Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme

Frans Pretorius

REVIEW

Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme

Frans Pretorius

General Relativity and Quantum Cosmology · Submitted 28 Feb 2006 · Published version · 45 references

Pith's verdict: A solid methods paper that shows the generalized harmonic scheme with constraint damping works for binary black hole mergers; the zoom-whirl result is honestly flagged as preliminary and not load-bearing.

T0 · AI review

How this review was made: An AI referee (deepseek-v4-flash) read the paper on August 28, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 6 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDgr-qc/0602115 (version 2)

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

CitationFrans Pretorius. "Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme." arXiv:gr-qc/0602115 (2006). https://pith.science/paper/NGNRAYOE

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Colleague,

The main thing to know: this paper does what it claims. It demonstrates that Pretorius's generalized harmonic scheme, with the constraint damping term (14) and the source-function gauge driver (16), can evolve binary black hole spacetimes stably through merger. The evidence is the convergence tests in Sec. IV: the Einstein residual converges at second order in the axisymmetric head-on runs, apparent-horizon mass conservation improves with resolution, and turning off constraint damping crashes every run. That contrast is stark and convincing.

What's actually new here relative to the PRL and the CQG paper [1,14] is the detailed treatment of the damping and gauge terms, plus a candid account of the technical machinery: excision surface tracking, position-dependent dissipation, and the AH finder workarounds near merger. The paper is honest about the AH finder's fragility and the 'tricks' used to push through merger; you get a clear sense of where the method is solid and where it is held together with string.

The soft spots are real but not load-bearing. The zoom-whirl n(v) data in Sec. V is explicitly tentative. The per-orbit numerical error in AH mass (a few percent) is larger than the energy lost to gravitational waves, and the author says plainly that significant conclusions cannot be drawn yet. I agree with that self-assessment. The 3D 'comparison' in Fig. 8 is not a same-initial-data convergence test because the boost parameter is re-tuned per resolution; the paper discloses this, so it is a fair limitation, but it means quantitative 3D accuracy is less firmly established than the axisymmetric results. The lack of released code is a mild reproducibility ding, though the public adaptive mesh libraries are referenced. The free parameters (κ, ξ1, ξ2, η) are hand-picked, but the paper shows a range of κ works and the gauge parameters affect slicing rather than the physics, so this is not a fitting exercise. Citation pattern is appropriate: Gundlach et al. for constraint damping, Lindblom et al. for first-order GH, and the relevant numerical relativity literature.

Bottom line: this is a genuinely useful methods paper for anyone building or using generalized harmonic codes, and for numerical relativists assessing what was needed to break the binary black hole problem. It deserves serious peer review and, on the evidence here, acceptance. I would take the zoom-whirl part as a flagged observation, not a claim.

Referee report

Significance

If the scheme is accepted as working, this paper is an important methods contribution supporting the first successful full binary-black-hole coalescence simulation. The central claim is supported by concrete, reproducible evidence: the Einstein residual converges at approximately second order (Figs. 2-3), AH mass conservation improves monotonically with resolution (Fig. 1), and turning off constraint damping leads to rapid growth of constraints and crashes (Figs. 4-6), providing a controlled test of the damping mechanism. The paper is unusually transparent about limitations, including apparent-horizon-finder robustness issues near merger (Sec. III C), the fact that the 3D runs are not a same-initial-data convergence test because the boost parameter is re-tuned per resolution (Sec. IV D and Table III), and the explicit caveat that the tentative zoom-whirl claim is not yet supported by sufficiently accurate simulations (Sec. V). These disclosures do not undermine the central capability claim; they correctly delimit its quantitative scope.

Minor objections (6)

[Sec. IV A, Table I] In Table I the word 'summerized' should be 'summarized', and the phrase 'were each resolution is labeled' should read 'where each resolution is labeled.'
[Sec. III C] The sentence beginning 'In leu of a more robust AH finder' has a typo: 'leu' should be 'lieu.'
[Sec. II B] The phrase 'the GH numerical code descrided here' contains a typo: 'descrided' should be 'described.'
[Sec. IV C] The text 'at t = 200M αmin = 0.458' appears to be missing the subscript 0 on M; it should read 't = 200M0' for consistency with the rest of the paper.
[Sec. V] There are a few missing spaces and minor typos in the prose, e.g., 'for somev =vc' should be 'for some v = vc', and 'v⋆ loosely defined above' would be clearer as 'the loosely defined v⋆.'
[Sec. IV D / Sec. V] The paper notes that the 3D simulations are not a same-initial-data convergence test because the boost parameter differs slightly between resolutions; this is a real limitation of the quantitative 3D accuracy assessment, and the author should consider stating this more prominently in the discussion of Fig. 8, though the point is already disclosed.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Generalized harmonic coordinates with constraint damping and a lapse-driving source function give stable, convergent evolution of binary black hole spacetimes through merger, with a tentative hint of zoom-whirl orbits.

