Transition from inspiral to plunge in precessing binaries of spinning black holes

Alessandra Buonanno; Thibault Damour; Yanbei Chen

REVIEW

Transition from inspiral to plunge in precessing binaries of spinning black holes

Alessandra Buonanno, Yanbei Chen, Thibault Damour

General Relativity and Quantum Cosmology · Submitted 16 Aug 2005 · 59 references

Pith's verdict: A careful, transparent EOB modeling paper with a genuinely new spin-dependent radiation-reaction force; the headline |J|/E^2 < 1 claim is real but truncation-dependent for exactly the aligned case where the margin is tightest.

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CitationAlessandra Buonanno, Thibault Damour, Yanbei Chen. "Transition from inspiral to plunge in precessing binaries of spinning black holes." arXiv:gr-qc/0508067 (2005). https://pith.science/paper/CIFPLGCY

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Editor's note

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This is the Buonanno-Chen-Damour EOB paper on precessing spinning binaries, and the thing worth your time is the radiation-reaction derivation in Sec. III. They build a spin-dependent RR force for quasi-circular orbits (Eq. 3.27, with the f3SO correction in Eq. 3.22) and check it against Will (2005), which appeared after they finished. That independent agreement is the strongest evidence in the paper. The rest is careful EOB machinery: they show the PN-expanded Hamiltonian has no LSSO at all (Fig. 1), which is a clean argument for resummation, and the overlap tables (I, II) showing Taylor and EOB models are not close (down to 0.32) are a useful negative result for template builders. The waveforms and energy estimates are laid out step by step and the authors are explicit that the ringdown matching is illustrative (Sec. VI B). Credit where due: this is honest modeling work, not a claim of precision.

Referee report

Significance

This is a substantial methodological contribution. The radiation-reaction derivation in §III is carried out explicitly, including the spin-dependent transverse term, and the authors report agreement with the independent circular-orbit result of Will [34]; that cross-check is a genuine strength. The comparison of Taylor and EOB models in Tables I–II is a useful, falsifiable statement about which family of templates can describe the late inspiral. The paper also makes a concrete, checkable prediction (|J|/E^2 < 1 at the end of the inspiral, permitting Kerr formation) and provides three separate estimators of the radiated energy (Fig. 11). The waveform construction in §VI.B is explicitly labelled preliminary, which is appropriate. The main quantitative deliverables, however, are the energy releases quoted in the abstract and Table VII, and those depend on modeling choices that are not stress-tested here.

Major objections (3)

[§IV, Eq. (4.1a–d); Table VII; abstract s4] The energy releases quoted in the abstract (0.6% M anti-aligned, 5% M aligned, 1.8% M non-spinning) and tabulated in Table VII are integrals taken up to the first violation of criteria (4.1a–d). The coefficients 0.3 in (4.1a–b) and α in (4.1d) are asserted, not derived, and no sensitivity study is presented. This matters most for the aligned maximally-spinning (0°,0°,0°,0°) and generic-up (60°,90°,60°,0°) rows, where the LSSO is never reached (the parenthetical 1430 and 760 Hz in Table VII) and the ending frequencies of 474 and 440 Hz are therefore entirely a truncation artifact. A short study varying the 0.3 thresholds over, say, 0.1–0.5 and reporting the resulting change in δE_H/M would establish whether the one-significant-figure numbers in the abstract are stable. By contrast, the |J|/E^2 < 1 statement (abstract s5) appears robust to this choice: the lower panels of Fig. 12 show |J|/E^2 decreasing with frequency for all configurations, so extending the evolution past the 0.3 thresholds would push the value further below unity rather than above it. The paper should nevertheless say explicitly that this bound is a property of the computed models, not a proof, and that monotonicity through the plunge is observed rather than demonstrated.
[§VI, Fig. 11; Eqs. (3.14) and (3.27)] The three energy-loss estimators compared in Fig. 11 are not independent. The quantity δE_H is, by construction, the time integral of the same Padé-resummed flux that is inserted into the radiation-reaction force through Eq. (3.14) and Eq. (3.27); its agreement with δE_I and δE_h is therefore a consistency check of the quadrupole formula against the PN flux, not an independent validation of the radiated energy. The text's phrasing ('gives us some confidence') is appropriately hedged, but the abstract and conclusions should not leave the impression that three independent confirmations are on offer. It would help to state in one sentence what each estimator actually tests.
[§VI.B, Eq. (6.3); abstract s6] The 'complete waveforms' of Fig. 13 are matched at the first violation of criteria (4.1a–b), and the final black-hole mass and spin are read off from E_fin and |J|/E^2_fin at that same point via Eq. (6.3). The ringdown parameters therefore inherit the truncation ambiguity of the first comment. The paper acknowledges the single-QNM restriction and the possibility that l≠2 modes are excited, which is appropriate, but the abstract's claim to describe 'the entire process of coalescence' should carry the caveat that the matching point is a modeling choice rather than a physical event, and that the final mass and spin are not determined by an independent matching condition.

