regime of validity (weak-field, slow-motion for isolated systems) and noting that the formalism does not extend to the strong-field merger phase itself, consistent with the abstract's scope.
Section on eccentric orbits: the discussion of PN expansions for eccentric binaries could include a short remark on the convergence properties or the need for resummation techniques, as this is a common practical concern when applying these results.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript, the positive summary, and the recommendation to accept the review for publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in this review paper

full rationale

This manuscript is a review summarizing the established MPM-PN formalism and its applications to compact binaries, including prior results on equations of motion to 4PN and waveforms to 4.5PN. No new derivation chain, predictions, or first-principles results are presented that reduce to the paper's own inputs, fitted parameters, or self-defined quantities by construction. Self-citations refer to independent, peer-reviewed prior literature on the same formalism and do not create load-bearing circularity for the review's central statements.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The review relies on the standard assumptions of general relativity for isolated systems and the validity of the post-Newtonian expansion; no new free parameters, axioms, or invented entities are introduced by the paper itself.

assumptions (1)

domain assumption General relativity governs the dynamics and gravitational radiation of isolated compact binaries.
The entire MPM-PN scheme is constructed within the framework of GR.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Post-Newtonian Theory for Gravitational Waves." pith.science (2026). https://pith.science/paper/XEXURS7X

@misc{pith202613101528,
  author       = {Pith},
  title        = {Pith review of: Post-Newtonian Theory for Gravitational Waves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XEXURS7X}},
  note         = {Machine review of arXiv:1310.1528}
}

read the original abstract

To be observed and analyzed by the network of current gravitational wave detectors (LIGO, Virgo, KAGRA), and in anticipation of future third generation ground based (Einstein Telescope, Cosmic Explorer) and space borne (LISA) detectors, inspiralling compact binaries -- binary star systems composed of neutron stars and/or black holes in their late stage of evolution prior the final coalescence -- require high-accuracy predictions from general relativity. The orbital dynamics and emitted gravitational waves of these very relativistic systems can be accurately modelled using state-of-the-art post-Newtonian theory. In this article we review the Multipolar-Post-Minkowskian approximation scheme, merged to the standard Post-Newtonian expansion into a single formalism valid for general isolated matter system. This cocktail of approximation methods (called MPM-PN) has been successfully applied to compact binary systems, producing equations of motion up to the fourth-post-Newtonian (4PN) level, and gravitational waveform and flux to 4.5PN order beyond the Einstein quadrupole formula. We describe the dimensional regularization at work in such high post-Newtonian calculations, for curing both ultra-violet and infra-red divergences. Several landmark results are detailed: the definition of multipole moments, the gravitational radiation reaction, the conservative dynamics of circular orbits, the first law of compact binary mechanics, and the non-linear effects in the gravitational wave propagation (tails, iterated tails and non-linear memory). We also discuss the case of compact binaries moving on eccentric orbits, and the effects of spins (both spin-orbit and spin-spin) on the equations of motion and gravitational wave energy flux and waveform.

Discussion (0). Continue with ORCID to comment.

Forward citations

Showing 60 of 143 Pith papers that cite this

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. See all 143 Pith citations

GW231123: a Binary Black Hole Merger with Total Mass 190-265 $M_{\odot}$
astro-ph.HE 2025-07 accept novelty 9.0 of 10

A new gravitational wave event reveals a binary black hole merger with total mass 190-265 solar masses, indicating black holes can form via gravitational-wave driven mergers beyond standard stellar channels.
Binary black hole scattering with generic spins
gr-qc 2026-06 unverdicted novelty 8.0 of 10

First NR-PM comparison for generic-spin black hole scattering reveals strong-field precessional turning-point structure with polar-angle sign change absent from perturbative PM.
GW240925 and GW250207: Astrophysical Calibration of Gravitational-wave Detectors
gr-qc 2026-05 unverdicted novelty 8.0 of 10

The first informative astrophysical calibration of gravitational-wave detectors is reported using GW240925 and GW250207.
Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order
gr-qc 2025-11 unverdicted novelty 8.0 of 10

Derives the 4PN conservative map between constants of motion and fundamental frequencies for eccentric orbits, resummed over eccentricity and validated against circular-orbit and self-force results.
Spinning the Probe in Kerr with WQFT
hep-th 2025-06 conditional novelty 8.0 of 10

Using worldline quantum field theory, the authors derive the impulse and spin kick for a spinning probe scattering in Kerr spacetime through seventh physical post-Minkowskian order.
Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order
gr-qc 2025-04 conditional novelty 8.0 of 10

At 4PN order, the binding energy in the flux-balance law differs from the conservative energy by a hereditary 'pseudo-Schott' term, which exactly reproduces the previously postulated energy-frequency relation and conf...
Radiation-Reaction and Angular Momentum Loss at $\mathcal{O}(G^4)$
hep-th 2025-01 accept novelty 8.0 of 10

A closed-form, all-velocity expression for the O(G^4) radiated angular momentum in two-body gravitational scattering is derived, resumming all half-odd post-Newtonian corrections.
Emergence of Calabi-Yau manifolds in high-precision black hole scattering
hep-th 2024-11 unverdicted novelty 8.0 of 10

At 5PM-1SF order, Calabi-Yau three-fold periods emerge in radiation-reacted observables for classical black hole scattering computed with worldline QFT and advanced IBP/DE methods.
Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
gr-qc 2024-11 conditional novelty 8.0 of 10

Closed-form action and frequency formulas for spinning particles in Kerr spacetime are matched to the 1.5 post-Newtonian Hamiltonian of spinning binaries, yielding a gauge-invariant action dictionary.
Black Hole Binary Dynamics from the Double Copy and Effective Theory
hep-th 2019-08 accept novelty 8.0 of 10

The authors derive the complete conservative two-body Hamiltonian for spinless black holes at third post-Minkowskian order using scattering amplitudes and effective field theory.
Multimessenger Spectroscopy
astro-ph.IM 2026-09 accept novelty 7.0 of 10

LISA gravitational wave phase data can predict the orbital phase of ultracompact white dwarf binaries with sufficient accuracy to enable targeted optical spectroscopy, yielding component masses and distances.
Magnetized accretion onto rapidly spinning binary black holes: mini-disk thermodynamics, magnetic transport, and dual jets
astro-ph.HE 2026-09 conditional novelty 7.0 of 10

GRMHD simulations reveal persistent mini-disks, alternating magnetic flux, and dual jets in a widely separated, rapidly spinning binary black hole system.
One-cycle radiation-reaction Magnusian for eccentric binaries through relative 1PN order
gr-qc 2026-09 conditional novelty 7.0 of 10

A closed-form, eight-parameter gauge-independent one-cycle radiation-reaction Magnusian for eccentric binaries is derived through relative 1PN order without expanding in eccentricity.
Spacelike reduction of the gravitational topological terms and associated helicity densities
gr-qc 2026-08 accept novelty 7.0 of 10

Four helicity densities are obtained from the spacelike reduction of the Pontryagin and Nieh-Yan topological terms, separated into spin-1 and spin-2 gravitomagnetic and gravito-current helicities.
Defining higher memory signals and forecasting their observation prospects for binary-black-hole mergers with next-generation gravitational-wave detectors
gr-qc 2026-08 conditional novelty 7.0 of 10

With two Cosmic Explorer detectors, displacement memory should be detectable in tens of individual mergers per year, spin and center-of-mass memory in a one-year population, while the modeled part of ballistic memory ...
Supertranslations are Soft Dressings
hep-th 2026-08 conditional novelty 7.0 of 10

Coherent-state dressings by zero-energy gravitons are equivalent to BMS supertranslations, and the associated conserved charge produces a universal, all-orders shift of the scattering impact parameter.
High-Post-Newtonian-Order Dynamics Induced by Tail-of-Tail Interactions: The Non-Geodesic Terms
gr-qc 2026-08 conditional novelty 7.0 of 10

The authors compute tail-of-tail contributions to the effective-one-body Q potential through p_r^12 and derive new second-order self-force redshift predictions for eccentric binaries.
Kerr Soft Dressing and the $w_{1+\infty}$ Frame Algebra at Null Infinity
hep-th 2026-07 conditional novelty 7.0 of 10

The Kerr soft exponent generates a parity-alternating hierarchy of null-infinity frame generators—displacement memory at s=0, spin memory at s=1, and higher moments alternating by Kerr multipole parity—realized as the...
Nonlinear Dynamics near the Threshold of Gravitational Collapse
gr-qc 2026-07 conditional novelty 7.0 of 10

Perturbation theory around flat space fails before black hole formation once peak luminosity exceeds ~10^-2 L_Planck; near criticality the spectrum flattens to 1/ω, matching the prediction from discrete self-similarity.
Constraints on Line-of-Sight Acceleration from O1-O4
astro-ph.HE 2026-06 unverdicted novelty 7.0 of 10

All known compact binary mergers show line-of-sight accelerations consistent with zero under a new time-domain Doppler-shift model, with current detectors only sensitive to high-acceleration scenarios.
Binary Black Hole Coalescence and the Dynamics of Scalar Hair in Einstein-Maxwell-Scalar Theory
gr-qc 2026-06 unverdicted novelty 7.0 of 10

Numerical simulations of binary black hole coalescence in EMS theory show dynamic triggering of scalar hair depending on coupling strength and remnant charge.
Gravitational waveforms from binaries in higher-derivative gravity: a Love story
gr-qc 2026-06 unverdicted novelty 7.0 of 10

In higher-derivative gravity, the leading correction to extreme-mass-ratio inspiral waveforms and fluxes enters at 5PN order and is controlled by the ℓ=2 tidal Love number.
Horizon Multipole Moments of a Kerr Black Hole
gr-qc 2026-02 unverdicted novelty 7.0 of 10

Horizon multipole moments of a Kerr black hole are computed in closed form from two definitions, yielding different values for l >= 1 at nonzero spin and sharing parity and small-spin scaling with field multipoles.
Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order
hep-th 2026-01 conditional novelty 7.0 of 10

The conservative black-hole scattering angle at fifth post-Minkowskian and second self-force order is computed in terms of K3 periods, but contains a coefficient fixed only by an ad hoc 'γ-3' prescription.
Symplectic mechanics of relativistic spinning compact bodies. III. quadratic-in-spin integrability in Type-D Einstein spacetimes: persistence and breakdown
gr-qc 2026-01 conditional novelty 7.0 of 10

Quadratic-in-spin MPTD dynamics in type-D Einstein spacetimes with Killing–Yano symmetry admits five commuting first integrals—hence Liouville–Arnold integrability—only when the spin-induced quadrupole deformability p...
Black hole mergers beyond general relativity: a self-force approach
gr-qc 2025-10 unverdicted novelty 7.0 of 10

