Reducing orbital eccentricity in binary black hole simulations

Duncan A. Brown; Geoffrey Lovelace; Harald P. Pfeiffer; Lawrence E. Kidder; Lee Lindblom; Mark A. Scheel

REVIEW

Reducing orbital eccentricity in binary black hole simulations

Harald P. Pfeiffer, Duncan A. Brown, Lawrence E. Kidder, Lee Lindblom, Geoffrey Lovelace, Mark A. Scheel

General Relativity and Quantum Cosmology · Submitted 20 Feb 2007 · 41 references

Pith's verdict: A real, cheap methodological extension — radial velocity in quasi-equilibrium initial data — with a working tuning loop and an honestly stated ceiling on the headline overlap number.

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CitationDuncan A. Brown, Geoffrey Lovelace, Harald P. Pfeiffer, Lawrence E. Kidder, Lee Lindblom, Mark A. Scheel. "Reducing orbital eccentricity in binary black hole simulations." arXiv:gr-qc/0702106 (2007). https://pith.science/paper/3LF7DODH

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Worth your time, and short. The real contribution is Sec. 2.3: they extend the quasi-equilibrium/XCTS construction to nonzero radial velocity by adding a conformal Killing field with a radial piece at the inner boundaries (Eqs. 19–20). Because ξ_insp is still conformal Killing in the conformally flat case, the Appendix A argument goes through and the physical initial data actually changes — unlike the co-rotating-to-inertial relabeling in Sec. 2.2, which is pure gauge. That distinction is the cleanest thing in the paper and they state it plainly rather than dressing it up as two separate advances. Then Sec. 4 gives a working tuning loop: fit ds/dt to a line plus sinusoid, use the Newtonian estimates in Eqs. 22–23 to update Ω₀ and v_r, re-solve, re-evolve. Amplitude drops from 5.5e-3 to 4.1e-4. Cheap enough that other groups picked it up. The evidence is above the norm for the era: three resolutions with a ~20x error drop from low to medium, three outer boundary radii, and Appendix B actually derives the overlap error budget instead of hand-waving it. Soft spots, in order of size. The overlaps are upper bounds — Appendix B says so and says the systematic (~0.02 for m=2) exceeds the mismatch being reported. The abstract's “about 0.99” doesn't carry that clause; it's conservative relative to Table 2's 0.998, but a reader who stops at the abstract gets a ceiling presented as a measurement. One clause fixes it. Second, ΔT = 59±1 and Δφ = 1.83 are fixed from physical argument and the paper never shows how much μ moves when they vary; given the authors' own point that the systematic dominates, that sensitivity is the number I'd want. Third, eccentricity is measured relative to the F run's residual eccentricity — acknowledged, ~10% level, fine. None of this touches the qualitative claim. Even at the lower bound (~0.978) the dominant mode is largely unaffected over five orbits, and they scope that to five orbits and flag that spinning, precessing cases will need a different treatment. Send it out. It's the reference for eccentricity control in binary black hole initial data, and the caveats sit in the body where a referee can check them.

Referee report

Significance

This is a foundational methodological contribution to numerical relativity: it supplies a reproducible, physically motivated procedure for constructing low-eccentricity binary black hole initial data, and it quantifies how much the residual eccentricity of quasi-circular data matters for the waveform over the last several orbits before merger. The paper ships the full tuning algorithm, resolution and outer-boundary convergence tests (Fig. 2 insets, Table 1), and an explicit error analysis of the overlap integrals (Appendix B). The comparison to Peters (1964) is a falsifiable external benchmark rather than a fitted input, and the authors are candid about the systematic uncertainties in their headline number. The eccentricity-reduction procedure described here became standard practice in the field.