Minor objections (7)

[Figs. 5 and 6 captions vs. §III] The captions of Figs. 5 and 6 describe 'upper-diagonal' P-approximants, whereas §III states that the 'direct' (lower-diagonal) approximants were used instead of the 'inverse' (upper-diagonal) ones of [55]. These should be reconciled so the reader knows which approximant produced the plotted curves.
[§VI, paragraph following Fig. 12] The sentence 'can range from 0.6% of M in the (anti-aligned configuration) to 5% of M (anti-aligned configuration)' repeats 'anti-aligned'; the second occurrence should read 'aligned'.
[Captions of Tables I–VI] The column header reads '(θS1, φS2, θS1, φS2)', which presumably should be '(θS1, φS1, θS2, φS2)'. The word 'maximed' also appears in several captions and should be 'maximized'.
[Fig. 13 caption vs. §VI.B] The caption describes 'half-maximally spinning (15 + 15) M⊙ binaries', while §VI.B describes the same evolutions as 'maximally spinning'. One of the two should be corrected.
[Tables I and II] The ρmax,5 column is left blank for the non-spinning and aligned rows. Please state why the five-parameter maximization was not performed or not reported for those configurations.
[§IV, criterion (4.1d)] The parameter α is given only as '~1' for the Taylor-expanded Hamiltonian and '~2' for the EOB Hamiltonian. Please give the precise numerical values used in the runs, since this criterion sets the endpoint whenever the others do not fire.
[§II.E–F and Table VII] The spherical-orbit construction and the LSSO determination assume spin-orbit interactions only. Please state explicitly that the LSSO frequencies quoted in Table VII are computed in that approximation, so the reader does not confuse them with the full spin-spin evolution.

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The paper

The paper claims

A resummed effective-one-body model with spin-dependent radiation reaction follows precessing spinning black holes through the inspiral-to-plunge transition and finds that the final state respects the Kerr bound.

The reading

The paper asks whether an analytic, Effective One-Body (EOB) description of two spinning black holes can be carried through the last orbits, the inspiral-to-plunge transition, and into a ringdown, for generic precessing spin orientations. The authors add spin-orbit and spin-spin terms to the conservative Hamiltonian, derive a radiation-reaction force that matches known spin-dependent energy and angular-momentum losses on quasi-circular orbits, and evolve the system until circularity criteria fail. For equal-mass binaries they find that the energy radiated between 40 Hz and the model's endpoint ranges from about $0.6% M$ for anti-aligned maximal spins to about $5% M$ for aligned maximal spins, with about $1.8% M$ when there is no spin. The result matters because heavy black-hole binaries put most of their detectable signal in exactly this late, non-adiabatic regime, and because the model gives a way to attach a ringdown and produce complete waveforms rather than stopping at the last stable orbit.

What carries the argument

The load-bearing object is the EOB Hamiltonian: a resummation of the post-Newtonian two-body problem into an effective test-particle motion in a deformed Schwarzschild-like geometry, here augmented by spin-orbit and spin-spin terms. Radiation reaction is inserted as a non-conservative force whose longitudinal part is fixed by the known energy flux and whose spin-dependent transverse part is fixed by angular-momentum flux; the flux can be left as a Taylor series or Pade-resummed. The last stable spherical orbit, found from the conservative Hamiltonian, marks where adiabatic inspiral ends, and the evolution is continued into the plunge until circularity or flux criteria fail. A least-damped $l=m=2$ quasi-normal mode is then matched to the end of the plunge to make a complete waveform.

Extended reading notes

Core claim

The central claim is that a resummed EOB Hamiltonian with spin couplings and a matching spin-dependent radiation-reaction force can follow precessing spinning black-hole binaries through the non-adiabatic end of inspiral and plunge, and that the resulting state is consistent with formation of a single Kerr black hole. Across the configurations studied, the dimensionless rotation parameter $|J|/E^2$ remains below unity at the end of the inspiral, so the final compact object need not be spun above the Kerr limit; the paper reads this as removing an obstacle to matching the plunge directly to a Kerr ringdown. The same evolution yields concrete energy releases, with aligned maximal spins producing several times more radiation in the detector band than anti-aligned spins, and it supplies complete inspiral-plunge-ringdown waveforms for precessing binaries.