Self-force theory is extended to compute merger and ringdown waveforms in beyond-GR black hole binaries under the extreme mass-ratio approximation, with first calculations of self-force corrections to the merger waveform.
Perturbations of Plane Waves and Quadratic Quasinormal Modes on the Lightring
gr-qc 2025-09 conditional novelty 7.0 of 10

Second-order gravitational perturbations on plane waves are solved with a GHP master equation and tensor harmonics, yielding quadratic quasinormal mode ratios and selection rules.
Generalized Perturbed Kepler Problem: Gravitational Wave Imprints from Eccentric Compact Binaries
gr-qc 2025-08 unverdicted novelty 7.0 of 10

A unified framework for the perturbed Kepler problem derives modified eccentric orbits and gravitational wave imprints from a general perturbed potential, offering a source-specific alternative to post-Newtonian expansions.
High-post-Newtonian-order dynamical effects induced by tail-of-tail interactions in a two body system
gr-qc 2025-07 accept novelty 7.0 of 10

The paper derives 6.5PN tail-of-tail contributions to binary dynamics and finds agreement with independent self-force and worldline-EFT results.
Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework
gr-qc 2025-07 conditional novelty 7.0 of 10

A pseudo-Hamiltonian reformulation of 1PA self-force dynamics yields local, invariant action-angle evolution equations and an embedded conservative Hamiltonian whose on-shell energy equals the first-law binding energy.
From spatial to null infinity: Connecting initial data to peeling
gr-qc 2025-07 conditional novelty 7.0 of 10

For asymptotically regular spacetimes, parity-time reversal symmetry of the leading and subleading initial data implies the Weyl scalars Psi2 and Psi1 peel at null infinity with rates 1/r^3 and 1/r^4.
Nonlinear Gravitational Memory in the Post-Minkowskian Expansion
hep-th 2025-06 conditional novelty 7.0 of 10

Exact-in-velocity formulas for the O(G^3) nonlinear gravitational memory multipoles from two-body scattering, derived with scattering amplitudes and reverse unitarity, and matched to post-Newtonian results.
Non-adiabatic dynamics of eccentric black-hole binaries in post-Newtonian theory
gr-qc 2025-02 unverdicted novelty 7.0 of 10

New non-orbit-averaged 2.5PN equations for eccentric non-spinning black-hole binaries derived via energy-momentum mappings, showing Peters 1964 orbit-averaged equations break at first pericenter.
Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions
gr-qc 2025-01 conditional novelty 7.0 of 10

A new hypergeometric representation of the confluent Heun equation resums infinite PM/PN correction series and yields the circular-orbit energy flux to 30PN order, matching independent numerical black-hole perturbatio...
Effective-one-body model for coalescing binary neutron stars: Incorporating tidal spin and enhanced radiation from dynamical tides
gr-qc 2025-01 conditional novelty 7.0 of 10

A new EOB model for BNS/NSBH inspirals adds tidal-spin back-reaction and finite-frequency radiation corrections, yielding waveform phase shifts up to a few radians that previous effective Love number models miss.
Black Hole Tomography: Unveiling Black Hole Ringdown via Gravitational Wave Observations
gr-qc 2025-01 conditional novelty 7.0 of 10

Infalling and outgoing gravitational radiation around a perturbed Schwarzschild horizon share the same quasi-normal mode spectrum, with an explicit transfer formula between the horizon and null infinity.
Tidal Love Numbers of Neutron Stars in Horndeski Theories
gr-qc 2025-01 accept novelty 7.0 of 10

In scalar-tensor theories, the 1/r^3 term used to extract neutron star tidal Love numbers contains a Love-number-independent contamination, computed here for minimally coupled and DEF scalar fields.
Tidal contributions to the full gravitational waveform to the second-and-a-half post-Newtonian order
gr-qc 2024-12 conditional novelty 7.0 of 10

Tidal contributions to all gravitational waveform amplitude modes up to l=7 are derived to 2.5PN for quasi-circular non-spinning compact binaries, with flux and phasing provided at the same order.
Third post-Newtonian dynamics for eccentric orbits and aligned spins in the effective-one-body waveform model SEOBNRv5EHM
gr-qc 2024-12 conditional novelty 7.0 of 10

The authors obtain, for the first time, 3PN-accurate eccentric-orbit fluxes, radiation-reaction force, and waveform modes in the effective-one-body formalism, and use them to build the SEOBNRv5EHM inspiral model.
A geometric template bank for the detection of spinning low-mass compact binaries with moderate orbital eccentricity
gr-qc 2024-12 conditional novelty 7.0 of 10

A geometric template bank including eccentricity recovers moderately eccentric BNS/NSBH signals with less than 6% loss, while quasi-circular banks miss up to 40%.
Post-Newtonian expansion of gravitational energy and angular momentum fluxes: inclined spherical orbits about a Kerr black hole
gr-qc 2024-11 conditional novelty 7.0 of 10

The paper derives 12PN flux formulas for inclined spherical Kerr orbits, exact in spin and inclination.
Spinning bodies in general relativity from bosonic worldline oscillators
hep-th 2024-11 conditional novelty 7.0 of 10

A bosonic-oscillator worldline action for spinning compact bodies in general relativity is constructed, and it reproduces known post-Minkowskian scattering results while remaining valid to all orders in spin.
Tidal effects up to next-to-next-to leading post-Newtonian order in massless scalar-tensor theories
gr-qc 2023-10 unverdicted novelty 7.0 of 10

Derives NNLO post-Newtonian tidal contributions to conservative dynamics and ten conserved quantities in massless scalar-tensor theories for spinless sources, with extension to Einstein-scalar-Gauss-Bonnet gravity.
Analytic Waveforms for Eccentric Gravitational Wave Bursts
gr-qc 2019-09 conditional novelty 7.0 of 10

A new analytic 'effective fly-by' waveform family for eccentric gravitational wave bursts, validated against numerical and numerical-relativity waveforms.
Point particles in general relativity: beyond linear perturbation theory
gr-qc 2026-09 conditional novelty 6.0 of 10

The authors derive a skeletonized, distributionally well-defined form of the second-order Einstein equations sourced by a point particle, and prove its equivalence to Hadamard regularization and standard counterterm methods.
Parity symmetry as a diagnostic for spin-precessing binary-black-hole waveform models
gr-qc 2026-09 accept novelty 6.0 of 10

Applying parity symmetry as a consistency test to seven spin-precessing binary-black-hole waveform models reveals violations in four models, traceable to observer-dependent phase anchors or non-invariant parameterizat...
Charged black-hole binary radiation at second post-Newtonian order
gr-qc 2026-09 conditional novelty 6.0 of 10

2PN-accurate energy flux and waveform modes are computed for charged black-hole binaries on circular orbits, using two independent formalisms that agree exactly.
Radiation-reaction driven dynamics at the third-and-a-half post-Newtonian order in different gauges
gr-qc 2026-08 conditional novelty 6.0 of 10

A method is given for obtaining the 3.5PN radiation-reaction force and orbit correction in any Hamiltonian coordinate system by transforming from harmonic coordinates.
A parametrized test of general relativity for inspiralling eccentric binaries in LISA
gr-qc 2026-08 conditional novelty 6.0 of 10

For eccentric black-hole binaries observed by LISA, a parametrized deformation of the periastron-precession rate could be constrained to |δα|≲10^-4 at 90% credibility with the full-model template.
Innermost stable circular orbit (ISCO) of arbitrary-mass compact binaries with spins at the fourth post-Newtonian order
gr-qc 2026-08 conditional novelty 6.0 of 10

A new 4PN gauge-invariant ISCO criterion for aligned-spin compact binaries is derived, recovering Kerr in the test-mass limit and matching numerical self-force results for retrograde and moderate spins.
Celephais: efficient spectral initial data code for precessing compact binaries
gr-qc 2026-08 conditional novelty 6.0 of 10

Celephais constructs spectrally accurate binary-neutron-star and black-hole-neutron-star initial data with arbitrary spin orientations, using a sparse Jacobian, adaptive hp-refinement, and PN-informed eccentricity reduction.
Testing the spin-induced multipole moments of compact binary coalescences using the flexible theory-independent framework
gr-qc 2026-08 conditional novelty 6.0 of 10

A flexible gravitational-wave test constrains spin-induced quadrupole and octupole moments, finds consistency with Kerr black holes in current data, and projects order 10^-2 to 10^-1 bounds for Einstein Telescope and ...
Gravitational Wave Modeling of White-Dwarf--Compact-Object Binaries and Observational Outlook
astro-ph.HE 2026-07 conditional novelty 6.0 of 10

WD–CO binaries produce unique GW waveforms with a sharp f_max cutoff; LGWA/DECIGO will detect many end stages, while terrestrial detectors will not mistake them for sub-solar compact objects.
The Magnusian generator for dissipative systems and application to leading 2.5PN radiation-reaction dynamics
gr-qc 2026-07 accept novelty 6.0 of 10

The Magnusian is generalized via the in-in formalism to dissipative and nonlocal dynamics, yielding an explicit one-period generator for Newtonian binaries with 2.5PN radiation reaction that agrees with numerics.
Angular momentum flux through post-Newtonian order for noncircular nonspinning black-hole binaries in Einstein-Maxwell-dilaton theory
gr-qc 2026-07 conditional novelty 6.0 of 10

The scalar, electromagnetic, and tensor contributions to the angular momentum flux from noncircular EMd binaries are derived through 1PN order.
Relativistic Tidal Transitions of Saturated Kerr Boson Clouds
astro-ph.GA 2026-07 conditional novelty 6.0 of 10

Relativistic Kerr wavefunctions change tidal transition matrix elements of saturated boson clouds by up to 21.7% relative to the hydrogenic approximation, with the radial profile responsible for ~80% of the change.
Convergence of post-Newtonian for quasi-circular non-precessing comparable mass ratios BBHs
gr-qc 2026-05 unverdicted novelty 6.0 of 10

For orbital velocities below 0.45, PN energy flux agreement with NR improves up to incomplete 6PN with non-monotonic behavior, but convergence is lost near v approximately 0.5.
Ringdown and lensing of triple systems
gr-qc 2026-05 unverdicted novelty 6.0 of 10

Numerical relativity simulations of triple black hole systems reveal redshift effects and gravitational lensing in ringdown signals from head-on mergers, with no additional black hole formation from amplified waves.
The Classical Gravitational Impulse at High Energies
hep-th 2026-05 unverdicted novelty 6.0 of 10

The gravitational impulse for ultrarelativistic massive scalars is resummed to all orders in G_N at fixed G_N s/mb, recovering post-Minkowski results and predicting the leading high-energy behavior to eleventh post-Mi...
Polarization Analysis of Ringdown Signals
gr-qc 2026-05 conditional novelty 6.0 of 10

Constrained polarization model for Kerr ringdown modes enables inclination inference from two-detector data for non-precessing mergers but introduces biases when applied to precessing systems.

