Evolution of Binary Black Hole Spacetimes

Frans Pretorius

REVIEW

Evolution of Binary Black Hole Spacetimes

Frans Pretorius

General Relativity and Quantum Cosmology · Submitted 4 Jul 2005 · 20 references

Pith's verdict: The paper that first carried a non-axisymmetric binary through merger and ringdown; the qualitative claim has held up for twenty years, the quantitative numbers are rougher than the abstract's tone suggests.

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arXiv IDgr-qc/0507014 (version 1)

Pith ID2FDDEMHA, Pith's permanent record of this paper and its review

CitationFrans Pretorius. "Evolution of Binary Black Hole Spacetimes." arXiv:gr-qc/0507014 (2005). https://pith.science/paper/2FDDEMHA

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Editor's note

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You already know the headline: this is the paper that first got a full 3D, non-axisymmetric binary black hole through plunge, merger, and ringdown. That claim has held up. The ingredients are borrowed — generalized harmonic formulation from Garfinkle, constraint damping from Gundlach et al., dynamical excision, compactified outer boundaries, AMR — but the combination is the contribution, and it works. The paper is also unusually honest about what it can't yet do: it says outright that resolution far from the binary prevents an accurate energy estimate, that the amplitude falloff with radius is numerical dissipation, that the extraction radii may be too close, and that the horizon formulas may be applied before the remnant is stationary. That candor is worth crediting, not penalizing. The stress-test's central worry is fair, though: the abstract's 'with sufficient resolution' is backed by convergence tests that are deferred to 'elsewhere' (Sec. I). For a letter that's normal, but it means the resolution study is asserted, not shown, and the spread across the three runs — final masses 1.77/1.85/1.90 M0, spins 0.74/0.73/0.70, radiated energy at r=25M0 of 7.1/5.1/4.7% — is wide enough that the high-resolution numbers aren't demonstrably converged. The 5% figure should be read as order-of-magnitude; the paper's own numbers span 2.1 to 7.1% with no quoted uncertainty. On the spin: the stress-test is right that the two J estimates share the axisymmetry assumption (rotation axis orthogonal to z=0, azimuthal orbits in z=constant), so their agreement is consistency, not independent validation. The paper does flag the assumption as needing confirmation, so it's acknowledged rather than hidden, but the point stands. The Kerr-calibrated Eq. (5) applied to a still-ringing horizon is the weakest single step, partly offset by the dynamical-horizon estimate. None of this touches the existence result. Who should read it: numerical relativists, and anyone building waveform models who needs to know the merger segment is now computable. It deserves a serious referee — accept.

Referee report

Significance

If the result holds, this is a genuine milestone: the last uncomputed segment of the binary black hole waveform — late inspiral, plunge, merger and ringdown — becomes accessible to numerical solution, which is precisely the regime where post-Newtonian and perturbative methods are expected to fail. The paper is candid about what is and is not established, and the qualitative claim (the code survives through coalescence and produces a physically sensible horizon track and waveform) is directly demonstrated by the runs shown in Figs. 1–3 rather than merely asserted. The methodological ingredients — generalized harmonic evolution with constraint damping, excision tracking, compactified outer boundaries — are described concretely enough to be reproduced, and the paper is appropriately framed as a Letter reporting early success rather than a precision measurement. The quantitative layer (remnant parameters, radiated energy) is weaker and is largely flagged as such by the authors themselves.

Major objections (3)