Load-bearing premise

The load-bearing premise is that a radiation-reaction force calibrated on quasi-circular orbits, together with fixed circularity cutoffs such as $|dR/dt|<0.3|V_t|$, still gives a physically meaningful endpoint for the non-adiabatic plunge and therefore for the quoted energy releases and waveform endings.

Editorial extensions

If this is right

Aligned maximal spins can radiate about $5% M$ between 40 Hz and the model endpoint, while anti-aligned maximal spins radiate about $0.6% M$; spin orientation therefore changes both the amplitude and the usable signal duration in ground-based detectors.
Because $|J|/E^2<1$ at the end of inspiral, the plunge need not be followed by a large burst before a Kerr hole forms; the paper uses this to justify matching directly to a ringdown.
The last stable spherical orbit frequency varies strongly with the effective spin, so adiabatic template banks that fix the ending frequency at the Schwarzschild value can miss the true end of inspiral.
The transverse spin-dependent part of the radiation-reaction force has little effect on overlaps, so a simplified force along the orbital momentum captures most of the dynamics.
The construction gives an analytic family of complete inspiral-plunge-ringdown waveforms for precessing spinning binaries, which can be used as templates before numerical-relativity waveforms are available.

Reading between the lines

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

The Kerr-bound check could be turned into a cheap diagnostic for numerical-relativity initial data: any initial slice whose evolved total $|J|/E^2$ exceeds unity at the inspiral endpoint is suspect.
If the EOB endpoint is calibrated against a few numerical-relativity mergers, the same matching could supply prior distributions for final mass and spin in parameter estimation, rather than requiring a full numerical waveform for every source.
The strong alignment dependence of radiated energy suggests a selection effect in detected black-hole binaries: aligned-spin systems are visible to larger distances and may dominate high-mass detections, which population studies could test.
The arbitrary $0.3$ circularity cutoffs are the natural place to improve the model; replacing them with a physically matched transition to ringdown or perturbation theory would make the quoted energy releases less dependent on a stopping rule.

Original abstract

We investigate the non-adiabatic dynamics of spinning black hole binaries by using an analytical Hamiltonian completed with a radiation-reaction force, containing spin couplings, which matches the known rates of energy and angular momentum losses on quasi-circular orbits. We consider both a straightforward post-Newtonian-expanded Hamiltonian (including spin-dependent terms), and a version of the resummed post-Newtonian Hamiltonian defined by the Effective One-Body approach. We focus on the influence of spin terms onto the dynamics and waveforms. We evaluate the energy and angular momentum released during the final stage of inspiral and plunge. For an equal-mass binary the energy released between 40Hz and the frequency beyond which our analytical treatment becomes unreliable is found to be, when using the more reliable Effective One-Body dynamics: 0.6% M for anti-aligned maximally spinning black holes, 5% M for aligned maximally spinning black hole, and 1.8% M for non-spinning configurations. In confirmation of previous results, we find that, for all binaries considered, the dimensionless rotation parameter J/E^2 is always smaller than unity at the end of the inspiral, so that a Kerr black hole can form right after the inspiral phase. By matching a quasi-normal mode ringdown to the last reliable stages of the plunge, we construct complete waveforms approximately describing the gravitational wave signal emitted by the entire process of coalescence of precessing binaries of spinning black holes.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,884 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.91 · human participants 0.01 · controlled comparison 0.20 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.89 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We investigate the non-adiabatic dynamics of spinning black hole binaries by using an analytical Hamiltonian completed with a radiation-reaction force, containing spin couplings, which matches the known rates of energy and angular momentum losses on quasi-circular orbits. We consider both a straightforward post-Newtonian-expanded Hamiltonian (including spin-dependent terms), and a version of the resummed post-Newtonian Hamiltonian defined by the Effective One-Body approach. We focus on the influence of spin terms onto the dynamics and waveforms. We evaluate the energy and angular momentum released during the final stage of inspiral and plunge. For an equal-mass binary the energy released between 40Hz and the frequency beyond which our analytical treatment becomes unreliable is found to be, when using the more reliable Effective One-Body dynamics: 0.6% M for anti-aligned maximally spinning black holes, 5% M for aligned maximally spinning black hole, and 1.8% M for non-spinning configurations. In confirmation of previous results, we find that, for all binaries considered, the dimensionless rotation parameter J/E^2 is always smaller than unity at the end of the inspiral, so that a Kerr black hole can form right after the inspiral phase. By matching a quasi-normal mode ringdown to the last reliable stages of the plunge, we construct complete waveforms approximately describing the gravitational wave signal emitted by the entire process of coalescence of precessing binaries of spinning black holes.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the non-adiabatic dynamics of spinning black hole binaries by using an analytical Hamiltonian completed with a radiation-reaction force, containing spin couplings, which matches the known rates of energy and angular momentum losses on quasi-circular orbits.	method 0.79	0.94	0.05	asserted 0.99
s1	We consider both a straightforward post-Newtonian-expanded Hamiltonian (including spin-dependent terms), and a version of the resummed post-Newtonian Hamiltonian defined by the Effective One-Body approach.	method 0.98	0.75	0.03	asserted 0.91
s2	We focus on the influence of spin terms onto the dynamics and waveforms.	contribution 0.96	0.61	0.04	unclear 0.84
s3	We evaluate the energy and angular momentum released during the final stage of inspiral and plunge.	contribution 0.89	0.95	0.06	asserted 0.81
s4	For an equal-mass binary the energy released between 40Hz and the frequency beyond which our analytical treatment becomes unreliable is found to be, when using the more reliable Effective One-Body dynamics: 0.6% M for anti-aligned maximally spinning black holes, 5% M for aligned maximally spinning black hole, and 1.8% M for non-spinning configurations.	result 1.00	0.96	0.25	asserted 1.00
s5	In confirmation of previous results, we find that, for all binaries considered, the dimensionless rotation parameter J/E^2 is always smaller than unity at the end of the inspiral, so that a Kerr black hole can form right after the inspiral phase.	result 0.87	0.87	0.21	asserted 1.00
s6	By matching a quasi-normal mode ringdown to the last reliable stages of the plunge, we construct complete waveforms approximately describing the gravitational wave signal emitted by the entire process of coalescence of precessing binaries of spinning black holes.	contribution 0.52	0.96	0.23	asserted 0.94