Major objections (2)

[Table 2 and Appendix B] The authors correctly state that the overlaps in Table 2 are upper bounds, with a systematic of order 12/(πN_cyc)² ≈ 0.02 for the m=2 modes, and that this exceeds the actual mismatch. What remains unresolved is the sensitivity of μ to the two alignment parameters. The paper fixes ΔT = 59 ± 1 M_ADM and Δφ = 1.83 rad from physical arguments and explicitly declines to maximize over them (Sec. 5.4: 'maximizing the overlaps by varying ΔT and Δφ as independent parameters is not justified'). But a ±1 M_ADM uncertainty in ΔT, and an unquantified uncertainty in Δφ, could shift μ at the same 0.02 level as the Appendix B systematic. A short table or figure of μ versus ΔT and Δφ over the stated ranges would establish whether the quoted 0.998 is robust to these choices; without it the reader cannot tell whether 0.998 reflects the waveforms or the alignment convention.
[Fig. 6 and Sec. 5.2] The power-law fits in Fig. 6 span s/M_ADM ≈ 8-12, a factor of about 1.5, with roughly 10% errors on the eccentricity estimates. The fitted exponents are 1.19 (es) and 1.51 (eω); Peters predicts 19/12 ≈ 1.58. No uncertainty on the fitted exponents is quoted, so the statement that eω 'follows this prediction quite closely' (abstract:s4) is not established at a meaningful confidence level: a factor-1.5 lever arm with 10% errors cannot distinguish 1.51 from 1.58, nor from 1.4. Please quote fit uncertainties and, if possible, extend the fit range or state the degeneracy explicitly.

Minor objections (8)

[Sec. 2.3] The statement that 'the needed expansion factors, vr/r0, are expected to be the same for the two holes' in unequal-mass systems is asserted without derivation or citation; since the generalization to unequal masses is one of the method's selling points, a post-Newtonian justification or an explicit softening would help.
[Sec. 5.2] The claim that the eccentricity estimates are affected by the residual eccentricity of the F run 'at only the 10% level' is asserted but not derived; a one-line estimate such as e_F ≈ B_F/(ω d) would make the error budget checkable.
[Eq. 21] The single-frequency sinusoid assumes constant ω over the fit window; a sentence on why this is adequate given the orbital chirp, and on how the fit window was chosen, would strengthen the tuning procedure.
[Table 1] A sentence noting that the J_ADM/M²_ADM and M_irr/M_ADM differences between the QC and F data are consistent with the 0.6% change in Ω0 would help the reader interpret the table.
[Appendix B] The bound on ||ε||²/||h||² is estimated using a pure sine wave; a sentence on why this is representative of the chirping waveform over the integration interval would strengthen the argument.
[Sec. 4] Typographical issues: 'comparible' should be 'comparable', 'simultanously' should be 'simultaneously', and Sec. 1 contains 'the the orbital frequency'.
[Sec. 5, Fig. 4 discussion] The symbol '§' in 'the low-eccentricity initial data E §' appears to be a stray character and should be removed or clarified.
[Fig. 6] The caption lists three power laws but does not clearly indicate which fitted curve corresponds to es and which to eω; labeling the curves directly would improve readability.

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The paper

The paper claims

Adding tunable radial velocities to quasi-equilibrium binary black hole initial data reduces orbital eccentricity by about a factor of ten, and the resulting gravitational waveforms overlap the eccentric ones at roughly 0.99.

The reading

Numerical relativity simulations of two black holes spiraling together must start from a snapshot: positions, masses and velocities that satisfy Einstein's constraint equations. The standard recipe assumes the holes sit on perfectly circular orbits at that instant, with zero radial velocity. In practice the simulated orbits wobble, partly because a real inspiraling binary is already falling inward and partly because the initial data are not a perfect snapshot of the inspiral. The authors extend the standard construction so each hole can be given a radial velocity, controlled by one extra number. They then run a feedback loop: evolve the data for about two orbits, fit the measured separation speed to a straight line plus a sine wave, and read off the sine amplitude, which measures the wobble. Adjusting the orbital frequency and the radial velocity using simple Newtonian estimates, then iterating, drives that amplitude down by roughly a factor of ten. Comparing five-orbit evolutions of the original and the tuned data, the authors find most of the difference is a shift in time and phase: the original data simply start at a slightly later point in the inspiral. Once that shift is removed, the two orbits agree, with the original wobbling around the tuned one. The gravitational waveforms agree closely, with overlaps near 0.99 in the dominant quadrupole mode. The eccentricity of the original data also decays as the holes spiral in, at a rate consistent with the classic 1964 Peters prediction when measured from orbital frequency variations, though a different definition of eccentricity gives a shallower decay.