The reading

This paper seeks to establish that the Einstein equations, recast in generalized harmonic coordinates with two additions—a constraint-damping term and a dynamical equation for the time source function—can be evolved numerically through the full binary black hole process: inspiral, merger, ringdown, and gravitational-wave extraction. A sympathetic reader would care because this is the kind of stable, convergent evolution needed to predict the gravitational-wave signals that ground-based detectors are designed to observe. The paper shows convergence of the solutions, demonstrates that without constraint damping the simulations crash before merger, and shows that the gauge-driving equation keeps the lapse from collapsing near horizons. It also presents an early, explicitly tentative result: equal-mass, nonspinning binaries formed by scalar-field collapse appear to whirl for more orbits the closer the initial boost is to a threshold value, reminiscent of zoom-whirl geodesics. The paper itself cautions that accumulating numerical error makes this last observation preliminary.

What carries the argument

The load-bearing object is the generalized harmonic decomposition of the Einstein equations, in which the coordinates are promoted to dynamical variables through source functions $H^a$, making the metric equations manifestly hyperbolic. Two mechanisms carry the argument: the constraint-damping modification (Eq. 14), which adds terms proportional to the constraint functions $C_a$ with coefficient $\kappa$ so that constraint-violating modes decay rather than grow, and the source-function evolution equation (Eq. 16), a damped wave equation for $H^t$ that drives the lapse toward 1 and prevents coordinate collapse near black holes. The scheme is completed by black-hole excision guided by apparent horizons, adaptive mesh refinement, and Kreiss-Oliger dissipation near the holes.

Extended reading notes

Core claim

The central claim is that the generalized harmonic system, with the constraint-damping term of Eq. (14) and the source-function evolution law of Eq. (16), is a workable scheme for binary black hole spacetimes. In the paper's words, it provides further details of the scheme 'shown to be capable of simulating binary black hole coalescence.' Concretely: with constraint damping parameter $\kappa$ of order $1/M_0$, the constraint-violating modes that otherwise grow and crash the runs are suppressed, and the lapse-driving equation prevents the lapse from falling to values near $0.1$ that cause instabilities in pure harmonic gauge. The secondary, tentative discovery is that for equal-mass nonspinning binaries from scalar-field collapse, the number of orbits before merger or separation increases as the boost parameter $v$ approaches a threshold $v_\star$, a fully nonlinear analogue of the zoom-whirl behavior of point-particle geodesics; the paper shows data at three resolutions but explicitly warns that numerical error per orbit is comparable to radiation-reaction energy loss, 'so one cannot yet draw significant conclusions from these early results.'

Load-bearing premise

The numerical error accumulated per orbit (a few percent change in apparent-horizon mass at the finest runs) must be smaller than the physical radiation-reaction effect that decides whether the binary merges or separates near the threshold boost; the paper states this error is relatively large and that the zoom-whirl conclusion is therefore tentative.

Editorial extensions

If this is right

If the scheme is correct, complete inspiral–merger–ringdown waveforms for equal-mass nonspinning binaries are computable in full general relativity, providing direct predictions for gravitational-wave observatories.
Constraint damping of the kind used here should suppress constraint-violating modes in other hyperbolic formulations of Einstein's equations, since the paper demonstrates it works in a fully nonlinear strong-field setting without fine-tuning $\kappa$.
The source-function driving law yields a 'symmetry-seeking' gauge that settles to a nearly time-independent lapse at late times, which simplifies horizon finding and wave extraction for long evolutions.
The fine-tuned scalar-field binaries give a one-parameter family in which the merger-versus-separation outcome is extremely sensitive to the boost $v$, offering a controlled probe of strong-field black-hole interactions if the per-orbit numerical error can be reduced.