What kind of paper the classifier reports this is: theoretical result 0.75 · evidence from proof or derivation 0.54.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: The energy for circular orbits as function of the freq

**Figure 2.** FIG. 2: The energy for circular orbits as function of the freq

**Figure 3.** FIG. 3: The energy (left panel) and the frequency (right pane

**Figure 4.** FIG. 4: Signal-to-noise ratio versus binary total mass at 10

**Figure 5.** FIG. 5: Newton-normalized flux in the equal-mass case with bo

**Figure 6.** FIG. 6: Newton-normalized flux in the equal-mass case with bo

**Figure 7.** FIG. 7: Comparison between the T- and (upper diagonal) P-app

**Figure 8.** FIG. 8: Oscillations in ˙r

**Figure 9.** FIG. 9: Relative orbital phase measured with respect to

**Figure 10.** FIG. 10: Comparison between waveforms from configurations w

**Figure 11.** FIG. 11: Comparison between the three different prescriptio

**Figure 12.** FIG. 12: Accumulative energy release (upper panels) and ins

**Figure 13.** FIG. 13: Inspiral waveforms (which end at

Figures reproduced from arXiv:gr-qc/0508067 by the authors.

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gr-qc 2026-06 unverdicted novelty 7.0 of 10

All five NSBH events are consistent with zero line-of-sight acceleration; the joint posterior for GW200105_162426 disfavors both zero LOSA and zero eccentricity at 90% credibility.
Accurate waveforms for generic planar-orbit binary black holes: The multipolar effective-one-body model SEOBNRv6EHM
gr-qc 2026-05 unverdicted novelty 7.0 of 10

SEOBNRv6EHM is a multipolar EOB model for eccentric planar-orbit BBHs calibrated to NR simulations, showing low waveform mismatches up to eccentricity 0.9.
From the confluent Heun equation to a new factorized and resummed gravitational waveform for circularized, nonspinning, compact binaries
gr-qc 2026-02 conditional novelty 7.0 of 10

A new resummation absorbs all test-mass logarithms and transcendental numbers into closed-form factors, leaving rational polynomial waveform corrections up to 10PN.
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.

Show 44 more citing papers

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.
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.
Accurate waveforms for eccentric, aligned-spin binary black holes: The multipolar effective-one-body model SEOBNRv5EHM
gr-qc 2024-12 conditional novelty 7.0 of 10

SEOBNRv5EHM, a new effective-one-body waveform model with third-post-Newtonian eccentricity corrections, reaches a median 0.02% mismatch against eccentric numerical-relativity simulations, about an order of magnitude ...
Multi-timescale analysis of phase transitions in precessing black-hole binaries
gr-qc 2015-06 accept novelty 7.0 of 10

Analytic solutions for black-hole spin precession plus a precession-averaged evolution equation let binary black hole inspirals be computed efficiently from arbitrarily large separations.
Inspiral-merger-ringdown waveforms of spinning, precessing black-hole binaries in the effective-one-body formalism
gr-qc 2013-07 conditional novelty 7.0 of 10