Extended reading notes

Core claim

The central claim is that the eccentricity inherent in quasi-circular initial data does not materially change the gravitational waveform over the last roughly five orbits before merger: 'The gravitational waveforms, which contain ~8 cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99' (abstract; Table 2 reports 0.998 for l=m=2 at both medium and high resolution). If correct, groups using zero-radial-velocity initial data were not injecting a significant waveform systematic over this inspiral length.

Load-bearing premise

The 0.99 overlap rests on comparing h(t) obtained by double-integrating Psi4 with two integration constants C_lm and D_lm that are unknown for a truncated waveform and are fixed by an arbitrary convention (Eq. 35: zero mean and zero first moment over [t1,t2]). Appendix B shows this makes every quoted overlap an upper bound, with a systematic of order 12/(pi N_cyc)^2, about 0.02 for the m=2 modes, which the authors state exceeds the actual mismatch. The headline number is therefore a ceiling rather than a measurement, and the true agreement could sit near 0.97.

Original abstract

Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time. The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964). The gravitational waveforms, which contain $\sim 8$ cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99.

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, 5,727 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.39 · human participants 0.01 · controlled comparison 0.91 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time. The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964). The gravitational waveforms, which contain $\sim 8$ cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99.

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	Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities.	background 1.00	0.23	0.04	asserted 1.00
s1	In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data.	contribution 0.62	0.92	0.07	asserted 1.00
s2	New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data.	method 0.70	0.96	0.26	asserted 1.00
s3	Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time.	result 0.99	0.89	0.08	asserted 1.00
s4	The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964).	result 0.82	0.79	0.07	asserted 0.80
s5	The gravitational waveforms, which contain $\sim 8$ cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data.	result 0.98	0.92	0.21	asserted 1.00
s6	The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99.	result 0.99	0.95	0.25	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.63 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

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.** Evolution of quasi-circular initial data. The left panel shows the proper separation s between the apparent horizons, computed at constant coordinate time along the coordinate line connecting the centers of the horizons, and the right panel shows its time derivative ds/dt. This evolution was run at three different resolutions, with the medium and high resolution tracking each other very closely through the run. the large computational cost of these simulations, only a small number of orbits can be followed. Therefore it is important to begin these simulations with initial data that…

**Figure 2.** Evolution of the orbital phase. The main panel shows the phase of the trajectories of the centers of the apparent horizons as a function of time for the quasicircular (dotted curves) and low-eccentricity (solid curves) initial data. The top left inset shows the phase differences between different resolution runs, which decreases at higher resolutions. The lower right inset shows the difference in the orbital phase between evolutions with different outer boundary locations. 0 200 400 -0.009 -0.006 -0.003 0 d(d)/dt t/MADM QC E2 F2 0 200 400 -0.012 -0.008 -0.004 0 t/MADM ds/dt QC E2 F2

**Figure 3.** Radial velocity during evolutions of quasi-circular and low-eccentricity initial data. The left panel shows the coordinate velocity ˙d(t), the right panel the velocity determined from the intra-horizon proper separation ˙s(t). the influence of the outer boundary on our results to be significant. Our analysis in Sec. 5 is based mostly on comparisons between the high resolution QC and F2 runs

**Figure 4.** Trajectories of the center of the apparent horizons in asymptotically inertial coordinates for the runs E1 (left plot) and QC (right plot). The solid/dashed line distinguish the two black holes; the circles and ellipsoids in the left figure denote the location of the apparent horizon at the beginning and end of the evolution. 5.1. Time shift The black holes approach each other more quickly in the QC run, with the time of coalescence appearing to be about 60MADM earlier than in the F2 run

**Figure 5.** Proper separation (left) and orbital frequency (right) for evolutions of the QC and F initial data. The lower panels show the differences between the time-shifted QC and the F2 runs. The dotted lines in the lower panels show the differences between the E1 and F2 runs, providing an estimate of the remaining eccentricity in the F2 run. the same ∆T = 59MADM also lines up the frequency curves very well. The lower right plot shows the difference in orbital frequency between the F2 run and the time-shifted QC run, δω = ωF(t) − ωQC(t − ∆T). The differences δs and δω are very sensitive to…