[Sec. III, Table I and Fig. 2] The two determinations of the remnant angular momentum are presented as mutually corroborating, but they are not independent in the way the text implies. The dynamical-horizon estimate explicitly assumes that the rotation axis is orthogonal to the z=0 orbital plane and that each closed orbit of the azimuthal vector field lies in a z=constant surface; the circumference-ratio method of Eq. (5) likewise assumes the polar axis of the horizon coincides with z. Both methods therefore share the same axisymmetry and axis-alignment assumptions, so their agreement constrains the magnitude of J but not the orientation or the axisymmetry of the remnant. A concrete test would be to repeat the Cr-based estimate using polar circles defined about a tilted axis and report the sensitivity of a to that choice; if a is stable at the few-percent level under such variation, the agreement becomes meaningful evidence rather than a consistency check of a shared premise.
[Sec. III, Eq. (5) and Fig. 2 (right panel)] Equation (5) is a fitting formula calibrated to stationary Kerr horizons, so applying it to a highly distorted apparent horizon shortly after merger and recovering a Kerr-like value is partly built into the procedure. The authors acknowledge the timing concern in the sentence beginning 'Remarkably, the dynamical horizon estimate...', but the concern is not resolved by the agreement of the two numbers, since both are calibrated against stationarity. A more probative test would be to show that the recovered a is constant in time over the ringdown once the horizon has settled, and to quantify the residual deviation of the horizon geometry from Kerr (for example, the size of the higher multipole moments of the horizon mass or curvature) as a function of time. If those residuals decay on the ringdown timescale, the claim that the remnant is Kerr with a≈0.70 is well supported; as presented, the claim rests on a formula whose domain of validity is exactly what is in question.
[Sec. III, Eq. (6) and footnote [20]] The radiated-energy estimates decrease monotonically with extraction radius — 4.7%, 3.2%, 2.7%, 2.3% at r = 25, 50, 75, 100 M0 in the high-resolution run — and the paper attributes the decrease to numerical dissipation in the low-resolution wave zone. This means the r→∞ extrapolation is not under control, and the abstract's 'on the order of 5%' is in fact the smallest-radius, most contaminated number. The independent horizon-mass-difference estimate (≈5%) is a useful cross-check, but it carries its own systematic from the same numerical loss of mass after merger that the paper notes in the Fig. 2 caption. The abstract should either quote the full range across extraction radii or attribute the 5% explicitly to the horizon-mass method, and the text should state what fraction of the discrepancy between the two methods is attributable to dissipation rather than to the finite-radius validity of Eq. (6).

Minor objections (7)

[Sec. I, final paragraph of the outline] The outline states 'We conclude in Sec. V', but the manuscript contains no Sec. IV; the sections run I, II, III, then V. Either a section was removed in preparation or the numbering should be corrected.
[Table I, 'initial BH masses' row] The caption defines M0 as the mass of one initial black hole 'measured from the higher resolution simulation', so the high-resolution entry of exactly M0 is definitional rather than a measurement, and only the 0.97M0 and 0.99M0 entries carry information. This should be stated in the caption so the row is not read as three independent determinations.
[Sec. III, Fig. 1 and Table I] The orbital eccentricity is quoted only as a range, 0–0.2, inferred by overlaying reference ellipses. Since the paper's stated goal is to extract orbital information from the waveform, the residual eccentricity matters for the phasing; the authors should state whether the range reflects genuine uncertainty in the initial data parameters or a fit degeneracy, and whether the measured orbit is consistent with zero eccentricity at the available resolution.
[Sec. II, Eq. (1)] The symmetrization notation in the term 2H(α,β) is not defined, and the index structure of the constraint-damping term (in particular the placement of n^γ C_γ relative to g_{αβ}) would benefit from one explicit sentence. The same applies to Eq. (3), where the dimensions of the ξ1 term and the meaning of the η offset in the lapse sector are not explained.
[Sec. III, Fig. 3] The caption notes that the waveforms must be shifted by more than the light travel time between extraction radii, which the authors interpret as evidence that the extraction points are too close to the source. It would help to state the implied systematic on the phase of the extracted waveform, since phase accuracy is what matters for matched filtering.
[Abstract and Sec. V] The 5% figure is quoted relative to 2M0, but the ADM mass of the spacetime is 2.39M0 and roughly 15% of the scalar-field energy does not collapse. The abstract's phrase 'initial rest mass of the system' is therefore ambiguous; the denominator should be stated explicitly wherever the percentage appears.
[Sec. III, waveform discussion] No comparison is made between the extracted waveform and a post-Newtonian or perturbative prediction in the regime where those should still be approximately valid. Even a qualitative overlay during the early inspiral would strengthen the claim that the numerical waveform is physically faithful rather than merely plausible in shape.

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The paper

The paper claims

A numerical code evolves two black holes through their final orbit, merger, and ringdown, producing the first complete strong-field waveform from a non-axisymmetric binary.