See all 143 Pith citations

Reference graph

Works this paper leans on

299 extracted references · 299 canonical work pages · cited by 143 Pith papers (see all)

[1]

Observation of Gravitational Waves from a Binary Black Hole Merger

Observation of Gravitational Waves from a Binary Black Hole Merger. doi:10.1103/PhysRevLett.116.061102 , eid =. arXiv , author =:1602.03837 , journal =

work page Pith review arXiv doi:10.1103/physrevlett.116.061102
[2]

Abbott, B. P. and others , title = ". Phys. Rev. Lett. , year =. doi:10.1103/PhysRevLett.119.161101 , archiveprefix =. 1710.05832 , primaryclass =

work page Pith review arXiv doi:10.1103/physrevlett.119.161101
[3]

Multi-messenger Observations of a Binary Neutron Star Merger

Abbott, B. and others , Journal =. Multi-messenger Observations of a Binary Neutron Star Merger. 2017 , Pages =. arXiv:1710.05833 , primaryClass =

work page Pith review arXiv 2017
[4]

Abramowicz, M. A. and Klu. A precise determination of black hole spin in GRO J1655-40. Astron. Astrophys. , pages =. doi:10.1051/0004-6361:20010791 , eprint =

work page doi:10.1051/0004-6361:20010791
[5]

and Iyer, B

Ajith, P. and Iyer, B. R. and Robinson, C. A. K. and Sathyaprakash, B. S. , eid =. New class of post- Newtonian approximants to the waveform templates of inspiralling compact binaries: Test mass in the Schwarzschild spacetime. gr-qc/0412033 , journal =

work page Pith review arXiv
[6]

2008, PhRvD, 77, 104017, doi: 10.1103/PhysRevD.77.104017

Template bank for gravitational waveforms from coalescing binary black holes: Nonspinning binaries. doi:10.1103/PhysRevD.77.104017 , eid =. arXiv , author =:0710.2335 , journal =

work page doi:10.1103/physrevd.77.104017
[7]

Energy and angular momentum flow into a black hole in a binary. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.64.104020 , eprint =

work page doi:10.1103/physrevd.64.104020
[8]

Third post- Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM - Hamiltonian formalisms. Class. Quantum Grav. , pages =. doi:10.1088/0264-9381/18/5/301 , eprint =

work page doi:10.1088/0264-9381/18/5/301

Show all 299 references

[9]

Anderson, J. L. and DeCanio, T. C. , doi =. Equations of hydrodynamics in general relativity in the slow motion approximation. Gen. Relativ. Gravit. , pages =
[10]

Anderson, J. L. and Kates, R. E. and Kegeles, L. S. and Madonna, R. G. , doi =. Divergent integrals of post- Newtonian gravity: Nonanalytic terms in the near-zone expansion of a gravitationally radiating system found by matching. Phys. Rev. D , pages =
[11]

Apostolatos, T. A. and Cutler, C. and Sussman, G. J. and Thorne, K. S. , doi =. Spin induced orbital precession and its modulation of the gravitational wave forms from merging binaries. Phys. Rev. D , pages =
[12]

Arun, K. G. and Blanchet, L. and Iyer, B. R. and Qusailah, M. S. S. , doi =. The 2.5PN gravitational wave polarizations from inspiralling compact binaries in circular orbits. gr-qc/0404185 , journal =
[13]

Arun, K. G. and Iyer, B. R. and Sathyaprakash, B. S. and Sundararajan, P. A. , doi =. Parameter estimation of inspiralling compact binaries using 3.5 post- Newtonian gravitational wave phasing: The nonspinning case. gr-qc/0411146 , journal =
[14]

Testing post- Newtonian theory with gravitational wave observations. Class. Quantum Grav. , pages =. doi:10.1088/0264-9381/23/9/L01 , eprint =

doi
[15]

Arun, K. G. and Iyer, B. R. and Qusailah, M. S. S. and Sathyaprakash, B. S. , doi =. Probing the non-linear structure of general relativity with black hole binaries. gr-qc/0604067 , journal =
[16]

doi:10.1103/PhysRevD.77.064034 , eid =

Tail effects in the 3PN gravitational wave energy flux of compact binaries in quasi-elliptical orbits. doi:10.1103/PhysRevD.77.064034 , eid =. arXiv , author =:0711.0250 , journal =

doi
[17]

doi:10.1103/PhysRevD.77.064035 , eid =

Inspiralling compact binaries in quasi-elliptical orbits: The complete 3PN energy flux. doi:10.1103/PhysRevD.77.064035 , eid =. arXiv , author =:0711.0302 , journal =

doi
[18]

doi:10.1103/PhysRevD.75.124002 , eid =

Higher harmonics increase LISA's mass reach for supermassive black holes. doi:10.1103/PhysRevD.75.124002 , eid =. arXiv , author =:0704.1086 , journal =

doi
[19]

doi:10.1103/PhysRevD.76.104016 , eid =

Higher signal harmonics, LISA's angular resolution, and dark energy. doi:10.1103/PhysRevD.76.104016 , eid =. arXiv , author =:0707.3920 , journal =

doi
[20]

Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.79.104023 , eprint =

doi
[21]

doi:10.1103/PhysRevD.80.124018 , eid =

Third post- Newtonian angular momentum flux and the secular evolution of orbital elements for inspiralling compact binaries in quasi-elliptical orbits. doi:10.1103/PhysRevD.80.124018 , eid =. arXiv , author =:0908.3854 , journal =

doi
[22]

and Israel, W

Bailey, I. and Israel, W. , doi =. Lagrangian dynamics of spinning particles and polarized media in general relativity. Commun. Math. Phys. , pages =
[23]

doi:10.1103/PhysRevLett.96.111102 , eid =

Gravitational-Wave Extraction from an Inspiraling Configuration of Merging Black Holes. doi:10.1103/PhysRevLett.96.111102 , eid =. arXiv , author =:gr-qc/0511103 , journal =

doi
[24]

doi:10.1103/PhysRevLett.102.191101 , eid =

Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole. doi:10.1103/PhysRevLett.102.191101 , eid =. arXiv , author =:0902.0573 , journal =

doi
[25]

doi:10.1088/0264-9381/26/21/213001 , eid =

Gravitational self-force in extreme mass-ratio inspirals. doi:10.1088/0264-9381/26/21/213001 , eid =. arXiv , author =:0908.1664 , journal =

doi
[26]

, booktitle =

Barack, L. , booktitle =. Computational Methods for the Self-Force in Black Hole Spacetimes , volume =. doi:10.1007/978-90-481-3015-3_12 , editor =

doi
[27]

Hamiltonian of a spinning test particle in curved spacetime. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.80.104025 , eprint =

doi
[28]

Bardeen, J. M. and Carter, B. and Hawking, S. W. , doi =. The Four Laws of Black Hole Mechanics. Commun. Math. Phys. , pages =
[29]

Barker, B. M. and. Gravitational two-body problem with arbitrary masses, spins, and quadrupole moments. doi:10.1103/PhysRevD.12.329 , journal =

doi
[30]

Barker, B. M. and. The Gravitational Interaction: Spin, Rotation, and Quantum Effects -- A Review. doi:10.1007/BF00756587 , journal =

doi
[31]

Baumgarte, T. W. , doi =. Phys. Rev. D , title = "
[32]

Bekenstein, J. D. , doi =. Gravitational Radiation Recoil and Runaway Black Holes. Astrophys. J. , pages =
[33]

and Damour, T

Bel, L. and Damour, T. and Deruelle, N. and Ib. Poincar \'e -Invariant Gravitational Field and Equations of Motion of two Pointlike Objects: The Postlinear Approximation of General Relativity. doi:10.1007/BF00756073 , journal =

doi
[34]

doi:10.12942/lrr-2013-4 , eid =

Relativistic Binaries in Globular Clusters. doi:10.12942/lrr-2013-4 , eid =. arXiv , author =:1110.4423 , journal =

2013 doi
[35]

doi:10.1103/PhysRevD.76.064034 , eid =

Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis. doi:10.1103/PhysRevD.76.064034 , eid =. arXiv , author =:gr-qc/0703053 , journal =

doi
[36]

and Pleba

Bertotti, B. and Pleba. Theory of gravitational perturbations in the fast motion approximation. doi:10.1016/0003-4916(60)90132-9 , journal =

doi
[37]

doi:10.1103/PhysRevD.87.121501 , eid =

Analytical determination of the two-body gravitational interaction potential at the fourth post- Newtonian approximation. doi:10.1103/PhysRevD.87.121501 , eid =. arXiv , author =:1305.4884 , journal =

doi
[38]

doi:10.1103/PhysRevD.89.064063 , eid =

High-order post- Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations. doi:10.1103/PhysRevD.89.064063 , eid =. arXiv , author =:1312.2503 , journal =

doi
[39]

doi:10.1103/PhysRevD.89.104047 , eid =

Analytic determination of the eight-and-a-half post- Newtonian self-force contributions to the two-body gravitational interaction potential. doi:10.1103/PhysRevD.89.104047 , eid =. arXiv , author =:1403.2366 , journal =

doi
[40]

Confirming and improving post- Newtonian and effective-one-body results from self-force computations along eccentric orbits around a Schwarzschild black hole. Phys. Rev. D , year =. doi:10.1103/PhysRevD.93.064023 , archivePrefix =. 1511.04533 , primaryClass =

doi
[41]

and Lee, M

Blaes, O. and Lee, M. H. and Socrates, A. , doi =. The Kozai mechanism and the evolution of binary supermassive black holes. astro-ph/0203370 , journal =
[42]

and Damour, T

Blanchet, L. and Damour, T. , doi =. Multipolar radiation reaction in general relativity. Phys. Lett. A , pages =
[43]

and Damour, T

Blanchet, L. and Damour, T. , doi =. Radiative gravitational fields in general relativity I . G eneral structure of the field outside the source. Philos. Trans. R. Soc. London, Ser. A , pages =
[44]

Blanchet, L. , doi =. Radiative gravitational fields in general-relativity. II . A symptotic-behaviour at future null infinity. Proc. R. Soc. London, Ser. A , pages =
[45]

and Damour, T

Blanchet, L. and Damour, T. , doi =. Tail-transported temporal correlations in the dynamics of a gravitating system. Phys. Rev. D , pages =
[46]

and Damour, T

Blanchet, L. and Damour, T. , journal =. Post- Newtonian generation of gravitational waves
[47]