**Figure 6.** Orbital eccentricity of the QC evolution estimated from variations in proper separation, es, and from variations in orbital frequency, eω. Also shown in this log-log plot are best-fit power laws to each set of data, as well as the scaling predicted by Peters [8] with power 19/12 ≈ 1.58. data, we expect these eccentricity estimates to be affected by the residual eccentricity of the F run at only the 10% level. The orbital eccentricity of the QC run, estimated using Eqs. (24) and (25), is plotted as a function of proper separation between the black holes in

**Figure 7.** Waveforms for the F2 run. Plotted are the six dominant Ψlm 4 coefficients, scaled by the factor 1000 rMADM. Solid lines represent the real parts and dashed lines the imaginary parts of Ψlm 4 . The time axes are labeled in geometric units at the bottom, and in SI units for a 20+20 M⊙ binary at the top. waveforms at very large radii. The extracted wave signal lags the dynamics of the binary by the light-travel time to the extraction radius, and our evolutions currently fail shortly before merger. So extracting the wave signal at a very large radius would miss the most interesting part…

**Figure 8.** Frequency Ω22 of the gravitational waves extracted from the phase of Ψ22 4 . The left/bottom axes show geometric units, the right/top axes present SI-units for a 20+20 M⊙ binary. The dotted line in the lower panel represents the difference between the E1 and F2 runs. associated with Ψlm 4 is then defined as Ωlm = dφlm dt . (31)

**Figure 9.** Waveforms h lm + (normalized by r/MADM) for the six dominant −2Y lm modes. The solid lines represent evolution of the low-eccentricity initial data (run F2). The dashed lines represent evolution of QC initial data time-shifted by ∆T = 59MADM and phase-rotated by ∆φ = 1.83. The time axes are labeled in geometric units at the bottom and in SI-units for a 20+20 M⊙ inspiral at the top

Figures reproduced from arXiv:gr-qc/0702106 by the authors.

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Adding the neutron star's fundamental oscillation mode to effective-one-body waveforms shifts the predicted gravitational-wave phase by roughly 20 to 30 percent of the static tidal effect, and the extended model match...

Show 48 more citing papers

Binary Neutron Stars with Generic Spin, Eccentricity, Mass ratio, and Compactness - Quasi-equilibrium Sequences and First Evolutions
gr-qc 2015-07 conditional novelty 7.0 of 10

Binary neutron star initial data can now be generated across spin, eccentricity, mass ratio and compactness, and three proof-of-principle evolutions show pre-merger mass transfer, a precession imprint in the (2,1) mod...
Fast and accurate prediction of numerical relativity waveforms from binary black hole coalescences using surrogate models
gr-qc 2015-02 accept novelty 7.0 of 10

A reduced-order surrogate trained on 22 numerical relativity simulations predicts non-spinning binary black hole waveforms across mass ratios 1 to 10 in about a second, with errors comparable to the simulations' numer...
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...
High-accuracy waveforms for binary black hole inspiral, merger, and ringdown
gr-qc 2008-10 accept novelty 7.0 of 10

The first spectral numerical evolution of an equal-mass black hole binary through 16 orbits, merger, and ringdown yields waveforms with roughly 0.02 radians of accumulated phase error and a final hole of mass 0.95162 ...
Maximum gravitational recoil
gr-qc 2007-02 conditional novelty 7.0 of 10

Equal-mass black-hole mergers with counter-aligned in-plane spins produce a gravitational recoil that varies sinusoidally with spin orientation and reaches about 1876 km/s at half-maximal spin, extrapolating to roughl...
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...
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.
Challenges in the nonlinear evolution of unequal mass binaries in sGB gravity
gr-qc 2025-07 conditional novelty 6.0 of 10

First full merger simulations of 2:1 and 3:1 black hole binaries in scalar-Gauss-Bonnet gravity, with weak-coupling dephasing matching PN predictions but strong-coupling results limited by initial-data transients.
The error budget of binary neutron star merger simulations for configurations with high spin
gr-qc 2025-06 accept novelty 6.0 of 10

For highly spinning (chi=0.5) binary neutron stars, evolution code choice is the largest numerical waveform error, and current analytical models disagree with numerical relativity beyond that error after the stars touch.
Black hole merger simulations in wave dark matter environments
gr-qc 2022-10 accept novelty 6.0 of 10

Wave dark matter around an equal-mass black hole binary settles into a persistent, growing spiral cloud, and naive superposition of such a cloud onto a circular binary induces spurious orbital eccentricity.
Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory
gr-qc 2022-09 conditional novelty 6.0 of 10