Reading between the lines

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

If higher-resolution runs confirm the growth of orbit number near $v_\star$, binary black hole mergers would exhibit a form of extreme sensitivity to initial conditions, meaning small perturbations could decide whether a near-threshold binary merges or separates; this would be a genuinely non-perturbative strong-field effect rather than a radiation-reaction feature.
The pattern $n(v)$ rising as $v\to v_\star$ suggests a scaling law analogous to critical gravitational collapse, such as $n\sim -\gamma\ln|v-v_\star|$; testing this scaling at the next few resolutions would give a quantitative falsifier beyond the present qualitative observation.
Because the scalar-field initial data starts the binary in a strongly interacting state, the zoom-whirl suggestion may be tied to this particular data; applying the same gauge and damping scheme to quasi-circular, astrophysically motivated initial data would show whether the effect persists in more realistic binaries.

Original abstract

A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole problem. This includes demonstrations of the effectiveness of constraint damping, and how the time slicing can be controlled through the use of a source function evolution equation. In addition, some results from an ongoing study of binary black hole coalescence, where the black holes are formed via scalar field collapse, are shown. Scalar fields offer a convenient route to exploring certain aspects of black hole interactions, and one interesting, though tentative suggestion from this early study is that behavior reminiscent of "zoom-whirl" orbits in particle trajectories is also present in the merger of equal mass, non-spinning binaries, with appropriately fine-tuned initial conditions.

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, 3,702 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.83 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.13 · 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.

A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole problem. This includes demonstrations of the effectiveness of constraint damping, and how the time slicing can be controlled through the use of a source function evolution equation. In addition, some results from an ongoing study of binary black hole coalescence, where the black holes are formed via scalar field collapse, are shown. Scalar fields offer a convenient route to exploring certain aspects of black hole interactions, and one interesting, though tentative suggestion from this early study is that behavior reminiscent of "zoom-whirl" orbits in particle trajectories is also present in the merger of equal mass, non-spinning binaries, with appropriately fine-tuned initial conditions.

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	A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole problem.	contribution 0.77	0.77	0.09	asserted 0.98
s1	This includes demonstrations of the effectiveness of constraint damping, and how the time slicing can be controlled through the use of a source function evolution equation.	method 0.52	0.85	0.08	asserted 1.00
s2	In addition, some results from an ongoing study of binary black hole coalescence, where the black holes are formed via scalar field collapse, are shown.	contribution 0.81	0.92	0.06	asserted 1.00
s3	Scalar fields offer a convenient route to exploring certain aspects of black hole interactions, and one interesting, though tentative suggestion from this early study is that behavior reminiscent of "zoom-whirl" orbits in particle trajectories is also present in the merger of equal mass, non-spinning binaries, with appropriately fine-tuned initial conditions.	result 0.67	0.88	0.23	hedged possibility 0.96

What kind of paper the classifier reports this is: simulation study 0.60 · 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.** FIG. 1: The normalized sum of total AH mass (29) as a func

**Figure 3.** FIG. 3: The order of convergence (37) calculated from the

**Figure 4.** FIG. 4: The normalized sum of total AH mass (29) as a func

**Figure 5.** FIG. 5: A norm of the residual of the Einstein equations (2),

**Figure 6.** FIG. 6: Norms of the residual of the Einstein equations

**Figure 7.** FIG. 7: The lapse function

**Figure 8.** FIG. 8: Comparison plots of the norm of the residual of the

**Figure 10.** FIG. 10: Estimates of the angular momentum of the fi

**Figure 11.** FIG. 11: A plot of the orbits of the 3

**Figure 12.** FIG. 12: A plot of the orbit of the

**Figure 13.** FIG. 13: A plot of the orbits of two of the 6

**Figure 14.** FIG. 14: Gravitational waveforms from the two simulations

Showing 12 of the paper's 14 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:gr-qc/0602115 by the authors.

References

Works cited (45)

[1]

F. Pretorius, “Evolution of Binary Black Hole Space- times”, Phys. Rev. Lett. 95, 121101 (2005)

View on Pith 2005
[2]

M. Campanelli, C.O. Lousto, P. Marronetti and Y. Zlo- chower, “Accurate Evolutions of Orbiting Black-Hole Bi- naries Without Excision”, Phys. Rev. Lett. 96, 111101 (2006)

View on Pith 2006
[3]

J. G. Baker, J. Centrella, D. Choi, M. Koppitz and J. van Meter, “Gravitational Wave Extraction from an In- spiraling Conﬁguration of Merging Black Holes”, Phys. Rev. Lett.96, 111102 (2006)

View on Pith 2006
[4]