Blanchet, L. and Sch. Higher order gravitational radiation losses in binary systems. doi:10.1093/mnras/239.3.845 , journal =

doi
[48]

, school =

Blanchet, L. , school =. Contribution \` a l'\' e tude du rayonnement gravitationnel \' e mis par un syst\` e me isol\' e
[49]

Contribution \`a l'\'etude du rayonnement gravitationnel \'emis par un syst\`eme isol\'e

Blanchet, Luc. Contribution \`a l'\'etude du rayonnement gravitationnel \'emis par un syst\`eme isol\'e. 1990

1990
[50]

and Damour, T

Blanchet, L. and Damour, T. , doi =. Hereditary effects in gravitational radiation. Phys. Rev. D , pages =
[51]

Blanchet, L. , doi =. Time asymmetric structure of gravitational radiation. Phys. Rev. D , pages =
[52]

Blanchet, L. and Sch. Gravitational wave tails and binary star systems. doi:10.1088/0264-9381/10/12/026 , journal =

doi
[53]

and Sathyaprakash, B

Blanchet, L. and Sathyaprakash, B. S. , doi =. Signal analysis of gravitational wave tails. Class. Quantum Grav. , pages =
[54]

and Sathyaprakash, B

Blanchet, L. and Sathyaprakash, B. S. , doi =. Detecting a Tail Effect in Gravitational-Wave Experiments. Phys. Rev. Lett. , pages =
[55]

Blanchet, L. , doi =. Second-post- Newtonian generation of gravitational radiation. gr-qc/9501030 , journal =
[56]

and Damour, T

Blanchet, L. and Damour, T. and Iyer, B. R. and Will, C. M. and Wiseman, A. G. , doi =. Gravitational-Radiation Damping of Compact Binary Systems to Second Post- Newtonian Order. gr-qc/9501027 , journal =
[57]

and Damour, T

Blanchet, L. and Damour, T. and Iyer, B. R. , doi =. Gravitational waves from inspiralling compact binaries: Energy loss and wave form to second post- Newtonian order. gr-qc/9501029 , journal =
[58]

and Iyer, B

Blanchet, L. and Iyer, B. R. and Will, C. M. and Wiseman, A. G. , doi =. Gravitational wave forms from inspiralling compact binaries to second-post- Newtonian order. gr-qc/9602024 , journal =
[59]

Blanchet, L. , doi =. Energy losses by gravitational radiation in inspiralling compact binaries to five halves post- Newtonian order. gr-qc/9603048 , journal =
[61]

Blanchet, L. , doi =. Gravitational radiation reaction and balance equations to post- Newtonian order. gr-qc/9609049 , journal =
[62]

Blanchet, L. , doi =. Quadrupole-quadrupole gravitational waves. gr-qc/9710037 , journal =
[63]

Blanchet, L. , doi =. Gravitational-wave tails of tails. gr-qc/9710038 , journal =
[64]

Blanchet, L. , doi =. On the multipole expansion of the gravitational field. gr-qc/9801101 , journal =
[65]

and Faye, G

Blanchet, L. and Faye, G. and Ponsot, B. , doi =. Gravitational field and equations of motion of compact binaries to 5/2 post- Newtonian order. gr-qc/9804079 , journal =
[66]

and Faye, G

Blanchet, L. and Faye, G. , doi =. Equations of motion of point-particle binaries at the third post- Newtonian order. gr-qc/0004009 , journal =
[67]

and Faye, G

Blanchet, L. and Faye, G. , doi =. Hadamard regularization. gr-qc/0004008 , journal =
[68]

and Faye, G

Blanchet, L. and Faye, G. , doi =. Lorentzian regularization and the problem of point-like particles in general relativity. gr-qc/0006100 , journal =
[69]

and Faye, G

Blanchet, L. and Faye, G. , doi =. General relativistic dynamics of compact binaries at the third post- Newtonian order. gr-qc/0007051 , journal =
[70]

and Iyer, B

Blanchet, L. and Iyer, B. R. and Joguet, B. , eid =. Gravitational waves from inspiralling compact binaries: Energy flux to third post- Newtonian order. gr-qc/0105098 , journal =
[71]

and Faye, G

Blanchet, L. and Faye, G. and Iyer, B. R. and Joguet, B. , doi =. Gravitational-wave inspiral of compact binary systems to 7/2 post- Newtonian order. gr-qc/0105099 , journal =
[72]

Blanchet, L. , doi =. Innermost circular orbit of binary black holes at the third post- Newtonian approximation. gr-qc/0112056 , journal =
[73]

and Iyer, B

Blanchet, L. and Iyer, B. R. , doi =. Third post- Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame. gr-qc/0209089 , journal =
[74]

and Damour, T

Blanchet, L. and Damour, T. and Esposito-Far. Dimensional regularization of the third post- Newtonian dynamics of point particles in harmonic coordinates. doi:10.1103/PhysRevD.69.124007 , eid =. gr-qc/0311052 , journal =

doi
[75]

and Damour, T

Blanchet, L. and Damour, T. and Esposito-Far. Gravitational radiation from inspiralling compact binaries completed at the third post- Newtonian order. doi:10.1103/PhysRevLett.93.091101 , eid =. gr-qc/0406012 , journal =

doi
[76]

and Iyer, B

Blanchet, L. and Iyer, B. R. , doi =. Hadamard regularization of the third post- Newtonian gravitational wave generation of two point masses. gr-qc/0409094 , journal =
[77]

and Damour, T

Blanchet, L. and Damour, T. and Iyer, B. R. , doi =. Surface-integral expressions for the multipole moments of post- Newtonian sources and the boosted Schwarzschild solution. gr-qc/0410021 , journal =
[78]

and Damour, T

Blanchet, L. and Damour, T. and Esposito-Far. Dimensional regularization of the third post- Newtonian gravitational wave generation of two point masses. doi:10.1103/PhysRevD.71.124004 , eid =. gr-qc/0503044 , journal =

doi
[79]

and Faye, G

Blanchet, L. and Faye, G. and Nissanke, S. , doi =. Phys. Rev. D , title = "
[80]

and Qusailah, M

Blanchet, L. and Qusailah, M. S. and Will, C. M. , doi =. Gravitational recoil of inspiraling black-hole binaries to second post- Newtonian order. astro-ph/0507692 , journal =
[81]

and Buonanno, A

Blanchet, L. and Buonanno, A. and Faye, G. , doi =. Higher-order spin effects in the dynamics of compact binaries II . R adiation field. gr-qc/0605140 , journal =
[82]

doi:10.1088/0264-9381/25/16/165003 , eid =

The third post- Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits. doi:10.1088/0264-9381/25/16/165003 , eid =. arXiv , author =:0802.1249 , journal =

doi
[83]

doi:10.1103/PhysRevD.81.064004 , eid =

Post- Newtonian and numerical calculations of the gravitational self-force for circular orbits in the Schwarzschild geometry. doi:10.1103/PhysRevD.81.064004 , eid =. arXiv , author =:0910.0207 , journal =

doi
[84]

doi:10.1103/PhysRevD.81.084033 , eid =

Higher-order Post- Newtonian fit of the gravitational self-force for circular orbits in the Schwarzschild geometry. doi:10.1103/PhysRevD.81.084033 , eid =. arXiv , author =:1002.0726 , journal =

doi
[85]

Mass and Motion in General Relativity , conference =

Post- Newtonian theory and the two-body problem. Mass and Motion in General Relativity , conference =. doi:10.1007/978-90-481-3015-3_5 , editor =. arXiv , author =:0907.3596 , pages =

doi
[86]

doi:10.1103/PhysRevD.84.064041 , eid =

Tail-induced spin-orbit effect in the gravitational radiation of compact binaries. doi:10.1103/PhysRevD.84.064041 , eid =. arXiv , author =:1104.5659 , journal =

doi
[87]

doi:10.1103/PhysRevD.87.024030 , eid =

First law of mechanics for black hole binaries with spins. doi:10.1103/PhysRevD.87.024030 , eid =. arXiv , author =:1211.1060 , journal =

doi
[88]

doi:10.1103/PhysRevD.89.064026 , eid =

Half-integral conservative post- Newtonian approximations in the redshift factor of black hole binaries. doi:10.1103/PhysRevD.89.064026 , eid =. arXiv , author =:1312.2975 , journal =

doi
[89]

doi:10.1103/PhysRevD.90.044017 , eid =

High-order half-integral conservative post- Newtonian coefficients in the redshift factor of black hole binaries. doi:10.1103/PhysRevD.90.044017 , eid =. arXiv , author =:1405.5151 , journal =

doi
[90]

arXiv , author =:1212.5520 , journal =

Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binary systems. arXiv , author =:1212.5520 , journal =
[91]

arXiv , author =:1303.7412 , journal =

Next-to-next-to-leading order spin-orbit effects in the gravitational wave flux and orbital phasing of compact binaries. arXiv , author =:1303.7412 , journal =
[92]

doi:10.1088/0264-9381/32/19/195010 , eid =

Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order. doi:10.1088/0264-9381/32/19/195010 , eid =. arXiv , author =:1501.01529 , journal =

doi
[93]

Bollini, C. G. and Giambiagi, J. J. , doi =. Lowest order `divergent' graphs in v -dimensional space. Phys. Lett. B , pages =
[94]

Numerical models of irrotational binary neutron stars in general relativity. Phys. Rev. Lett. , pages =. doi:10.1103/PhysRevLett.82.892 , eprint =

doi
[95]

and van der Burg, M

Bondi, H. and van der Burg, M. G. J. and Metzner, A. W. K. , doi =. Gravitational Waves in General Relativity. VII . W aves from Axi-Symmetric Isolated Systems. Proc. R. Soc. London, Ser. A , pages =
[96]

Bonnor, W. B. , doi =. Spherical gravitational waves. Philos. Trans. R. Soc. London, Ser. A , pages =
[97]

Bonnor, W. B. and Rotenberg, M. A. , doi =. Transport of momentum by gravitational waves: Linear approximation. Proc. R. Soc. London, Ser. A , pages =
[98]

Bonnor, W. B. and Rotenberg, M. A. , doi =. Gravitational waves from isolated sources. Proc. R. Soc. London, Ser. A , pages =
[99]

Braginsky, V. B. and Thorne, K. S. , doi =. Gravitational-wave bursts with memory and experimental prospects. Nature , pages =
[100]