Numerical relativity and leading-order small-mass-ratio theory for eccentric binary black holes agree to roughly 10%, and the residual, rescaled by the cube of the symmetric mass ratio, collapses onto a single curve p...
Intermediate mass-ratio black hole binaries: Applicability of small mass-ratio perturbation theory
gr-qc 2020-06 conditional novelty 6.0 of 10

Fitting the post-adiabatic expansion to 55 numerical relativity simulations shows that the second-order term is small, so a two-term small-mass-ratio model may cover intermediate mass ratios.
Smooth equations of state for high-accuracy simulations of neutron star binaries
gr-qc 2019-08 conditional novelty 6.0 of 10

Spectral equations of state reduce cost and improve accuracy in SpEC neutron star merger simulations, but the most efficient choice requires an unrealistic low-density recipe.
Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order
gr-qc 2016-05 accept novelty 6.0 of 10

Explicit 3PN-order, leading-order-in-eccentricity phase corrections are derived for the TaylorT1, T2, T3, T4 and F2 post-Newtonian waveform approximants, with the analytic formulas valid up to initial eccentricity abo...
Low mass binary neutron star mergers : gravitational waves and neutrino emission
astro-ph.HE 2015-10 accept novelty 6.0 of 10

In fully general-relativistic mergers of two 1.2 solar-mass neutron stars, only the fundamental post-merger gravitational-wave mode persists, and neutrino transport versus leakage changes disk composition and outflows.
Improved methods for simulating nearly extremal binary black holes
gr-qc 2014-12 accept novelty 6.0 of 10

Improved excision-control and grid methods let numerical-relativity simulations reach black-hole spins of 0.994, producing converged waveforms and remnant data for three binaries, including the first precessing nearly...
Nearly extremal apparent horizons in simulations of merging black holes
gr-qc 2014-11 accept novelty 6.0 of 10

Merging black holes with near-extremal spins produce common apparent horizons that satisfy 8πS < A but approach equality to within 0.3 percent at formation, and a new gauge-invariant extremality lower bound confirms t...
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...
A catalog of 174 binary black-hole simulations for gravitational-wave astronomy
gr-qc 2013-04 conditional novelty 6.0 of 10

174 publicly released numerical binary black-hole simulations, 155 new, extend waveform coverage to 35 orbits, 91 precessing configurations, mass ratios to 8:1, and dimensionless spins to 0.98.
Black hole-neutron star mergers at realistic mass ratios: Equation of state and spin orientation effects
gr-qc 2012-12 accept novelty 6.0 of 10

At mass ratio 7 and black hole spin 0.9, a 2 km change in neutron star radius cuts the post-merger remnant mass by a factor of three, and tilting the black hole spin suppresses disk formation.
Gravitational Recoil From Accretion-Aligned Black-Hole Binaries
gr-qc 2012-01 conditional novelty 6.0 of 10

Partially aligned black-hole spins can produce merger recoils near 4000 to 5000 km/s, and accretion-aligned populations give roughly a 1-in-4000 chance of a line-of-sight kick above 2000 km/s.
Extracting equation of state parameters from black hole-neutron star mergers. I. Nonspinning black holes
astro-ph.HE 2011-09 conditional novelty 6.0 of 10

The tidal deformability of a neutron star, not the full equation of state, is the single parameter Advanced LIGO can extract from a black hole-neutron star merger waveform, to roughly 10-40% at 100 Mpc.
Intermediate-mass-ratio black hole binaries: intertwining numerical and perturbative techniques
gr-qc 2010-08 conditional novelty 6.0 of 10

Feeding numerical-relativity trajectories into a spin-extended Regge-Wheeler-Zerilli code reproduces full numerical waveforms for 1:10 and 1:15 mass-ratio black hole binaries at the 98 to 99.7 percent overlap level.
Simulations of black-hole binaries with unequal masses or non-precessing spins: accuracy, physical properties, and comparison with post-Newtonian results
gr-qc 2010-07 accept novelty 6.0 of 10