The reading

The last uncomputed stretch of a binary black hole's life is the one that matters most for gravitational wave detection: the final orbits, the plunge, the merger, and the ringdown, where perturbation theory stops working and only a full numerical solution of Einstein's equations will do. This paper reports that a code built on generalized harmonic coordinates can evolve an equal-mass, non-spinning binary through exactly that stretch without the simulation falling apart. The author runs one configuration through roughly a single orbit before coalescence, continues past merger, and reads off a remnant black hole with mass about $1.9M_0$ and spin parameter $a$ near $0.70$, plus a rough estimate that about 5% of the initial rest mass leaves as gravitational waves. The point is not the particular numbers, which the paper treats as provisional, but the demonstration that the scheme survives long enough, at achievable resolution, to hand over the waveform segment that analytic methods cannot supply.

What carries the argument

The load-bearing mechanism is the generalized harmonic formulation with constraint damping. Writing the field equations so that the coordinates satisfy a wave-like condition sourced by freely specifiable functions $H_μ$ turns the gauge choice into part of the evolution system rather than an external constraint; the residual constraint violation $C_μ$ is then damped by adding terms proportional to a positive constant $κ$ to the field equations, following the damping scheme the author credits to a Z4 treatment. Around this sit the practical supports that make a binary survivable: a compactified domain with physically correct outer boundary conditions, mesh refinement concentrated near the holes, excision boundaries that move with the apparent horizons, a slicing condition that slows the collapse of the lapse, and numerical dissipation. The paper's own assessment is that the damping terms had little effect without black holes present but a significant effect on how long a black hole evolution stays accurate.

Extended reading notes

Core claim

The claim is that a specific numerical scheme can carry a genuinely three-dimensional, non-axisymmetric binary black hole spacetime through coalescence and ring down, which the paper states had not been done before. The scheme combines several ingredients: field equations written in a generalized harmonic form with freely chosen source functions encoding the gauge, a damping term added to the constraints that the author reports makes a large difference to how long a black hole simulation runs accurately, a spatially compactified grid whose outer boundary sits at infinity, adaptive mesh refinement, and dynamical excision that follows each hole through the grid. The demonstration case is a binary of two equal-mass, non-spinning holes built from collapsing scalar field pulses, with initial proper separation about $16.6M_0$ and orbital angular velocity about $0.023/M_0$, evolved at three resolutions. The remnant is characterised two ways: from horizon area and angular momentum through the Smarr formula, and from the ratio of polar to equatorial horizon circumference through a Kerr fitting formula, with the angular momentum itself taken from a dynamical horizon calculation. Both routes give $a$ between about 0.70 and 0.74, and the paper notes their agreement even shortly after merger, when neither method would obviously be expected to apply.

Load-bearing premise

The remnant's mass and spin are read off a highly distorted, still-changing apparent horizon using formulas derived for stationary black holes, together with an angular momentum estimate that assumes the rotation axis is perpendicular to the orbital plane and that the horizon's rotational orbits lie in flat slices.

Editorial extensions

If this is right

Gravitational wave searches gain access to the merger and ringdown segment of the waveform, the part matched filtering needs and perturbation theory cannot supply.
The radiated energy and final spin of an equal-mass non-spinning merger become quantities a numerical code can compute and other methods can be checked against.
The generalized harmonic formulation with constraint damping becomes a candidate platform for a wider family of binary configurations rather than a one-off.
Because the outer boundary is placed at spatial infinity, wave extraction is not contaminated by an artificial outer edge, in principle.
Constraint damping is identified as a practical lever on simulation lifetime, separate from resolution.

Reading between the lines

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

The paper's own energy estimate varies by roughly a factor of two across extraction radii (4.7% down to 2.3%), which is the signature of dissipation eating the wave amplitude with distance; a converged answer would need the wave zone resolved as well as the holes, and the author says as much.
If the scheme generalises, the natural next tests are unequal masses and non-zero spins, since spin-orbit and spin-spin couplings change both the waveform phasing and the remnant spin, and neither is exercised here.
The agreement between the two independent spin estimators so soon after merger is a check worth pushing harder: if they continue to agree in better-resolved runs, the circumference-ratio formula becomes a cheap diagnostic for near-stationary horizons in dynamical settings.
The scalar field construction of initial data is a workaround for the lack of a clean binary black hole initial data prescription; a reader could reasonably expect the method's real test to come once puncture-style or excision-compatible data are fed to it.