Astrophys

Constraining Black Hole Spin via X-Ray Spectroscopy. Astrophys. J. , pages =. doi:10.1086/508146 , eprint =

doi
[101]

doi:10.1088/0004-637X/736/2/103 , eid =

The Spin of the Supermassive Black Hole in NGC 3783. doi:10.1088/0004-637X/736/2/103 , eid =. arXiv , author =:1104.1172 , journal =

doi
[102]

doi:10.1103/PhysRevD.76.124038 , eid =

High-accuracy comparison of numerical relativity simulations with post- Newtonian expansions. doi:10.1103/PhysRevD.76.124038 , eid =. arXiv , author =:0710.0158 , journal =

doi
[103]

High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post- Newtonian approximants. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.78.104020 , eprint =

doi
[104]

and Maison, D

Breitenlohner, P. and Maison, D. , doi =. Dimensional renormalization and the action principle. Commun. Math. Phys. , pages =
[105]

and Rudolph, E

Breuer, R. and Rudolph, E. , doi =. Radiation reaction and energy loss in the post- Newtonian approximation of general relativity. Gen. Relativ. Gravit. , pages =
[106]

doi:10.1103/PhysRevD.59.084006 , eid =

Effective one-body approach to general relativistic two-body dynamics. doi:10.1103/PhysRevD.59.084006 , eid =. arXiv , author =:gr-qc/9811091 , journal =

doi
[107]

doi:10.1103/PhysRevD.62.064015 , eid =

Transition from inspiral to plunge in binary black hole coalescences. doi:10.1103/PhysRevD.62.064015 , eid =. arXiv , author =:gr-qc/0001013 , journal =

doi
[108]

and Chen, Y

Buonanno, A. and Chen, Y. and Vallisneri, M. , doi =. Detection template families for gravitational waves from the final stages of binary black-holes binaries: Nonspinning case. gr-qc/0205122 , journal =
[109]

and Chen, Y

Buonanno, A. and Chen, Y. and Vallisneri, M. , doi =. Detection template families for precessing binaries of spinning compact binaries: Adiabatic limit. gr-qc/0211087 , journal =
[110]

and Cook, G

Buonanno, A. and Cook, G. B. and Pretorius, F. , doi =. Inspiral, merger, and ring-down of equal-mass black-hole binaries. gr-qc/0610122 , journal =
[111]

doi:10.1103/PhysRevD.79.124028 , eid =

Effective-one-body waveforms calibrated to numerical relativity simulations: Coalescence of nonspinning, equal-mass black holes. doi:10.1103/PhysRevD.79.124028 , eid =. arXiv , author =:0902.0790 , journal =

doi
[112]

doi:10.1103/PhysRevD.80.084043 , eid =

Comparison of post- Newtonian templates for compact binary inspiral signals in gravitational-wave detectors. doi:10.1103/PhysRevD.80.084043 , eid =. arXiv , author =:0907.0700 , journal =

doi
[113]

doi:10.1103/PhysRevD.87.044009 , eid =

Spin effects on gravitational waves from inspiralling compact binaries at second post- Newtonian order. doi:10.1103/PhysRevD.87.044009 , eid =. arXiv , author =:1209.6349 , journal =

doi
[114]

Burke, W. L. and Thorne, K. S. , booktitle =. Gravitational Radiation Damping , year =
[115]

Burke, W. L. , doi =. Gravitational radiation damping of slowly moving systems calculated using matched asymptotic expansions. J. Math. Phys. , pages =
[116]

doi:10.1103/PhysRevLett.96.111101 , eid =

Accurate Evolutions of Orbiting Black-Hole Binaries without Excision. doi:10.1103/PhysRevLett.96.111101 , eid =. arXiv , author =:gr-qc/0511048 , journal =

doi
[117]

Astrophys

Large merger recoils and spin flips from generic black-hole binaries. Astrophys. J. Lett. , pages =. doi:10.1086/516712 , eprint =

doi
[118]

Campbell, W. B. and Morgan, T. A. , doi =. Debye Potentials For Gravitational Field. Physica , number =
[119]

Campbell, W. B. and Macek, J. and Morgan, T. A. , doi =. Relativistic time-dependent multipole analysis for scalar, electromagnetic, and gravitational fields. Phys. Rev. D , pages =
[120]

Carmeli, M. , doi =. The equations of motion of slowly moving particles in the general theory of relativity. Nuovo Cimento , pages =
[121]

Chandrasekhar, S. , doi =. The Post- Newtonian Equations of Hydrodynamics in General Relativity. Astrophys. J. , pages =
[122]

and Nutku, Y

Chandrasekhar, S. and Nutku, Y. , doi =. The Second Post- Newtonian Equations of Hydrodynamics in General Relativity. Astrophys. J. , pages =
[123]

and Esposito, F

Chandrasekhar, S. and Esposito, F. P. , doi =. The 2 1 2 -Post- Newtonian Equations of Hydrodynamics and Radiation Reaction in General Relativity. Astrophys. J. , pages =
[124]

doi:10.1103/PhysRevD.87.044022 , eid =

Tidal heating and torquing of a Kerr black hole to next-to-leading order in the tidal coupling. doi:10.1103/PhysRevD.87.044022 , eid =. arXiv , author =:1211.1686 , journal =

doi
[125]

and Kopeikin, S

Chicone, C. and Kopeikin, S. M. and Mashhoon, B. and Retzloff, D. G. , doi =. Delay equations and radiation damping. gr-qc/0101122 , journal =
[126]

, booktitle =

Bruhat, Y. , booktitle =. The
[127]

Christodoulou, D. , doi =. Reversible and irreversible transformations in black-hole physics. Phys. Rev. Lett. , pages =
[128]

and Ruffini, R

Christodoulou, D. and Ruffini, R. , doi =. Reversible transformations of a charged black hole. Phys. Rev. D , pages =
[129]

and Schmidt, B

Christodoulou, D. and Schmidt, B. G. , doi =. Convergent and Asymptotic Iteration Methods in General Relativity. Commun. Math. Phys. , pages =
[130]

Christodoulou, D. , doi =. Nonlinear Nature of Gravitation and Gravitational-Wave Experiments. Phys. Rev. Lett. , pages =
[131]

Collins, J. C. , gbs_id =. Renormalization: An introduction to renormalization, the renormalization group, and the operator-product expansion , year =
[132]

and Cook, G

Caudill, M. and Cook, G. B. and Grigsby, J. D. and Pfeiffer, H. P. , doi =. Circular orbits and spin in black-hole initial data. gr-qc/0605053 , journal =
[133]

Cook, G. B. , doi =. Three-dimensional initial data for the collision of two black holes. II . Q uasicircular orbits for equal-mass black holes. Phys. Rev. D , pages =
[134]

Cook, G. B. and Pfeiffer, H. P. , doi =. Excision boundary conditions for black hole initial data. Phys. Rev. D , numpages =
[135]

Cooperstock, F. I. and Booth, D. J. , doi =. Angular-Momentum Flux For Gravitational Radiation to Octupole Order. Nuovo Cimento B , number =
[136]

and Papapetrou, A

Corinaldesi, E. and Papapetrou, A. , doi =. Spinning test-particles in general relativity. II. Proc. R. Soc. London, Ser. A , pages =
[137]

Crowley, R. J. and Thorne, K. S. , doi =. Generation of gravitational waves. II . P ost-linear formalism revisited. Astrophys. J. , pages =
[138]

and Apostolatos, T

Cutler, C. and Apostolatos, T. A. and Bildsten, L. and Finn, L. S. and Flanagan,. The Last Three Minutes: Issues in Gravitational-Wave Measurements of Coalescing Compact Binaries. Phys. Rev. Lett. , pages =. doi:10.1103/PhysRevLett.70.2984 , eprint =

doi
[139]

and Finn, L

Cutler, C. and Finn, L. S. and Poisson, E. and Sussman, G. J. , doi =. Gravitational radiation from a particle in circular orbit around a black hole. II . N umerical results for the nonrotating case. Phys. Rev. D , pages =
[140]

Gravitational waves from merging compact binaries: How accurately can one extract the binary's parameters from the inspiral wave form?. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.49.2658 , eprint =

doi
[141]

, gbs_id =

D'Alembert, J. , gbs_id =. Trait\'e de Dynamique , year =
[142]

and Deruelle, N

Damour, T. and Deruelle, N. , doi =. Radiation reaction and angular momentum loss in small angle gravitational scattering. Phys. Lett. A , pages =
[143]

and Deruelle, N

Damour, T. and Deruelle, N. , journal =. Lagrangien g \'e n \'e ralis \'e du syst \`e me de deux masses ponctuelles, \`a l'approximation post-post-newtonienne de la relativit \'e g \'e n \'e rale
[144]

, journal =

Damour, T. , journal =. Probl \`e me des deux corps et freinage de rayonnement en relativit \'e g \'e n \'e rale
[145]

, booktitle =

Damour, T. , booktitle =. Gravitational radiation and the motion of compact bodies , year =
[146]

Damour, T. , doi =. Gravitational radiation reaction in the binary pulsar and the quadrupole formula controvercy. Phys. Rev. Lett. , pages =
[147]

Damour, T. and Sch. Lagrangians for n Point Masses at the Second Post- Newtonian Approximation of General Relativity. doi:10.1007/BF00773685 , journal =

doi
[148]

and Deruelle, N

Damour, T. and Deruelle, N. , journal =. General relativistic celestial mechanics of binary systems I . T he post- Newtonian motion
[149]

and Deruelle, N

Damour, T. and Deruelle, N. , journal =. General relativistic celestial mechanics of binary systems II . T he post- Newtonian timing formula
[150]

, booktitle =

Damour, T. , booktitle =. An Introduction to the Theory of Gravitational Radiation , volume =
[151]

, booktitle =

Damour, T. , booktitle =. The problem of motion in
[152]

Damour, T. and Sch. Higher-Order Relativistic Periastron Advances in Binary Pulsars. doi:10.1007/BF02828697 , journal =

doi
[153]

and Schmidt, B

Damour, T. and Schmidt, B. G. , doi =. Reliability of perturbation theory in general relativity. J. Math. Phys. , pages =
[154]

and Iyer, B

Damour, T. and Iyer, B. R. , cited =. Post- Newtonian generation of gravitational waves. II . T he spin moments. Ann. Inst. Henri Poincare A , url =
[155]

and Iyer, B

Damour, T. and Iyer, B. R. , doi =. Multipole analysis for electromagnetism and linearized gravity with irreducible Cartesian tensors. Phys. Rev. D , pages =
[156]

and Soffel, M

Damour, T. and Soffel, M. and Xu, C. , doi =. General-relativistic celestial mechanics. I . M ethod and definition of reference systems. Phys. Rev. D , pages =
[157]

and Taylor, J

Damour, T. and Taylor, J. H. , doi =. On the Orbital Period Change of the Binary Pulsar PSR 1913+16. Astrophys. J. , pages =