New numerical-relativity waveforms for spinning equal-mass and nonspinning unequal-mass black-hole binaries show TaylorT1 is the most robust post-Newtonian phase approximant for spinning cases, while TaylorT4 remains ...
Measuring orbital eccentricity and periastron advance in quasi-circular black hole simulations
gr-qc 2010-04 conditional novelty 6.0 of 10

The gravitational-wave phase gives the cleanest eccentricity estimate for near-circular binary black hole simulations, and the numerically measured periastron advance differs from the 3PN prediction by 3 to 5 percent.
Simulations of Binary Black Hole Mergers Using Spectral Methods
gr-qc 2009-09 conditional novelty 6.0 of 10

A damped-wave gauge, a non-overlapping cubed-sphere grid with spectral filtering, and a compact-support shape-control map let the SpEC spectral code evolve six binary black hole systems through merger and ringdown wit...
High accuracy simulations of black hole binaries:spins anti-aligned with the orbital angular momentum
gr-qc 2009-09 conditional novelty 6.0 of 10

A spectral numerical-relativity simulation follows an equal-mass black hole binary with anti-aligned spins through 10.6 orbits to merger, yielding a calibrated gravitational waveform and remnant mass and spin.
Testing gravitational-wave searches with numerical relativity waveforms: Results from the first Numerical INJection Analysis (NINJA) project
gr-qc 2009-01 accept novelty 6.0 of 10

Blind injection of 126 numerical-relativity black-hole waveforms into simulated LIGO/Virgo noise shows existing search pipelines detect them at expected rates while recovering their masses poorly.
Comparison of Numerical and Post-Newtonian Waveforms for Generic Precessing Black-Hole Binaries
gr-qc 2008-08 conditional novelty 6.0 of 10

For a precessing, unequal-mass black-hole binary, 3.5PN waveforms overlap the numerical ones at 97 to 99 percent over the first six cycles, clearly beating 2.5PN, with agreement degrading as merger approaches.
Binary-black-hole initial data with nearly-extremal spins
gr-qc 2008-05 accept novelty 6.0 of 10

Superposed Kerr-Schild initial data can produce binary black holes with initial spins up to 0.9997, and the spin barely changes during initial relaxation, unlike conformally-flat data.
Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity
gr-qc 2007-10 conditional novelty 6.0 of 10

Equal-mass black hole binaries transition from inspiral to plunge at orbital angular momentum L approximately 0.8 M squared, and orbits at that threshold produce the largest remnant Kerr parameter seen, j approximately 0.724.
A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries
gr-qc 2007-10 conditional novelty 6.0 of 10

A two-parameter analytic waveform family matches numerical-relativity-calibrated binary black hole signals at better than 99% and is significantly more sensitive than inspiral-only or ring-down-only searches over a br...
Where post-Newtonian and numerical-relativity waveforms meet
gr-qc 2007-06 conditional novelty 6.0 of 10

Numerical-relativity and post-Newtonian waveforms for an equal-mass black-hole binary agree in phase within numerical error but differ in amplitude by about 6 percent, and that offset is nearly constant, so only about...
A data-analysis driven comparison of analytic and numerical coalescing binary waveforms: nonspinning case
gr-qc 2007-04 conditional novelty 6.0 of 10

Time-domain effective-one-body and modified frequency-domain templates reach fitting factors above 0.96 against numerical relativity waveforms for nonspinning binary black holes up to 120 solar masses, provided templa...
Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
gr-qc 2007-03 conditional novelty 6.0 of 10

Across seven mass ratios from 1 to 4, post-Newtonian amplitude-frequency relations match numerical black hole merger waveforms until near merger, and cross-checking ringdown fits between multipoles yields final mass a...
Second release of the CoRe database of binary neutron star merger waveforms
gr-qc 2022-10 accept novelty 5.0 of 10

A public catalog of 590 numerical-relativity binary neutron star merger simulations across 254 configurations, with a resolution-based accuracy audit and new fits for merger amplitude, merger frequency, peak luminosit...
A new public code for initial data of unequal-mass, spinning compact-object binaries
gr-qc 2021-03 accept novelty 5.0 of 10

A public Kadath-based solver suite produces constraint-satisfying, eccentricity-reduced initial data for unequal-mass, spinning black-hole, neutron-star, and mixed binaries, including a mass-ratio 0.455 binary neutron...
The SXS Collaboration catalog of binary black hole simulations
gr-qc 2019-04 accept novelty 5.0 of 10