Original abstract

We describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary systems for enough time to extract information about the orbit, merger and gravitational waves emitted during the event. As an example we show results from the evolution of a binary composed of two equal mass, non-spinning black holes, through a single plunge-orbit, merger and ring down. The resultant black hole is estimated to be a Kerr black hole with angular momentum parameter a~0.70. At present, lack of resolution far from the binary prevents an accurate estimate of the energy emitted, though a rough calculation suggests on the order of 5% of the initial rest mass of the system is radiated as gravitational waves during the final orbit and ringdown.

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, 4,333 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.97 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.06 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

We describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary systems for enough time to extract information about the orbit, merger and gravitational waves emitted during the event. As an example we show results from the evolution of a binary composed of two equal mass, non-spinning black holes, through a single plunge-orbit, merger and ring down. The resultant black hole is estimated to be a Kerr black hole with angular momentum parameter a~0.70. At present, lack of resolution far from the binary prevents an accurate estimate of the energy emitted, though a rough calculation suggests on the order of 5% of the initial rest mass of the system is radiated as gravitational waves during the final orbit and ringdown.

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 describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates.	contribution 0.73	0.93	0.12	asserted 1.00
s1	Indications are that with sufficient resolution this scheme is capable of evolving binary systems for enough time to extract information about the orbit, merger and gravitational waves emitted during the event.	interpretation 0.79	0.65	0.42	hedged possibility 1.00
s2	As an example we show results from the evolution of a binary composed of two equal mass, non-spinning black holes, through a single plunge-orbit, merger and ring down.	contribution 0.65	0.95	0.11	asserted 1.00
s3	The resultant black hole is estimated to be a Kerr black hole with angular momentum parameter a~0.70.	result 0.99	0.91	0.17	asserted 0.69
s4	At present, lack of resolution far from the binary prevents an accurate estimate of the energy emitted, though a rough calculation suggests on the order of 5% of the initial rest mass of the system is radiated as gravitational waves during the final orbit and ringdown.	limitation 0.98	0.91	0.09	hedged possibility 0.94

What kind of paper the classifier reports this is: simulation study 0.98 · evidence from simulation or computation 1.00.

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: A depiction of the orbit for the simulation described

**Figure 2.** FIG. 2: The plot to the left shows the net black hole mass

**Figure 3.** FIG. 3: A sample of the gravitational waves emitted during

Figures reproduced from arXiv:gr-qc/0507014 by the authors.

References

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L. Smarr, Ph.D. thesis, University of Texas, Austin, 197 5

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O. Brodbeck, S. Frittelli, P. Huebner and O. A. Reula, J.Math.Phys. 40, 909 (1999)

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C. Gundlach, J.M. Martin-Garcia, G. Calabrese and I. Hinder, gr-qc/0504114 (2005)

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G. B. Cook, Living Rev.Rel. 3, 5 (2000)

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[18]

Typical runtimes on 128 nodes of a Xeon Linux cluster are on the order of a few days for the lowest resolutions attempted, to several months at the higher resolutions

View on Pith
[19]

At this stage we are ignoring all the subtleties in choos ing an “appropriate” tetrad

View on Pith
[20]

the corresponding numbers from the medium(low) res. runs are 5 .1(7.1)%, 3 .5(4.6)%, 2 .5(3.2)%, 1 .7(2.1)%

View on Pith

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GRACE is a validated, open-source, Kokkos+p4est GPU-portable framework that evolves ideal GRMHD with constrained transport self-consistently coupled to Z4c Einstein equations on fixed or adaptive meshes.
Black Hole Black Boxes: Numerical Black Hole Metrics via AInstein Neural Networks
gr-qc 2026-07 conditional novelty 6.0 of 10

Unsupervised Lorentzian PINNs with embedded S^{2} topology recover maximally extended Schwarzschild and yield candidate Petrov type-I vacuum black-hole metrics with genuinely trapped interiors.
Impact of numerical-relativity waveform calibration on parametrized post-Einsteinian tests
gr-qc 2026-03 accept novelty 6.0 of 10

NR late-inspiral calibration systematics in IMRPhenomD produce false ppE GR violations at O5 SNRs ≳60; an uncertainty-aware baseline restores consistency with GR up to SNR 330.
Plunge-Merger-Ringdown Tests of General Relativity with GW250114
gr-qc 2026-01 unverdicted novelty 6.0 of 10