T. Nakamura, K. Oohara and Y. Kojima, Prog. Theor. Phys. Suppl. 90, 1 (1987)

View on Pith 1987
[5]

M. Shibata and T. Nakamura, “Evolution of three- dimensional gravitational waves: Harmonic slicing case”, Phys. Rev. D52, 5428 (1995)

View on Pith 1995
[6]

T. W. Baumgarte and S.L. Shapiro, “Numerical inte- gration of Einstein’s ﬁeld equations”, Phys. Rev. D59, 024007 (1999)

View on Pith 1999
[7]

M. Campanelli, C.O. Lousto and Y. Zlochower, “The Last Orbit of Binary Black Holes”, Phys. Rev. D73, 061501 (2006)

View on Pith 2006
[8]

J. G. Baker, J. Centrella, D. Choi, M. Koppitz and J. van Meter, “Binary Black Hole Merger Dynamics and Waveforms”, Phys. Rev. D73, 104002 (2006)

View on Pith 2006
[9]

F. Herrmann, D. Shoemaker and P. Laguna, “Unequal- Mass Binary Black Hole Inspirals”, gr-qc/0601026 (2006)

View on Pith Pith review arXiv 2006
[10]

J. G. Baker, J. Centrella, D. Choi, M. Koppitz, J. van Meter and M. Coleman Miller, “Getting a kick out of numerical relativity”, astro-ph/0603204 (2006)

View on Pith Pith review arXiv 2006
[11]

M. Campanelli, C.O. Lousto and Y. Zlochower, “Gravi- tational radiation from spinning-black-hole binaries: Th e orbital hang up”, gr-qc/0604012 (2006)

View on Pith Pith review arXiv 2006
[12]

B. Brugmann, “Binary Black Hole Mergers in 3d Numer- ical Relativity,” Int. J. Mod. Phys. D 8, 85 (1999)

View on Pith 1999
[13]

B. Bruegmann, W. Tichy and N. Jansen “Numerical simulation of orbiting black holes”, Phys.Rev.Lett. 92 211101, (2004)

View on Pith 2004
[14]

F. Pretorius, “Numerical Relativity Using a Generaliz ed Harmonic Decomposition”, Class. Quant. Grav. 22 425, (2005)

View on Pith 2005
[15]

L. Lindblom, M. A. Scheel, L. E. Kidder, R. Owen and O. Rinne, “A New Generalized Harmonic Evolution Sys- tem”, gr-qc/0512093 (2005)

View on Pith Pith review arXiv 2005
[16]

G. B. Cook and H. P. Pfeiﬀer, “Excision boundary condi- tions for black hole initial data,” Phys. Rev. D 70, 104016 (2004)

View on Pith 2004
[17]

A. Buonanno, G. Cook and F. Pretorius, in preparation

View on Pith
[18]

D. Garﬁnkle, “Harmonic coordinate method for simulat- ing generic singularities”, Phys.Rev. D65, 044029 (2002)

View on Pith 2002
[19]

B. Szilagyi, B. G. Schmidt and J. Winicour, “Boundary conditions in linearized harmonic gravity,” Phys. Rev. D 65, 064015 (2002)

View on Pith 2002
[20]

B. Szilagyi and J. Winicour, “Well-Posed Initial- Boundary Evolution in General Relativity”, Phys.Rev. D68, 041501 (2003)

View on Pith 2003
[21]

M. C. Babiuc, B. Szilagyi and J. Winicour, “Test- 16 ing numerical relativity with the shifted gauge wave,” gr-qc/0511154 (2005)

View on Pith Pith review arXiv 2005
[22]

M. C. Babiuc, B. Szilagyi and J. Winicour, “Har- monic Initial-Boundary Evolution in General Relativity,” Phys.Rev. D73, 064017 (2006)

View on Pith 2006
[23]

C. Gundlach, J. M. Martin-Garcia, G. Calabrese and I. Hinder, “Constraint damping in the Z4 formulation and harmonic gauge,” Class. Quant. Grav. 22, 3767 (2005)

View on Pith 2005
[24]

O. Brodbeck, S. Frittelli, P. Hubner and O. A. Reula, “Einstein’s equations with asymptotically stable con- straint propagation,” J. Math. Phys. 40, 909 (1999)

View on Pith 1999
[25]

C. Bona, T. Ledvinka, C. Palenzuela and M. Zacek, “General-covariant evolution formalism for Numerical Relativity”, Phys. Rev. D67, 104005 (2003)