The SXS Collaboration publishes 2018 numerical-relativity black-hole merger simulations with center-of-mass-corrected waveforms, documented file formats, and a resolution-based error budget near 10^-4 mismatch.
Post-Newtonian Quasicircular Initial Orbits for Numerical Relativity
gr-qc 2017-02 conditional novelty 5.0 of 10

Across 40 numerical-relativity runs of spinning black-hole binaries, initial data built from the complete 3PN Hamiltonian plus a radiation-reaction radial momentum produces the lowest residual eccentricity, beating 3P...
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...
The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries
gr-qc 2012-01 conditional novelty 5.0 of 10

A cross-validated catalog of 63 hybrid post-Newtonian/numerical-relativity black-hole waveforms, with cross-code overlaps above 0.97 once maximized over template mass, is released for gravitational-wave search testing.
Faithful Effective-One-Body waveforms of equal-mass coalescing black-hole binaries
gr-qc 2007-12 conditional novelty 5.0 of 10

The Effective-One-Body waveform family, with two tuned parameters, reproduces a numerical equal-mass black-hole merger to within plus or minus 0.005 gravitational-wave cycles over 12 cycles and to better than 1 percen...
Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral
gr-qc 2007-06 conditional novelty 5.0 of 10

Integrating post-Newtonian equations through hundreds of orbits and reading off the momenta at the desired starting separation reduces the eccentricity of equal-mass black-hole binary evolutions by at least a factor of five.
Remnant of binary black-hole mergers: New simulations and peak luminosity studies
gr-qc 2016-10 accept novelty 4.0 of 10

Refitting remnant mass, spin and recoil formulas on 175 binary black hole simulations and adding a new peak luminosity formula, with residuals of about 0.1 to 0.2 percent for mass and spin and about 5 percent for reco...
Modeling the source of GW150914 with targeted numerical-relativity simulations
gr-qc 2016-07 accept novelty 4.0 of 10

Given the same black-hole masses and spins inferred for GW150914, two independent numerical-relativity codes produce waveforms that match to 99.8 percent and remnant masses and spins that agree to three significant figures.
Binary Black Hole Coalescence
gr-qc 2007-10 accept novelty 3.0 of 10

By 2007 numerical relativity had produced stable binary black hole merger simulations whose waveforms are simple enough to be stitched together from analytic inspiral and ringdown models.
Binary neutron-star mergers: a review of Einstein's richest laboratory
gr-qc 2016-07 accept novelty 2.0 of 10

A comprehensive 2016 survey of binary neutron-star merger simulations, covering numerical methods, initial data, post-merger dynamics, magnetic fields, ejecta and nucleosynthesis, with the field's open questions catalogued.
Extraction of Gravitational Waves in Numerical Relativity
gr-qc 2016-06 accept novelty 2.0 of 10

A systematic review of the four methods used to extract gravitational waves from numerical relativity simulations, with first-principles derivations, implementation recipes, and an accuracy comparison.

How later papers used it

73 later papers cite it

Evidence: substantial. 41 of the citing papers share no author with it, and 15 of those carry a confident label from Pith's citation classifier.

Pith read 16 of the 122 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

5 later papers by other authors are listed below: 5 used its method or tool. 5 more papers by the same authors are listed: 5 used its method or tool.

Uses its method or tool 10 of 40 papers with this label · 5 by the same authors

Reduced the eccentricity of the numerical binary by adding small changes to the initial inspiral rate and orbital frequency using the techniques of this paper.

Inspiraling black-hole binary spacetimes: Challenges in transitioning from analytical to numerical techniques (2015) · 1.00 · paraphrased: the licence does not allow quoting
Specifically, we fit for the binary BS coordinate separation $d(t)$ using [equation] and correspondingly for the binary's radial velocity using the fit [equation] Based on this parameterization, the initial orbital frequency $Ω_0$ and initial radial velocity $v_r$ are corrected by [ref] [equation] at each eccentricity iteration step, where $d_0=A_-1$[Note, in general $d_0≠D_0$, as we show below explicitly.].

Generic initial data for binary boson stars (2023) · Eccentricity reduction · 0.99
Estimated the eccentricity with the method described in this paper or in the Appendix of another work, finding a maximum eccentricity after the first orbit of 0.005 except in the 0.3 case.