GW250114 data constrains GR deviations in merger amplitude to 10% and frequency to 4% at 90% CL, with first bounds on the (4,4) mode frequency at 6%.
Signatures of a subpopulation of hierarchical mergers in the GWTC-4 gravitational-wave dataset
gr-qc 2026-01 unverdicted novelty 6.0 of 10

Using a joint effective-spin and precession-spin model on 155 gravitational-wave events, the authors infer that the hierarchical (second-generation) merger fraction rises sharply above ~46 M_sun and peaks again near 1...
Quasinormal modes of rotating black holes beyond general relativity in the WKB approximation
gr-qc 2025-12 conditional novelty 6.0 of 10

Higher-order WKB accurately computes quasinormal mode frequencies for rotating black holes beyond general relativity, with errors below current GW measurement precision for GW250114.
First ICCUB Numerical Relativity Waveform Catalog of Eccentric Black Hole Binaries
gr-qc 2025-09 conditional novelty 6.0 of 10

A new open catalog of 128 eccentric equal-mass black hole binary waveform simulations, with up to three close encounters before merger, is released with post-processing tools.
Tidal Love numbers and quasi-normal modes of the ECO in a Dark Matter halo
gr-qc 2025-09 conditional novelty 6.0 of 10

An ECO embedded in a dark matter halo acquires dark-matter-dependent tidal Love numbers and, for a non-relativistic halo profile, gravitational-wave echoes clearly different from the vacuum case.
superB/NRPy: Scalable, Task-Based Numerical Relativity for 3G Gravitational Wave Science
gr-qc 2025-04 conditional novelty 6.0 of 10

superB/NRPy automatically generates distributed-memory Charm++ code from NRPy's BlackHoles@Home modules, showing bitwise agreement with the OpenMP version and strong scaling to 7168 cores.
Stable long-term evolution in numerical relativity
gr-qc 2025-01 conditional novelty 6.0 of 10

Two modified CCZ4 schemes that propagate momentum constraint violations without damping suppress a late-time instability seen in long BSSN black hole simulations.
Quantum correlations in a gravitational collapse simulation with SpheriCo.jl
gr-qc 2024-12 conditional novelty 6.0 of 10

SpheriCo.jl enables longer semiclassical collapse simulations and yields hints of non-trivial correlations of the scalar field across a dynamically formed apparent horizon.
Extracting linear and nonlinear quasinormal modes from black hole merger simulations
gr-qc 2023-10 conditional novelty 6.0 of 10

A public fitting pipeline recovers linear, retrograde and quadratic quasinormal modes from hundreds of binary black hole simulations and yields polynomial formulas for their amplitudes and phases in terms of mass rati...
Dissipative scattering of spinning black holes at fourth post-Minkowskian order
hep-th 2023-08 accept novelty 6.0 of 10

A worldline quantum field theory calculation yields the radiation-reacted momentum impulse, spin kick, scattering angle, and radiated energy and angular momentum for two spinning black holes at fourth post-Minkowskian...
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.
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...
Agnostic black hole spectroscopy: Quasinormal mode content of numerical relativity waveforms and limits of validity of linear perturbation theory
gr-qc 2023-02 conditional novelty 6.0 of 10

Higher quasinormal-mode overtones in binary black hole ringdown fits are overfitting artifacts, not physical modes; only the fundamental mode, the first overtone well after the peak, and spherical-spheroidal mode mixi...
Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
gr-qc 2022-11 conditional novelty 6.0 of 10

Recasting post-Minkowskian scattering results as an effective-one-body radial potential brings analytical predictions of black-hole scattering into roughly one-percent agreement with numerical relativity.
Quasinormal-mode filters: a new approach to analyze the gravitational-wave ringdown of binary black-hole mergers
gr-qc 2022-07 conditional novelty 6.0 of 10

Two frequency-domain filters remove selected quasinormal modes from binary black-hole ringdowns, making subdominant effects visible without time-domain overfitting.
Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
hep-th 2021-12 conditional novelty 6.0 of 10

The complete conservative two-body scattering amplitude and radial action at O(G^4), all orders in velocity, including the tail effect, are derived and checked against post-Newtonian expansions.
Mining the Geodesic Equation for Scattering Data
hep-th 2020-10 accept novelty 6.0 of 10