1913
[158]

and Esposito-Far

Damour, T. and Esposito-Far. Testing gravity to second post- Newtonian order: A field-theory approach. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.53.5541 , eprint =

doi
[159]

and Iyer, B

Damour, T. and Iyer, B. R. and Sathyaprakash, B. S. , doi =. Improved filters for gravitational waves from inspiraling compact binaries. gr-qc/9708034 , journal =
[160]

and Iyer, B

Damour, T. and Iyer, B. R. and Sathyaprakash, B. S. , doi =. Frequency-domain P-approximant filters for time-truncated inspiral gravitational wave signals from compact binaries. gr-qc/0001023 , journal =
[161]

and Jaranowski, P

Damour, T. and Jaranowski, P. and Sch. Dynamical invariants for general relativistic two-body systems at the third post- Newtonian approximation. gr-qc/9912092 , journal =
[162]

and Jaranowski, P

Damour, T. and Jaranowski, P. and Sch. Poincar\'e invariance in the ADM Hamiltonian approach to the general relativistic two-body problem. gr-qc/0003051 , journal =
[163]

and Jaranowski, P

Damour, T. and Jaranowski, P. and Sch. Equivalence between the ADM - Hamiltonian and the harmonic-coordinates approaches to the third post- Newtonian dynamics of compact binaries. doi:10.1103/PhysRevD.63.044021 , eid =. gr-qc/0010040 , journal =

doi
[164]

and Jaranowski, P

Damour, T. and Jaranowski, P. and Sch. On the determination of the last stable orbit for circular general relativistic binaries at the third post- Newtonian approximation. gr-qc/0005034 , journal =
[165]

and Jaranowski, P

Damour, T. and Jaranowski, P. and Sch. Dimensional regularization of the gravitational interaction of point masses. Phys. Lett. B , pages =. doi:10.1016/S0370-2693(01)00642-6 , eprint =

doi
[166]

and Iyer, B

Damour, T. and Iyer, B. R. and Sathyaprakash, B. S. , doi =. Comparison of search templates for gravitational waves from binary inspiral: 3.5PN update. gr-qc/0207021 , journal =
[167]

and Iyer, B

Damour, T. and Iyer, B. R. and Jaranowski, P. and Sathyaprakash, B. S. , doi =. Gravitational waves from black hole binary inspiral and merger: The span of third post- Newtonian effective-one-body templates. gr-qc/0211041 , journal =
[168]

doi:10.1103/PhysRevD.77.064032 , eid =

Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling. doi:10.1103/PhysRevD.77.064032 , eid =. arXiv , author =:0711.1048 , journal =

doi
[169]

and Gopakumar, A

Damour, T. and Gopakumar, A. and Iyer, B. R. , doi =. Phasing of gravitational waves from inspiralling eccentric binaries. gr-qc/0404128 , journal =
[170]

doi:10.1103/PhysRevD.81.024017 , eid =

Gravitational self-force in a Schwarzschild background and the effective one-body formalism. doi:10.1103/PhysRevD.81.024017 , eid =. arXiv , author =:0910.5533 , journal =

doi
[171]

and Nagar, A

Damour, T. and Nagar, A. , booktitle =. The Effective One-Body description of the Two-Body Problem , volume =. doi:10.1007/978-90-481-3015-3_7 , editor =

doi
[172]

doi:10.1103/PhysRevD.89.064058 , eid =

Non-local-in-time action for the fourth post- Newtonian conservative dynamics of two-body systems. doi:10.1103/PhysRevD.89.064058 , eid =. arXiv , author =:1401.4548 , journal =

doi
[173]

doi:10.1103/PhysRevD.91.084024 , eid =

Fourth post- Newtonian effective one-body dynamics. doi:10.1103/PhysRevD.91.084024 , eid =. arXiv , author =:1502.07245 , journal =

doi
[174]

doi:10.1103/PhysRevD.67.024025 , eid =

Self-force via a Green's function decomposition. doi:10.1103/PhysRevD.67.024025 , eid =. arXiv , author =:gr-qc/0202086 , journal =

doi
[175]

doi:10.1103/PhysRevD.77.124026 , eid =

Consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry. doi:10.1103/PhysRevD.77.124026 , eid =. arXiv , author =:0804.3529 , journal =

doi
[176]

, booktitle =

Detweiler, S. , booktitle =. Elementary Development of the Gravitational Self-Force , volume =. doi:10.1007/978-90-481-3015-3_10 , editor =

doi
[177]

Dixon, W. G. , booktitle =. Extended bodies in general relativity: Their description and motion , year =
[178]

, cited =

Eder, E. , cited =. Existence, uniqueness and iterative construction of motions of charged particles with retarded interactions. Ann. Inst. Henri Poincare A , url =
[179]

and Rosenblum, A

Ehlers, J. and Rosenblum, A. and Goldberg, J. N. and Havas, P. , doi =. Comments on gravitational radiation damping and energy loss in binary systems. Astrophys. J. Lett. , pages =
[180]

Ehlers, J. , doi =. Isolated systems in general relativity. Ann. N.Y. Acad. Sci. , pages =
[181]

, cited =

Einstein, A. , cited =. \" U ber Gravitationswellen. Sitzungsber. K. Preuss. Akad. Wiss. , url =
[182]

and Infeld, L

Einstein, A. and Infeld, L. and Hoffmann, B. , doi =. The Gravitational Equations and the Problem of Motion. Ann. Math. (2) , pages =
[183]

and Wagoner, R

Epstein, R. and Wagoner, R. V. , doi =. Post- Newtonian Generation of Gravitational Waves. Astrophys. J. , pages =
[184]

Esposito, L. W. and Harrison, E. R. , doi =. Properties of the Hulse - Taylor binary pulsar system. Astrophys. J. Lett. , pages =
[185]

doi:10.12942/lrr-2012-8 , eid =

Binary Neutron Star Mergers. doi:10.12942/lrr-2012-8 , eid =. arXiv , author =:1204.3858 , journal =

2012 doi
[186]

The X-ray spectra of accreting Kerr black holes. The. arXiv , author =:astro-ph/0507409 , publisher =
[187]

and Jaranowski, P

Faye, G. and Jaranowski, P. and Sch. Skeleton approximate solution of the Einstein field equations for multiple black-hole systems. doi:10.1103/PhysRevD.69.124029 , eid =. gr-qc/0311018 , journal =

doi
[188]

and Blanchet, L

Faye, G. and Blanchet, L. and Buonanno, A. , doi =. Higher-order spin effects in the dynamics of compact binaries I . E quations of motion. gr-qc/0605139 , journal =
[189]

doi:10.1088/0264-9381/29/17/175004 , eid =

The third and a half post- Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries. doi:10.1088/0264-9381/29/17/175004 , eid =. arXiv , author =:1204.1043 , journal =

doi
[190]

arXiv , author =:1409.3546 , journal =

Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post- Newtonian order. arXiv , author =:1409.3546 , journal =
[191]

doi:10.1103/PhysRevD.80.024002 , eid =

Post- Newtonian corrections to the gravitational-wave memory for quasicircular, inspiralling compact binaries. doi:10.1103/PhysRevD.80.024002 , eid =. arXiv , author =:0812.0069 , journal =

doi
[192]

doi:10.1103/PhysRevD.84.124013 , eid =

The gravitational-wave memory from eccentric binaries. doi:10.1103/PhysRevD.84.124013 , eid =. arXiv , author =:1108.3121 , journal =

doi
[193]

doi:10.1103/PhysRevD.83.024027 , eid =

Conservative self-force correction to the innermost stable circular orbit: comparison with multiple post- Newtonian -based methods. doi:10.1103/PhysRevD.83.024027 , eid =. arXiv , author =:1008.4622 , journal =

doi
[194]

doi:10.1103/PhysRevD.83.024028 , eid =

Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post- Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force. doi:10.1103/PhysRevD.83.024028 , eid =. arXiv , aut...

doi
[195]

Observing binary inspiral in gravitational radiation: One interferometer. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.47.2198 , eprint =

doi
[196]

Fitchett, M. J. , journal =. The influence of gravitational wave momentum losses on the centre of mass motion of a Newtonian binary system
[197]

doi:10.1103/PhysRevD.77.021502 , eid =

Constraining neutron star tidal Love numbers with gravitational wave detectors. doi:10.1103/PhysRevD.77.021502 , eid =. arXiv , author =:0709.1915 , journal =

1915 doi
[198]

Fock, V. A. , journal =. On motion of finite masses in general relativity
[199]

Fock, V. A. , publisher =. Theory of space, time and gravitation , year =
[200]

doi:10.1103/PhysRevD.84.044031 , eid =

Effective field theory calculation of conservative binary dynamics at third post- Newtonian order. doi:10.1103/PhysRevD.84.044031 , eid =. arXiv , author =:1104.1122 , journal =

doi
[201]

arXiv , author =:1206.7087 , journal =

The dynamics of the gravitational two-body problem in the post- Newtonian approximation at quadratic order in the Newton 's constant. arXiv , author =:1206.7087 , journal =
[202]

doi:10.1103/PhysRevD.87.044056 , eid =

Tail terms in gravitational radiation reaction via effective field theory. doi:10.1103/PhysRevD.87.044056 , eid =. arXiv , author =:1111.5488 , journal =

doi
[203]

doi:10.1088/0264-9381/31/4/043001 , eid =

Effective field theory methods to model compact binaries. doi:10.1088/0264-9381/31/4/043001 , eid =. arXiv , author =:1309.3474 , journal =

doi
[204]

Fokker, A. D. , doi =. Ein invarianter Variationssatz f \"u r die Bewegung mehrerer elektrischer Massenteilchen. Z. Phys. , pages =
[205]

Friedman, J. L. and Ury. Thermodynamics of binary black holes and neutron stars. Phys. Rev. D , note =. doi:10.1103/PhysRevD.65.064035 , eid =

doi
[206]

Gravitational Radiation for Extreme Mass Ratio Inspirals to the 14th Post- Newtonian Order. Prog. Theor. Phys. , pages =. doi:10.1143/PTP.127.583 , eprint =

doi
[207]

Gravitational Waves from a Particle in Circular Orbits around a Schwarzschild Black Hole to the 22nd Post- Newtonian Order. Prog. Theor. Phys. , pages =. doi:10.1143/PTP.128.971 , eprint =

doi
[208]

and Schutz, B

Futamase, T. and Schutz, B. F. , doi =. Newtonian and post- Newtonian approximations are asymptotic to general relativity. Phys. Rev. D , pages =
[209]