View on Pith 2003
[26]

H. Friedrich, “Hyperbolic reductions for Einstein’s e qua- tions”, Class. Quant. Grav. 13, 1451 (1996)

View on Pith 1996
[27]

J. Balakrishna, G. Daues, E. Seidel, W. Suen, M. Tobias, E. Wang, “Coordinate Conditions and Their Implemen- tation in 3D Numerical Relativity”, Class. Quant. Grav. 13, L135 (1996)

View on Pith 1996
[28]

M. Alcubierre, B. Bruegmann, P. Diener, M. Koppitz, D. Pollney, E. Seidel, R. Takahashi, “Gauge conditions for long-term numerical black hole evolutions without exci- sion”, Phys. Rev. D67, 084023 (2003)

View on Pith 2003
[29]

L. Lindblom and M.A. Scheel, “Dynamical Gauge Condi- tions for the Einstein Evolution Equations”, Phys. Rev. D67, 124005 (2003)

View on Pith 2003
[30]

M. Alcubierre, A. Corichi, J. A. Gonzalez, D. Nunez, FIG. 14: Gravitational waveforms from the two simulations depicted in Fig. 13. What is shown here are the two po- larizations of one of the dominant spin weight − 2 spherical harmonic components of Ψ 4 (32), calculated over a coordinate sphere a distance r = 50 M0 from the origin, and normalized by rM0....

View on Pith 2005
[31]

C. Bona, J. Carot and C. Palenzuela-Luque, “Almost- stationary motions and gauge conditions in general rela- tivity,” Phys. Rev. D 72, 124010 (2005)

View on Pith 2005
[32]

C. Bona, L. Lehner and C. Palenzuela-Luque, “Geomet- rically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementa- tions,” Phys. Rev. D 72, 104009 (2005)

View on Pith 2005
[33]

G. B. Cook, “Initial Data for Numerical Relativity”, Liv- ing Rev.Rel. 3, 5 (2000)

View on Pith 2000
[34]

R. Arnowitt, S. Deser and C.W. Misner, in Gravitation: An Introduction to Current Research, ed. L. Witten, New York, Wiley (1962)

View on Pith 1962
[35]

H. Friedrich, “On the Hyperbolicity of Einstein’s and Other Gauge Field Equations”, Commun. Math. Phys 100, 525 (1985)

View on Pith 1985
[36]

PAMR (Parallel Adaptive Mesh Reﬁnement) and AMRD (Adaptive Mesh Reﬁnement Driver) libraries (http://laplace.physics.ubc.ca/Group/Software.html)

View on Pith
[37]

G. Calabrese, “Finite diﬀerencing second order system s describing black hole spacetimes”, Phys. Rev. D 71, 027501 (2005)

View on Pith 2005
[38]

A. Ashtekar and B. Krishnan “Isolated and dynamical horizons and their applications,” Living Rev. Rel. 7, 10 (2004)

View on Pith 2004
[39]

S.R. Brandt and E. Seidel, “The Evolution of Dis- torted Rotating Black Holes II: Dynamics and Analysis”, Phys.Rev. D52, 870 (1995)

View on Pith 1995
[40]

A. Nerozzi, C. Beetle, M. Bruni, L. M. Burko and D. Poll- ney, “Towards wave extraction in numerical relativity: The quasi-Kinnersley frame,” Phys. Rev. D 72, 024014 (2005)

View on Pith 2005
[41]

L. Smarr, in Sources of Gravitational Radiation , ed. L. Smarr, Seattle, Cambridge University Press (1978)

View on Pith 1978
[42]

J. Thornburg, “Finding Apparent Horizons in Numerical Relativity”, Phys. Rev. D54, 4899 (1996)

View on Pith 1996
[43]

J. Thornburg, “Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity,” gr-qc/0512169 (2005)

View on Pith Pith review arXiv 2005
[44]

C. Cutler, D. Kenneﬁck and E. Poisson, “Gravita- tional radiation reaction for bound motion around a Schwarzschild black hole,” Phys. Rev. D 50, 3816 (1994)

View on Pith 1994
[45]

K. Glampedakis and D. Kenneﬁck, “Zoom and whirl: Ec- centric equatorial orbits around spinning black holes and their evolution under gravitational radiation reaction,” Phys. Rev. D 66, 044002 (2002)

View on Pith 2002

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 179 citations worldwide. Full citation record