The perturbed geodesic equation of a test particle can be converted, by a single algebraic substitution, into the leading post-Minkowskian scattering amplitude and isotropic Hamiltonian for tidal, higher-derivative, a...
Leading Nonlinear Tidal Effects and Scattering Amplitudes
hep-th 2020-10 accept novelty 6.0 of 10

Using scattering amplitudes in momentum and position space, the authors derive the leading post-Minkowskian two-body Hamiltonian and eikonal phase for infinitely many tidal operators, including nonlinear curvature pow...
The Eikonal Approximation and the Gravitational Dynamics of Binary Systems
hep-th 2020-09 conditional novelty 6.0 of 10

The thesis derives the conservative two-body dynamics of binaries in Einstein gravity, supergravity, and Kaluza-Klein theory from eikonal resummation, including a D-dimensional 2PM Hamiltonian.
Tidal Effects in the Post-Minkowskian Expansion
hep-th 2020-06 conditional novelty 6.0 of 10

The authors derive the leading and next-to-leading post-Minkowskian tidal corrections to the conservative two-body Hamiltonian for non-spinning neutron stars, including mass and current quadrupoles.
Ready for what lies ahead? -- Gravitational waveform accuracy requirements for future ground based detectors
gr-qc 2019-12 conditional novelty 6.0 of 10

Current gravitational waveform models need roughly three orders of magnitude lower mismatch (one order for numerical relativity waveforms) before third generation detectors can measure binary black hole parameters wit...
Heavy Black Hole Effective Theory
hep-ph 2019-08 conditional novelty 6.0 of 10

Heavy Black Hole Effective Theory derives a heavy-mass effective field theory for scalars and fermions in gravity and gives the second post-Minkowskian scattering amplitude including classical and leading quantum spin...
Spacetime structure near generic horizons and soft hair
hep-th 2019-08 conditional novelty 6.0 of 10

A family of horizon boundary conditions labeled by s yields BMS-like algebras with spin-s supertranslations, while another choice gives a non-linear Heisenberg-like algebra whose generators build the BMS-like ones.
High-accuracy mass, spin, and recoil predictions of generic black-hole merger remnants
gr-qc 2018-09 accept novelty 6.0 of 10

Gaussian-process fits trained directly on precessing numerical-relativity simulations predict black-hole merger remnant mass, spin, and recoil an order of magnitude more accurately than prior formulae, with public code.

See all 121 Pith citations

How later papers used it

422 later papers cite it

Evidence: substantial. 416 of the citing papers share no author with it, and 26 of those carry a confident label from Pith's citation classifier.

Pith read 38 of the 513 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

3 later papers by other authors are listed below: 2 used its method or tool and 1 used its data or values.

Uses its method or tool 2 of 12 papers with this label

Followed this paper's approach in its implementation of the cartoon method for suppressing one spatial dimension when treating axisymmetric data such as Brill waves.

Evolution of Brill waves with an adaptive pseudospectral method (2022) · 1.00 · paraphrased: the licence does not allow quoting
Considered initial data as a superposition of two equal boosted scalar field bubbles, similarly to what this paper did.

Binary Black Holes in Modified Gravity (2023) · 0.96 · paraphrased: the licence does not allow quoting

Uses its data or values 1 of 9 papers with this label

Used this paper's value of about 0.7 for the final spin of the remnant black hole when black holes have no spin before mergers.

Second Order Quasi-Normal Mode of the Schwarzschild Black Hole (2007) · 0.90 · paraphrased: the licence does not allow quoting

How the literature uses it

344 arXiv papers cite this in 417 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 · 176 sentences without a confident label

Uses its method or tool 12 papers

In this subsection, we will follow Refs. [ref] , and perform the 3+1D numerical relativity (NR) [In the past decades, NR has been developed significantly [ref] , which has been applied to the studies on non-perturbative cosmologies, e.g. [ref] .] simulation for the evolution of subcritical bubbles.

Towards supermassive primordial black holes from inflationary bubbles · General-relativistic collapse of subcritical bubble · 0.94
In this work, we will average over different realizations of $n$ by setting $n=0$ and use synthetic numerical relativity (NR) waveforms [ref] both as a model of the input GW signal $h_inj$ (or injection) and as templates $h(λ⃗)$.