Futamase, T. , doi =. Gravitational radiation reaction in the Newtonian limit. Phys. Rev. D , pages =
[210]

Futamase, T. , doi =. Strong-field point-particle limit and the equations of motion in the binary pulsar. Phys. Rev. D , pages =
[211]

and Itoh, Y

Futamase, T. and Itoh, Y. , doi =. Living Rev. Relativ. , title = "
[212]

doi:10.1016/0375-9601(80)90728-8 , journal =

Relativistic corrections to the gravitational radiation of a binary system and the fine structure of the spectrum. doi:10.1016/0375-9601(80)90728-8 , journal =

doi
[213]

Spin-spin effects in radiating compact binaries

Gergely, L. Spin-spin effects in radiating compact binaries. doi:10.1103/PhysRevD.61.024035 , eid =. gr-qc/9911082 , journal =

doi
[214]

Second post- Newtonian radiative evolution of the relative orientations of angular momenta in spinning compact binaries

Gergely, L. Second post- Newtonian radiative evolution of the relative orientations of angular momenta in spinning compact binaries. doi:10.1103/PhysRevD.62.024007 , eid =. gr-qc/0003037 , journal =

doi
[215]

Geroch, R. , doi =. Multipole Moments. II . C urved Space. J. Math. Phys. , pages =
[216]

and Horowitz, G

Geroch, R. and Horowitz, G. T. , journal =. Asymptotically simple does not imply asymptotically Minkowskian
[217]

doi:10.1103/PhysRevD.73.104029 , eid =

Effective field theory of gravity for extended objects. doi:10.1103/PhysRevD.73.104029 , eid =. arXiv , author =:hep-th/0409156 , journal =

doi
[218]

doi:10.1103/PhysRevD.81.124015 , eid =

Gravitational radiative corrections from effective field theory. doi:10.1103/PhysRevD.81.124015 , eid =. arXiv , author =:0912.4254 , journal =

doi
[219]

doi:10.1103/PhysRevD.89.124033 , eid =

Black hole mass dynamics and renormalization group evolution. doi:10.1103/PhysRevD.89.124033 , eid =. arXiv , author =:1211.6095 , journal =

doi
[220]

Gravitational waves from inspiraling compact binaries: Angular momentum flux, evolution of the orbital elements and the waveform to the second post- Newtonian order. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.56.7708 , eprint =

doi
[221]

Second post- Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.55.6030 , eprint =

doi
[222]

doi:10.1103/PhysRevD.65.084011 , eid =

Second post- Newtonian gravitational wave polarizations for compact binaries in elliptical orbits. doi:10.1103/PhysRevD.65.084011 , eid =. arXiv , author =:gr-qc/0110100 , journal =

doi
[223]

doi:10.1088/0004-637X/742/2/85 , eid =

The extreme spin of the black hole in Cygnus X-1. doi:10.1088/0004-637X/742/2/85 , eid =. arXiv , author =:1106.3690 , journal =

doi
[224]

and Grandcl

Gourgoulhon, E. and Grandcl. Quasi-equilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. doi:10.1103/PhysRevD.63.064029 , eid =. gr-qc/0007028 , journal =

doi
[225]

and Grandcl

Gourgoulhon, E. and Grandcl. Binary black holes in circular orbits. I. A global spacetime approach. doi:10.1103/PhysRevD.65.044020 , eid =. gr-qc/0106015 , journal =

doi
[226]

Gradshteyn, I. S. and Ryzhik, I. M. , publisher =. Table of Integrals, Series and Products , year =
[227]

doi:10.1088/0264-9381/25/20/205009 , eid =

A rigorous derivation of gravitational self-force. doi:10.1088/0264-9381/25/20/205009 , eid =. arXiv , author =:0806.3293 , journal =

doi
[228]

Binary black holes in circular orbits

Grandcl. Binary black holes in circular orbits. II . N umerical methods and first results. Phys. Rev. D , numpages =. doi:10.1103/PhysRevD.65.044021 , eid =

doi
[229]

doi:10.12942/lrr-2009-1 , eid =

Spectral Methods for Numerical Relativity. doi:10.12942/lrr-2009-1 , eid =. arXiv , author =:0706.2286 , journal =

2009 doi
[230]

Grishchuk, L. P. and Kopeikin, S. M. , booktitle =. Equations of motion for isolated bodies with relativistic corrections including the radiation-reaction force , year =
[231]

and Miller, M

Gultekin, K. and Miller, M. C. and Hamilton, D. P. , doi =. Growth of Intermediate-Mass Black Holes in Globular Clusters. astro-ph/0402532 , journal =
[232]

, publisher =

Hadamard, J. , publisher =. Le probl\`
[233]

doi:10.1103/PhysRevD.77.044020 , eid =

Where post- Newtonian and numerical-relativity waveforms meet. doi:10.1103/PhysRevD.77.044020 , eid =. arXiv , author =:0706.1305 , journal =

doi
[234]

Hansen, R. O. , doi =. Multipole moments of stationary space-times. J. Math. Phys. , pages =
[235]

Hanson, A. J. and Regge, T. , doi =. The Relativistic Spherical Top. Ann. Phys. (N.Y.) , pages =
[236]

doi:10.1103/PhysRevD.83.044008 , eid =

Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonian s for n gravitating spinning compact objects. doi:10.1103/PhysRevD.83.044008 , eid =. arXiv , author =:1011.1179 , journal =

doi
[237]

Next-to-next-to-leading order post- Newtonian spin-orbit Hamiltonian for self-gravitating binaries. Ann. Phys. (Berlin) , pages =. doi:10.1002/andp.201100094 , eprint =

doi
[238]

Next-to-next-to-leading order post- Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries. Ann. Phys. (Berlin) , pages =. doi:10.1002/andp.201100163 , eprint =

doi
[239]

Next-to-next-to-leading order post- Newtonian linear-in-spin binary Hamiltonians. Ann. Phys. (Berlin) , pages =. doi:10.1002/andp.201200271 , eprint =

doi
[240]

Hari Dass, N. D. and Soni, V. , doi =. Feynman graph derivation of the Einstein quadrupole formula. J. Phys. A: Math. Gen. , pages =
[241]

doi:10.1103/PhysRevD.77.104001 , eid =

Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates. doi:10.1103/PhysRevD.77.104001 , eid =. arXiv , author =:0712.1515 , journal =

doi
[242]

doi:10.1103/PhysRevD.78.124004 , eid =

Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincar\'e invariance. doi:10.1103/PhysRevD.78.124004 , eid =. arXiv , author =:0809.2208 , journal =

doi
[243]

doi:10.1088/0264-9381/27/13/135007 , eid =

The reduced Hamiltonian for next-to-leading-order spin-squared dynamics of general compact binaries. doi:10.1088/0264-9381/27/13/135007 , eid =. arXiv , author =:1002.2093 , journal =

doi
[244]

doi:10.1103/PhysRevD.93.044010 , eid =

Analytic self-force calculations in the post- Newtonian regime: eccentric orbits on a Schwarzschild background. doi:10.1103/PhysRevD.93.044010 , eid =. arXiv , author =:1512.01556 , journal =

doi
[245]

doi:10.1103/PhysRevD.87.044001 , eid =

Exploring tidal effects of coalescing binary neutron stars in numerical relativity. doi:10.1103/PhysRevD.87.044001 , eid =. arXiv , author =:1301.3555 , journal =

doi
[246]

Hunter, A. J. and Rotenberg, M. A. , doi =. The double-series approximation method in general relativity. I. Exact solution of the (24) approximation. II . D iscussion of `wave tails' in the (2s) approximation. J. Phys. A: Math. Gen. , pages =
[247]

Hulse, R. A. and Taylor, J. H. , doi =. Discovery of a pulsar in a binary system. Astrophys. J. , pages =
[248]

Isaacson, R. A. and Winicour, J. , doi =. Harmonic and Null Descriptions of Gravitational Radiation. Phys. Rev. , pages =
[249]

and Futamase, T

Itoh, Y. and Futamase, T. and Asada, H. , doi =. Equation of motion for relativistic compact binaries with the strong field point particle limit: Formulation, the first post- Newtonian order, and multipole terms. gr-qc/9910052 , journal =
[250]

and Futamase, T

Itoh, Y. and Futamase, T. and Asada, H. , doi =. Equation of motion for relativistic compact binaries with the strong field point particle limit: The second and half post- Newtonian order. gr-qc/0101114 , journal =
[251]

and Futamase, T

Itoh, Y. and Futamase, T. , doi =. New derivation of a third post- Newtonian equation of motion for relativistic compact binaries without ambiguity. gr-qc/0310028 , journal =
[252]

Itoh, Y. , doi =. Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post- Newtonian order. Phys. Rev. D , numpages =
[253]

doi:10.1103/PhysRevD.80.124003 , eid =

Third-and-a-half order post- Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit. doi:10.1103/PhysRevD.80.124003 , eid =. arXiv , author =:0911.4232 , journal =

doi
[254]

Iyer, B. R. and Will, C. M. , doi =. Post- Newtonian gravitational radiation reaction for two-body systems. Phys. Rev. Lett. , pages =
[255]

Iyer, B. R. and Will, C. M. , doi =. Post- Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies. Phys. Rev. D , pages =
[256]

Jaranowski, P. and Sch. Radiative 3.5 post- Newtonian ADM Hamiltonian for many-body point-mass systems. doi:10.1103/PhysRevD.55.4712 , journal =

doi
[257]

Jaranowski, P. and Sch. Third post- Newtonian higher order ADM Hamilton dynamics for two-body point-mass systems. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.57.7274 , eprint =

doi
[258]

Jaranowski, P. and Sch. Binary black-hole problem at the third post- Newtonian approximation in the orbital motion: Static part. doi:10.1103/PhysRevD.60.124003 , eid =. gr-qc/9906092 , journal =

doi
[259]

Jaranowski, P. and Sch. The binary black-hole dynamics at the third post- Newtonian order in the orbital motion. Ann. Phys. (Berlin) , pages =. doi:10.1002/(SICI)1521-3889(200005)9:3/5<378::AID-ANDP378>3.0.CO;2-M , eprint =

doi
[260]

doi:10.1103/PhysRevD.86.061503 , eid =

Towards the fourth post- Newtonian Hamiltonian for two-point-mass systems. doi:10.1103/PhysRevD.86.061503 , eid =. arXiv , author =:1207.5448 , journal =

doi
[261]

doi:10.1103/PhysRevD.87.081503 , eid =

Dimensional regularization of local singularities in the 4th post- Newtonian two-point-mass Hamiltonian. doi:10.1103/PhysRevD.87.081503 , eid =. arXiv , author =:1303.3225 , journal =

doi
[262]

doi:10.1103/PhysRevD.92.124043 , eid =

Derivation of the local-in-time fourth post- Newtonian ADM Hamiltonian for spinless compact binaries. doi:10.1103/PhysRevD.92.124043 , eid =. arXiv , author =:1508.01016 , journal =

doi
[263]