A precessing effective-one-body waveform model, built by rotating calibrated nonprecessing waveforms into a precessing frame and matching to ringdown in the final-spin frame, agrees with two numerical-relativity prece...
Post-adiabatic effective-one-body waveforms for coalescing compact binaries
gr-qc 2026-10 conditional novelty 6.0 of 10

A post-adiabatic equinoctial-element formulation speeds up eccentric effective-one-body waveform generation by a median of roughly 2.6x for neutron star binaries and 1.5x for black holes, with mismatches below 5e-7 fo...
NRSur7dq4v2: A multi-domain precessing surrogate model with improved accuracy
gr-qc 2026-09 accept novelty 6.0 of 10

A multi-domain surrogate model for precessing binary black hole waveforms achieves up to an order-of-magnitude better remnant mass and spin recovery by independently modeling inspiral and ringdown with a smooth blend.
Compactness Inference in Gravitational-Wave Mergers with PhenomDECO: Catalog Benchmarks and Robustness Diagnostics
gr-qc 2026-06 unverdicted novelty 6.0 of 10

PhenomDECO analysis of GWTC-3 events finds all considered signals consistent with binary black holes once low-frequency noise effects are addressed via higher starting frequencies.
Eccentric and unbound compact binaries in the LIGO-Virgo-KAGRA catalog: parameter estimation and waveform systematics with SEOBNRv6EHM
gr-qc 2026-05 unverdicted novelty 6.0 of 10

SEOBNRv6EHM reduces parameter biases for eccentric binaries versus prior models and shows mild support for eccentricity in five catalog events plus comparable unbound fits for three high-mass events.
A pre-merger-informed spectral-level ringdown inference framework for black-hole spectroscopy
gr-qc 2026-05 unverdicted novelty 6.0 of 10

SPRING framework propagates pre-merger information into spectral-level ringdown inference, improving Bayesian support for an agnostic two-damped-sinusoid model on GW250114 by ΔlnB ~5-10 while keeping remnant posterior...
Learning Post-Newtonian Corrections from Numerical Relativity
gr-qc 2025-11 conditional novelty 6.0 of 10

A PINN learns higher-order corrections to the TaylorT4 PN model from eight NR surrogate waveforms, reducing phase and amplitude errors in the inspiral while enforcing physical symmetries.
Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA
gr-qc 2024-04 unverdicted novelty 6.0 of 10

Bayesian inference on LVK O1-O3 events with eccentric aligned-spin waveforms yields log10 Bayes factors of 1.77-4.75 favoring eccentricity for GW200129, GW190701 and GW200208_22, and >99.5% probability that at least o...
Theoretical groundwork supporting the precessing-spin two-body dynamics of the effective-one-body waveform models SEOBNRv5
gr-qc 2023-03 accept novelty 6.0 of 10

A full 4PN precessing-spin effective-one-body Hamiltonian, a cheaper orbit-averaged version, and consistent post-Newtonian equations of motion are derived for the SEOBNRv5 waveform family.
SEOBNRv5PHM: Next generation of accurate and efficient multipolar precessing-spin effective-one-body waveforms for binary black holes
gr-qc 2023-03 accept novelty 6.0 of 10

A new open-source waveform model for precessing black-hole binaries reaches sub-1% disagreement with 84% of 1543 numerical-relativity simulations and runs 8 to 20 times faster than its predecessor.
Laying the foundation of the effective-one-body waveform models SEOBNRv5: improved accuracy and efficiency for spinning non-precessing binary black holes
gr-qc 2023-03 conditional novelty 6.0 of 10

SEOBNRv5HM is a recalibrated effective-one-body waveform model for spinning, non-precessing binary black holes that cuts median mismatch against numerical relativity by roughly a factor of seven and runs 10 to 50 time...
Radiation-reaction force and multipolar waveforms for eccentric, spin-aligned binaries in the effective-one-body formalism
gr-qc 2021-04 accept novelty 6.0 of 10

The paper derives eccentric-orbit radiation-reaction forces and gravitational-wave modes through 2PN order, including tail effects and aligned spins, in a factorized form that plugs into the SEOBNRv4HM waveform model.
Multipolar Effective-One-Body Waveforms for Precessing Binary Black Holes: Construction and Validation
gr-qc 2020-04 accept novelty 6.0 of 10

A new precessing, multipolar effective-one-body waveform model, uncalibrated in the precessing sector, matches 1523 numerical-relativity simulations with maximum mismatch below 3% for 94% of cases and below 1% for 57%.
A faithful analytical effective one body waveform model for spin-aligned, moderately eccentric, coalescing black hole binaries
gr-qc 2020-01 conditional novelty 6.0 of 10