General relativistic simulations of the quasi-circular inspiral and merger of charged black holes: GW150914 and fundamental physics implications (2020) · 1.00 · paraphrased: the licence does not allow quoting
Reduced the eccentricity by adjusting the initial orbital frequency and radial velocity using the iterative method in this paper, measuring the eccentricity using the puncture tracks.

Conformally curved initial data for charged, spinning black hole binaries on arbitrary orbits (2022) · 1.00 · paraphrased: the licence does not allow quoting
Estimated the residual eccentricity following this paper by fitting the time derivative of the coordinate separation of the two black holes with a function of the given form.

Numerical-relativity simulations of the quasi-circular inspiral and merger of non-spinning, charged black holes: methods and comparison with approximate approaches (2021) · 1.00 · paraphrased: the licence does not allow quoting

By the same authors

Tuned its initially guessed radial velocity and orbital frequency using the iterative scheme described in Sec. 4 of this paper to reduce the eccentricity of the SBS data.

Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data (2008) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Achieved initial eccentricities of at most 5e-4 following this paper, computing initial conditions as in another work.

Effects of neutron-star dynamic tides on gravitational waveforms within the effective-one-body approach (2016) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Adjusted its values following the eccentricity reduction method developed by Pfeiffer et al. in this paper.

Binary Neutron Stars with Arbitrary Spins in Numerical Relativity (2015) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Iteratively adjusted the initial angular and radial velocity of the neutron stars to reduce the initial eccentricity of the orbits to at most 0.002 utilizing the methods of this paper.

Gravitational Waves from Binary Neutron Star Mergers with a Spectral Equation of State (2023) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Obtained low eccentricity of at most 0.005 using the iterative method developed by Pfeiffer et al. in this paper.

Black hole-neutron star mergers for 10 solar mass black holes (2011) (same authors) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

65 arXiv papers cite this in 100 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 · 45 sentences without a confident label

Builds on it 1 paper

First, one can adapt iterative eccentricity-reduction schemes, such as those described in [ref] for uncharged black holes, to systems with charge.

Numerical-relativity simulations of the quasi-circular inspiral and merger of non-spinning, charged black holes: methods and comparison with approximate approaches · Controlling the eccentricity · 0.89

Uses its method or tool 38 papers

In addition, by adding small changes to the initial inspiral rate and orbital frequency, we significantly reduced the eccentricity of the numerical binary using the techniques of Ref. [ref] .

Inspiraling black-hole binary spacetimes: Challenges in transitioning from analytical to numerical techniques · Discussion · 1.00
To handle the above difficulties, we have adopted an iterative method for producing quasicircular NR initial data [ref] : An initial guess is chosen for NR initial data parameters, the binary is evolved for a few orbits using NR and the eccentricity is measured from that evolution, and then the initial guess is updated so as to give smaller eccentricity for the next iteration.

Eccentricity Reduction for Quasicircular Binary Evolutions · Introduction · 0.91
In particular, I use the eccentricity-reduction technique of [ref] (originally developed under the assumption of conformal flatness) so that sets CFMS and SBS both have very little orbital eccentricity.

Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data · Introduction · 0.99

Uses its data or values 1 paper

Figure [ref] shows the properties of the two sets of NR data considered in this study [ref] in terms of inverse mass ratio $m_2/m_1= 1/q$, effective spin parameter $χ_eff$ and precessing spin parameter $χ_p$.

Effective-one-body waveforms for precessing coalescing compact binaries with post-newtonian Twist · Numerical relativity data · 0.98

Cites it as background 3 papers

Additionally, significant effort has been put into generating binary compact object ID featuring low orbital eccentricities [ref] , or generalisations to arbitrary eccentricities [ref] .

A new public code for initial data of unequal-mass, spinning compact-object binaries · Introduction · 0.93
Typically, statements of eccentricity in NR simulations are made through particular measures of coordinate eccentricity [ref] , although there has been some work on applying PN orbital parameterizations a posteriori to NR simulations [ref] .

Nature Abhors a Circle · Introduction · 0.93
For more details see [ref] .

Gravitational waveforms for high spin and high mass-ratio binary black holes: A synergistic use of numerical-relativity codes · Introduction · 0.95

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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