Junker, W. and Sch. Binary systems: higher order gravitational radiation damping and wave emission. Mon. Not. R. Astron. Soc. , pages =
[264]

doi:10.1103/PhysRevD.92.084025 , eid =

Analytical high-order post- Newtonian expansions for extreme mass ratio binaries. doi:10.1103/PhysRevD.92.084025 , eid =. arXiv , author =:1503.02334 , journal =

doi
[265]

Kerlick, G. D. , doi =. Finite reduced hydrodynamic equations in the slow-motion approximation to general relativity. Part I . F irst post- Newtonian equations. Gen. Relativ. Gravit. , pages =
[266]

Kerlick, G. D. , doi =. Finite reduced hydrodynamic equations in the slow-motion approximation to general relativity. Part II . R adiation reaction and higher-order divergent terms. Gen. Relativ. Gravit. , pages =
[267]

Kidder, L. E. and Will, C. M. and Wiseman, A. G. , doi =. Spin effects in the inspiral of coalescing compact binaries. Phys. Rev. D , pages =. 1993 , Eprint =

1993
[268]

Kidder, L. E. and Will, C. M. and Wiseman, A. G. , doi =. Coalescing binary systems of compact objects to (post) ^ 5/2 - Newtonian order. III . T ransition from inspiral to plunge. Phys. Rev. D , pages =
[269]

Kidder, L. E. , doi =. Coalescing binary systems of compact objects to (post) ^ 5/2 - Newtonian order. V . S pin effects. Phys. Rev. D , pages =
[270]

doi:10.1103/PhysRevD.77.044016 , eid =

Using full information when computing modes of post- Newtonian waveforms from inspiralling compact binaries in circular orbits. doi:10.1103/PhysRevD.77.044016 , eid =. arXiv , author =:0710.0614 , journal =

doi
[271]

A note on the radiation reaction in the 2.5PN waveform from inspiralling binaries in quasi-circular orbits. Class. Quantum Grav. , pages =. doi:10.1088/0264-9381/24/20/N01 , eprint =

doi
[272]

Kochanek, C. S. , doi =. Coalescing binary neutron stars. Astrophys. J. , pages =
[273]

doi:10.1088/0264-9381/25/14/145011 , eid =

Non-relativistic gravitation: From Newton to Einstein and back. doi:10.1088/0264-9381/25/14/145011 , eid =. arXiv , author =:0712.4116 , journal =

doi
[274]

The binary black-hole dynamics at the third-and-a-half post- Newtonian order in the ADM -formalism

K. The binary black-hole dynamics at the third-and-a-half post- Newtonian order in the ADM -formalism. doi:10.1103/PhysRevD.68.044004 , eid =. astro-ph/0305048 , journal =

doi
[275]

Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post- Newtonian order

K. Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post- Newtonian order. doi:10.1103/PhysRevD.73.124012 , eid =. gr-qc/0603056 , journal =

doi
[276]

Kopeikin, S. M. , journal =. The equations of motion of extended bodies in general-relativity with conservative corrections and radiation damping taken into account
[277]

Kopeikin, S. M. , doi =. Celestial Coordinate Reference Systems in Curved Spacetime. Celest. Mech. , pages =
[278]

Kopeikin, S. M. and Sch. Astrometric and timing effects of gravitational waves from localized sources. doi:10.1103/PhysRevD.59.084023 , eid =. gr-qc/9811003 , journal =

doi
[279]

Kozai, Y. , doi =. Secular perturbations of asteroids with high inclination and eccentricity. Astron. J. , pages =
[280]

Estimation of the post- Newtonian parameters in the gravitational-wave emission of a coalescing binary

Kr. Estimation of the post- Newtonian parameters in the gravitational-wave emission of a coalescing binary. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.52.2089 , eprint =

doi
[281]

Landau, L. D. and Lifshitz, E. M. , edition =. The classical theory of fields , year =
[282]

doi:10.1088/0264-9381/27/4/045008 , eid =

The Close-Limit Approximation for Black Hole Binaries with Post- Newtonian Initial Conditions. doi:10.1088/0264-9381/27/4/045008 , eid =. arXiv , author =:0901.4593 , journal =

doi
[283]

doi:10.1088/0264-9381/27/1/012001 , eid =

Gravitational-Wave Recoil from the Ringdown Phase of Coalescing Black Hole Binaries. doi:10.1088/0264-9381/27/1/012001 , eid =. arXiv , author =:0901.4594 , journal =

doi
[284]

doi:10.1103/PhysRevD.85.064039 , eid =

First law of binary black hole mechanics in general relativity and post- Newtonian theory. doi:10.1103/PhysRevD.85.064039 , eid =. arXiv , author =:1111.5378 , journal =

doi
[285]

doi:10.1103/PhysRevLett.108.131103 , eid =

Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems. doi:10.1103/PhysRevLett.108.131103 , eid =. arXiv , author =:1111.5609 , journal =

doi
[286]

arXiv , author =:1106.3278 , journal =

Periastron Advance in Black-Hole Binaries. arXiv , author =:1106.3278 , journal =
[287]

doi:10.1103/PhysRevD.92.084021 , eid =

First law of mechanics for compact binaries on eccentric orbits. doi:10.1103/PhysRevD.92.084021 , eid =. arXiv , author =:1506.05648 , journal =

doi
[288]

doi:10.1103/PhysRevD.82.064029 , eid =

Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction. doi:10.1103/PhysRevD.82.064029 , eid =. arXiv , author =:0802.1508 , journal =

doi
[289]

doi:10.1103/PhysRevD.82.104004 , eid =

Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach. doi:10.1103/PhysRevD.82.104004 , eid =. arXiv , author =:1006.4139 , journal =

doi
[290]

doi:10.1103/PhysRevD.85.064043 , eid =

Binary dynamics from spin1-spin2 coupling at fourth post- Newtonian order. doi:10.1103/PhysRevD.85.064043 , eid =. arXiv , author =:1107.4322 , journal =

doi
[291]

doi:10.1088/1475-7516/2014/12/003 , eid =

Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals. doi:10.1088/1475-7516/2014/12/003 , eid =. arXiv , author =:1408.5762 , journal =

2014 doi
[292]

doi:10.1007/JHEP06(2015)059 , eid =

Leading order finite size effects with spins for inspiralling compact binaries. doi:10.1007/JHEP06(2015)059 , eid =. arXiv , author =:1410.2601 , journal =

2015 doi
[293]

doi:10.1007/JHEP09(2015)219 , eid =

Spinning gravitating objects in the effective field theory in the post- Newtonian scheme. doi:10.1007/JHEP09(2015)219 , eid =. arXiv , author =:1501.04956 , journal =

2015 doi
[294]

Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post- Newtonian scheme. J. Cosmol. Astropart. Phys. , year =. doi:10.1088/1475-7516/2016/01/011 , archivePrefix =. 1506.05056 , primaryClass =

2016 doi
[295]

Lidov, M. L. , doi =. The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. Planet. Space Sci. , pages =
[296]

doi:10.1103/PhysRevD.71.064012 , eid =

Last orbits of binary strange quark stars. doi:10.1103/PhysRevD.71.064012 , eid =. arXiv , author =:gr-qc/0411127 , journal =

doi
[297]

Lincoln, C. W. and Will, C. M. , doi =. Coalescing binary systems of compact objects to (post) ^ 5/2 - Newtonian order: Late-time evolution and gravitational-radiation emission. Phys. Rev. D , pages =
[298]

Lorentz, H. A. and Droste, J. , booktitle =. The motion of a system of bodies under the influence of their mutual attraction, according to. doi:10.1007/978-94-015-3445-1_11 , note =

doi
[299]

Astrophys

The Spin of the Near-Extreme Kerr Black Hole GRS 1915+105. Astrophys. J. , pages =. doi:10.1086/508457 , eprint =

1915 doi
[300]

doi:10.1088/0264-9381/30/5/055007 , eid =

Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems. doi:10.1088/0264-9381/30/5/055007 , eid =. arXiv , author =:1210.4143 , journal =

doi

Pith tools

Reviewed May 13, 2026 · model on record in the stance chip above.

[1] [1]

Observation of Gravitational Waves from a Binary Black Hole Merger

Observation of Gravitational Waves from a Binary Black Hole Merger. doi:10.1103/PhysRevLett.116.061102 , eid =. arXiv , author =:1602.03837 , journal =

work page Pith review arXiv doi:10.1103/physrevlett.116.061102

[2] [2]

Abbott, B. P. and others , title = ". Phys. Rev. Lett. , year =. doi:10.1103/PhysRevLett.119.161101 , archiveprefix =. 1710.05832 , primaryclass =

work page Pith review arXiv doi:10.1103/physrevlett.119.161101

[3] [3]

Multi-messenger Observations of a Binary Neutron Star Merger

Abbott, B. and others , Journal =. Multi-messenger Observations of a Binary Neutron Star Merger. 2017 , Pages =. arXiv:1710.05833 , primaryClass =

work page Pith review arXiv 2017

[4] [4]

Abramowicz, M. A. and Klu. A precise determination of black hole spin in GRO J1655-40. Astron. Astrophys. , pages =. doi:10.1051/0004-6361:20010791 , eprint =

work page doi:10.1051/0004-6361:20010791

[5] [5]

and Iyer, B

Ajith, P. and Iyer, B. R. and Robinson, C. A. K. and Sathyaprakash, B. S. , eid =. New class of post- Newtonian approximants to the waveform templates of inspiralling compact binaries: Test mass in the Schwarzschild spacetime. gr-qc/0412033 , journal =

work page Pith review arXiv

[6] [6]

2008, PhRvD, 77, 104017, doi: 10.1103/PhysRevD.77.104017

Template bank for gravitational waveforms from coalescing binary black holes: Nonspinning binaries. doi:10.1103/PhysRevD.77.104017 , eid =. arXiv , author =:0710.2335 , journal =

work page doi:10.1103/physrevd.77.104017

[7] [7]

Energy and angular momentum flow into a black hole in a binary. Phys. Rev. D , pages =. doi:10.1103/PhysRevD.64.104020 , eprint =

work page doi:10.1103/physrevd.64.104020

[8] [8]

Third post- Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM - Hamiltonian formalisms. Class. Quantum Grav. , pages =. doi:10.1088/0264-9381/18/5/301 , eprint =

work page doi:10.1088/0264-9381/18/5/301