Tracking black hole kicks from gravitational wave observations · Introduction · 0.91
Following [ref] we directly discretize the second-order-in time-wave-equations on the mesh, and use a point-wise Gauss-Seidel relaxation method to update the discrete unknowns at each time step.

Generalized harmonic formulation in spherical symmetry · Introduction · 0.99

Uses its data or values 7 papers

The kick velocity could reach thousands of $km s^-1$ for special cases [ref] , and in more ordinary conditions the velocity is on average $400 km s^-1$ (e.g. [ref] ).

Phase shift of gravitational waves induced by aberration · Introduction · 0.90
Different astrophysical models predict a variety of velocities for GW sources, where we consider the following three particularly interesting cases: (i) gravitational kicks which in average have a velocity of $400 km s^-1$ [ref] while extreme kicks of up to $5000 km s^-1$ can occur for some special configurations [ref] , (ii) BBHs, BNSs, and BHNSBs orbiting a SMBH in the center of a galaxy [ref] , where the velocity depends on the mass of the central SMBH and the radius of the orbit – for a SMBH with a typical mass of $10^7 M_⊙$ and for an orbital radius of $5 mpc$ the orbital velocity is around $3000 km s^-1$ while for an orbital radius of $100 R_s$ ($R_s = 2GM/c^2$ is the Schwarzschild radius of a BH with mass $M$) we have a velocity of around 7 % the speed of light, and (iii) the peculiar velocity of galaxies induced by the gravitational interaction of the host galaxy with its environ

Moving gravitational wave sources at cosmological distances: Impact on the measurement of the Hubble constant · Observables for high redshift and fast moving sources · 0.81
Figure [ref] is a reproduction of Figure 3 in of Pretorius' paper [ref] .

Numerical Relativity of Compact Binaries in the 21st Century · Breakthroughs in numerical relativity · 0.92

Compares with it 4 papers

Our studies of evolutions using several coordinate drivers lead us to conclude that, in spherical geometries, the gauge drivers discussed in [ref] are less effective relative to the $3+1$ simulations that use Cartesian coordinates, and it would be very interesting to understand this issue in more detail.

Generalized harmonic formulation in spherical symmetry · Conclusions · 0.94
This is markedly different than in GR [ref] or FJBD [ref] , where spherical dynamical simulations of compact objects present no such problems.

Dynamics of Screening in Modified Gravity · Introduction · 0.97
By looking the black hole as an arc of fixed length, this method will yield gravitational wave forms highly similar with those obtained in numeric relativity method [ref] and black hole perturbation theories [ref] .

Microscopic State of BHs and an Exact One Body Method for Binary Dynamics in General Relativity · Introduction · 0.98

Cites it as support 2 papers

A physical motivation is that the results of numerical relativity [ref] show that the pulse of radiation coming from the merger phase is very short and seems to connect smoothly to the previous inspiral and subsequent ringdown phases.

The Close-Limit Approximation for Black Hole Binaries with Post-Newtonian Initial Conditions · Introduction · 0.99
This desirable behavior can be rigorously shown to hold in perturbations off flat spacetime [ref] and also “experimentally” verified in simulations involving black holes and neutron stars (e.g. [ref] ).

Numerical Relativity and Astrophysics · Brief Review of Techniques, Methods and Information Obtainable from Gravitational Waves · 0.99

Cites it as background 197 papers

This is fundamentally dependent on the detailed knowledge about the structure of the GW emitted from a binary of CO (BH or NS) stemming from decades of analytical [ref] and numerical [ref] studies of GW from binary systems of CO.

Pi from the sky -- A null test of general relativity from a population of gravitational wave observations · Introduction · 0.86
In 2005, two complementary and independent methods were discovered that allowed numerical relativists to completely solve the black-hole binary problem in full strong-field gravity [ref] .

Comparison of Post-Newtonian and Numerical Evolutions of Black-Hole Binaries · Introduction · 0.97
This is the field of NR, which has seen exciting breakthroughs [ref] in the early 2000s, and great strides towards simulating merging black holes with different masses and spins [ref] .

Characterizing the Properties and Constitution of Compact Objects in Gravitational-Wave Binaries · Numerical Relativity Waveforms for the Merger and Ringdown · 0.93

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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