Dressing the circular EOB angular momentum flux with a Newtonian noncircular prefactor yields an eccentric waveform model with about 3% maximum mismatch against 22 SXS numerical relativity simulations.
Energetics of two-body Hamiltonians in post-Minkowskian gravity
gr-qc 2019-01 accept novelty 6.0 of 10

Third-order post-Minkowskian binding energies for circular binary orbits improve on lower PM orders but remain less accurate than the post-Newtonian effective-one-body models used to build LIGO/Virgo waveforms.
Time-domain effective-one-body gravitational waveforms for coalescing compact binaries with nonprecessing spins, tides and self-spin effects
gr-qc 2018-06 conditional novelty 6.0 of 10

A single effective-one-body code now covers spinning black holes, neutron star tides and equation-of-state dependent self-spin effects, matching numerical relativity to better than 0.25 percent unfaithfulness over mos...
Constructing Gravitational Waves from Generic Spin-Precessing Compact Binary Inspirals
gr-qc 2017-03 conditional novelty 6.0 of 10

An analytic, closed-form frequency-domain gravitational waveform for generic spin-precessing compact binary inspirals matches numerical post-Newtonian waveforms well enough for parameter estimation in 99.2% of simulat...
A new effective-one-body description of coalescing nonprecessing spinning black-hole binaries
gr-qc 2014-06 conditional novelty 6.0 of 10

A new effective-one-body waveform model, built on a 'centrifugal radius' coordinate, matches 15 numerical-relativity black-hole merger waveforms across spins -0.95 to +0.98 to within about 0.15 radians of phase.
A new analytic representation of the ringdown waveform of coalescing spinning black hole binaries
gr-qc 2014-06 conditional novelty 6.0 of 10

Dividing the ringdown waveform by the fundamental quasinormal mode leaves a residual whose amplitude and phase are well fit by hyperbolic-tangent templates, giving an accurate analytic ringdown representation for spin...
Frequency domain reduced order models for gravitational waves from aligned-spin compact binaries
gr-qc 2014-02 conditional novelty 6.0 of 10

A frequency-domain SVD surrogate reproduces the SEOBNRv1 aligned-spin waveform model with better than 0.1% mismatch at thousand-fold speedup, making spinning-waveform parameter estimation tractable.
Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
gr-qc 2013-07 conditional novelty 6.0 of 10

A cross-code audit of 25 numerical black-hole merger waveforms finds that the effective-one-body and phenomenological template families used in LIGO/Virgo searches recover them with over 99% overlap at total masses of...
Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion
gr-qc 2012-12 conditional novelty 6.0 of 10

A single tuned coefficient in the effective-one-body radial potential, fitted as a near-linear function of mass ratio, reproduces numerical-relativity black-hole-binary waveforms for mass ratios 1 through 6 to within ...
Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and non-precessing inspiral signals
gr-qc 2012-07 conditional novelty 6.0 of 10

Viewed in a frame that tracks the orbital plane, precessing-binary inspiral waveforms match non-precessing waveforms specified only by mass ratio and one effective spin, with best matches above 0.99 and spin biases at...
Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms
gr-qc 2012-02 conditional novelty 6.0 of 10

A calibrated effective-one-body model reproduces numerical-relativity waveforms of non-precessing spinning black-hole binaries with mismatch below 0.003 in the Advanced LIGO band for total masses of 20 to 200 solar masses.
Effective one body Hamiltonian of two spinning black-holes with next-to-next-to-leading order spin-orbit coupling
gr-qc 2011-06 accept novelty 6.0 of 10

The paper derives the next-to-next-to-leading-order spin-orbit contribution to the effective-one-body Hamiltonian for two spinning black holes, expressed as two effective gyro-gravitomagnetic ratios.
Tracking the precession of compact binaries from their gravitational-wave signal
gr-qc 2010-12 conditional novelty 6.0 of 10

Maximizing the (l=2, |m|=2) gravitational-wave amplitude over orientation angles yields a frame that tracks binary precession to a fraction of a degree and simplifies the waveform.
Comparing Effective-One-Body gravitational waveforms to accurate numerical data
gr-qc 2007-11 conditional novelty 6.0 of 10

A resummed Effective-One-Body waveform, with two flexibility parameters fitted to a 15-orbit numerical simulation, reproduces the numerical phase and amplitude of an equal-mass black hole binary to about 10^-3 gravita...
Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach
gr-qc 2006-02 conditional novelty 6.0 of 10

Gravitational recoil of merging non-spinning black holes is estimated at 49-172 km/s with a best-bet peak of about 74 km/s, driven by a burst of linear momentum flux during the plunge.
On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA
gr-qc 2005-12 accept novelty 6.0 of 10

A multi-mode Fisher-matrix formalism indicates that LISA could detect black hole ringdowns out to cosmological distances and measure mass and spin to percent-level accuracy, with two resolved modes needed to test the ...
Pushing the accuracy of the quasi-circular baseline for the SEOBNR family of models
gr-qc 2026-11 accept novelty 5.0 of 10

SEOBNRv5iHM achieves a median (2,2)-mode maximum unfaithfulness of 4.25e-5 against 591 numerical-relativity simulations, a factor 4.5 below SEOBNRv5HM and comparable to NRHybSur3dq8 at high masses.
Spin-spin coupling in stellar binaries
astro-ph.SR 2026-07 conditional novelty 5.0 of 10

A spin-spin resonance in binaries can pump the secondary's obliquity to high values as the primary's magnetic braking sweeps the precession frequencies through commensurability.
Effective-one-body waveforms for precessing coalescing compact binaries with post-newtonian Twist
gr-qc 2021-11 conditional novelty 5.0 of 10

The TEOBResumS effective-one-body model is extended to full inspiral-merger-ringdown for precessing binaries with higher modes, reaching median mismatches of roughly 4 to 7 parts in a thousand against numerical relativity.
Surrogate model for an aligned-spin effective one body waveform model of binary neutron star inspirals using Gaussian process regression
gr-qc 2018-12 accept novelty 5.0 of 10

A Gaussian-process surrogate reproduces the SEOBNRv4T binary neutron star waveform to a maximum Advanced LIGO mismatch of 4.5e-4 at 0.13 s per evaluation, roughly 1500 to 6000 times faster than the time-domain model.
An improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors
gr-qc 2016-11 accept novelty 5.0 of 10

Recalibrating the effective-one-body waveform model against 141 numerical-relativity simulations brings it above 99% faithfulness across spinning, nonprecessing black-hole binaries, and a reduced-order version makes i...
Validating the effective-one-body model of spinning, precessing binary black holes against numerical relativity
gr-qc 2016-07 conditional novelty 5.0 of 10

The precessing effective-one-body waveform model SEOBNRv3 matches 70 numerical-relativity precessing black-hole simulations to within roughly 3 percent unfaithfulness for Advanced LIGO design noise at total masses 10 ...
An improved analysis of GW150914 using a fully spin-precessing waveform model
gr-qc 2016-06 conditional novelty 5.0 of 10

Re-analysing GW150914 with a fully spin-precessing effective-one-body waveform gives component masses near 35 and 30 solar masses and 90% upper bounds of 0.65 and 0.75 on the two black-hole spin magnitudes, consistent...
Energetics and phasing of nonprecessing spinning coalescing black hole binaries
gr-qc 2015-06 conditional novelty 5.0 of 10

A recalibrated effective-one-body model for nonprecessing spinning black hole binaries matches about fifty numerical relativity waveforms with faithfulness between 99.49% and 99.98%, and its binding-energy versus angu...
Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries
gr-qc 2010-05 accept novelty 5.0 of 10

A frequency-domain hybrid of post-Newtonian and numerical relativity waveforms yields a nine-parameter analytic model that matches the hybrids at better than 97% overlap for Advanced LIGO, with post-Newtonian truncati...
Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
gr-qc 2008-03 conditional novelty 5.0 of 10

Adding next-to-leading-order spin-orbit terms to the Effective One Body description of spinning black hole binaries cuts the predicted last-stable-orbit binding energy for maximal aligned spins from about 30% to about...
PRECESSION: Dynamics of spinning black-hole binaries with python
astro-ph.HE 2016-05 conditional novelty 4.0 of 10

PRECESSION packages published post-Newtonian spin-precession equations, a precession-averaged inspiral integrator and numerical-relativity remnant fits into a documented Python module that runs roughly 70 times faster...

How later papers used it

111 later papers cite it

Evidence: substantial. 67 of the citing papers share no author with it, and 17 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 187 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

6 later papers by other authors are listed below: 6 used its method or tool.

Uses its method or tool 6 of 26 papers with this label

Used this paper's leading spin-orbit and spin-spin coupling to the radiation reaction for the dissipative part.

Comparison of Post-Newtonian and Numerical Evolutions of Black-Hole Binaries (2009) · 0.87 · paraphrased: the licence does not allow quoting
Obtained its equations of motion from Eqs. (2.23)-(2.25) and (3.1) of this paper, and its radiation reaction force from Eq. (3.27) there.

Post-Newtonian Quasicircular Initial Orbits for Numerical Relativity (2017) · 0.99 · paraphrased: the licence does not allow quoting
Performed numerical integrations of the 3.5PN equations of motion coupled with the spin evolution of this paper for randomly varied spin magnitudes and orientations.

Spin flips in generic black hole binaries (2015) · 1.00 · paraphrased: the licence does not allow quoting
Used the set of equations given in this paper.

Hybrid black-hole binary initial data (2010) · 0.95 · paraphrased: the licence does not allow quoting
Followed Eqs. (4.8) and (4.9) of this paper to solve for r, p̃_r and p̃_ϕ.

A waveform model for eccentric binary black hole based on effective-one-body-numerical-relativity (EOBNR) formalism (2017) · 1.00 · paraphrased: the licence does not allow quoting
The radial momentum is derived by equating the initial conservative radial velocity $ṙ_dyn = ξ∂ℋ_real/∂p_r_*$ to the radial velocity due to radiation reaction $ṙ_rad = ṙ_dyn$ in the adiabatic limit, with $ṙ_rad$ given by [ref] [equation] The initial phase $ϕ_0$ is set to zero.

Spinning Effective-to-Backwards One Body ($\texttt{SEBOB}$): combining Effective One-Body inspirals and Backwards One-Body merger-ringdowns for aligned spin black hole binaries (2025) · Initial Conditions · 0.97

How the literature uses it

95 arXiv papers cite this in 169 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 84 sentences without a confident label

Contests it 1 paper

Such a contribution was generally neglected in previous EOB papers, or replaced (e.g. in [ref] ) by an expression which was not consistently derived.

Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion · Improved radiation reaction: Including horizon absorption and a radial component $_r_*$ · contest 0.73

Builds on it 2 papers

This consolidates and extends previous analyses for equal [ref] and small mass ratios [ref] .

Asymptotically matched quasi-circular inspiral and transition-to-plunge in the small mass ratio expansion · Conclusion · 0.96
We then obtained initial conditions for the binary evolution which generalize those from Ref. [ref] to eccentric orbits, and which allow starting the binary's evolution from a specified initial frequency at periastron and an initial eccentricity (in the Keplerian parametrization).

Radiation-reaction force and multipolar waveforms for eccentric, spin-aligned binaries in the effective-one-body formalism · Conclusions · 1.00

Uses its method or tool 22 papers

In this paper, we use the PN equations of motion (EOM) based on [ref] .

Comparison of Post-Newtonian and Numerical Evolutions of Black-Hole Binaries · Gravitational waveforms in the PN approach · 1.00
The equations of motion were obtained from Eqs. (2.23)-(2.25) and (3.1) in Ref. [ref] , and the radiation reaction force from Eq. (3.27) there, as well.

Post-Newtonian Quasicircular Initial Orbits for Numerical Relativity · Orbital Evolution · 0.99
In order to evaluate the probabilities of a flip-flop angle to occur, we have performed numerical integrations of the 3.5PN equations of motion [ref] coupled with the spin evolution ([ref]) for randomly varied spin magnitudes and orientations (thus representing unbiased initial conditions).

Spin flips in generic black hole binaries · Statistics · 1.00

Compares with it 3 papers

We also compare our results with the corresponding 3.5PN integration of the equations of motion and spin evolution [ref] .

Flip-flopping binary black holes · Introduction · 1.00
A first validation of our initial instantaneous eccentricity estimate can be performed by comparing our analytical results with the numerical integrations of the conservative 3PN equation of motion [ref] , where we suppressed the 2.5PN radiative terms.

Eccentricity estimation from initial data for Numerical Relativity Simulations · Comparison with numerical integrations of 3PN equations of motion · 0.93
Note that, by contrast, Pan et al. [ref] , who use the less accurate post-circular initial data of Ref. [ref] , start their EOB runs at an initial radius $R_0≳50M$ (corresponding to an initial GW frequency $Mω_22≤0.005$) in order to get a good circularization of the dynamics at the frequency where numerical simulations start.

Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion · Post-post-circular initial data · 0.98

Cites it as background 41 papers

The transition from inspiral to plunge was modeled for quasi-circular inspirals in the equatorial plane by Ori and Thorne [ref] within black hole perturbation theory under some simplifying assumptions (see also the EOB framework [ref] and [ref] for extensions).

Transition from inspiral to plunge into a highly spinning black hole · Introduction · 0.95
Let us recall that the EOB approach to the general relativistic two-body dynamics is a nonperturbatively resummed analytic technique which has been developed in Refs. [ref] .

Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis · Relative dynamics · 0.88
In the EOB formalism [ref] , the two-body dynamics is mapped onto the effective dynamics of a test body in a deformed Schwarzschild or Kerr background, with the deformation parametrized by the symmetric mass-ratio $ν$.

Laying the foundation of the effective-one-body waveform models SEOBNRv5: improved accuracy and efficiency for spinning non-precessing binary black holes · The SEOBNRv5 aligned-spin Hamiltonian and equations of motion · 0.95

Discussion

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