Evolution of Einstein-scalar-Gauss-Bonnet gravity using a modified harmonic formulation
gr-qc 2020-11 conditional novelty 8.0 of 10

Full nonlinear three-dimensional evolutions of Einstein-scalar-Gauss-Bonnet gravity, including a binary black hole merger, are stable and convergent once the generalized harmonic formulation is modified with auxiliary...
Large Merger Recoils and Spin Flips From Generic Black-Hole Binaries
gr-qc 2007-01 accept novelty 8.0 of 10

A generic spinning, unequal-mass black-hole merger produces recoil kicks up to about 1830 km/s (extrapolating to nearly 4000 km/s for maximal spins) and flips the remnant spin by 103 degrees.
Spinning-black-hole binaries: The orbital hang up
gr-qc 2006-04 conditional novelty 8.0 of 10

Equal-mass black hole binaries with spins aligned with the orbital angular momentum merge later, radiate more energy, and leave a faster-spinning remnant than anti-aligned or spinless binaries.
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...
Getting a kick out of numerical relativity
astro-ph 2006-03 conditional novelty 7.0 of 10

A 1.5:1 nonspinning black-hole merger recoils at about 92 km/s according to numerical relativity, a value between the leading post-Newtonian estimates.

Show 3 more citing papers

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...
Post-Newtonian corrections to the gravitational-wave memory for quasicircular, inspiralling compact binaries
gr-qc 2008-11 accept novelty 5.0 of 10

The post-Newtonian corrections to the Christodoulou gravitational-wave memory for quasicircular inspiralling binaries are computed to 3PN order, with explicit expressions for the plus polarization and the m=0 spherica...
Review of strongly coupled regimes in gravity with Dyson-Schwinger approach
gr-qc 2026-03 unverdicted novelty 3.0 of 10

Dyson-Schwinger methods applied to gravity theories produce conformally flat metrics and a sequence of cosmological phase transitions from conformal symmetry breaking that non-minimal scalar couplings can suppress.

How the literature uses it

17 arXiv papers cite this in 27 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 · 15 sentences without a confident label

Uses its method or tool 4 papers

In our implementation we follow Pretorius [ref] by adding constraint damping terms in a fashion inspired by studies of the so-called $$-systems [ref] .

Generalized harmonic formulation in spherical symmetry · Generalized harmonic formulation · 1.00
A method that we use to damp constraints violations consists of adding to the equations ([ref]) the term of the form [ref] ,

On critical collapse of gravitational waves · The equations and a method of their solution · 0.98
We solve the equations of motion [ref] using the generalized harmonic formulation as described in [ref] .

Evolution of black holes through a nonsingular cosmological bounce · Numerical methodology · 1.00

Compares with it 1 paper

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

Cites it as support 1 paper

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 4 papers

Recent developments in Numerical Relativity (NR) have provided complete simulations of BBH dynamics in the strong-field regime, i.e. during the late-inspiral and merger phases [ref] .

Template Banks for Binary black hole searches with Numerical Relativity waveforms · Introduction · 0.86
Since the first stable evolutions of black-hole-binary mergers [ref] , and after it was established that the gravitational waveforms from these evolutions were universal, and consistent across codes and methodologies [ref] , researchers have turned their attention to how the results of numerical relativity can most usefully be supplied to the gravitational-wave data-analysis community.

Mergers of black-hole binaries with aligned spins: Waveform characteristics · Introduction · 0.93
The recent impressive breakthroughs in numerical relativity (NR) [ref] have given us access to extremely valuable, and reliable, information about the dynamics and radiation of binary black hole coalescence.

Comparing Effective-One-Body gravitational waveforms to accurate numerical data · Introduction · 0.83

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.

[1] [1]

F. Pretorius, “Evolution of Binary Black Hole Space- times”, Phys. Rev. Lett. 95, 121101 (2005)

View on Pith 2005

[2] [2]

M. Campanelli, C.O. Lousto, P. Marronetti and Y. Zlo- chower, “Accurate Evolutions of Orbiting Black-Hole Bi- naries Without Excision”, Phys. Rev. Lett. 96, 111101 (2006)

View on Pith 2006

[3] [3]

J. G. Baker, J. Centrella, D. Choi, M. Koppitz and J. van Meter, “Gravitational Wave Extraction from an In- spiraling Conﬁguration of Merging Black Holes”, Phys. Rev. Lett.96, 111102 (2006)

View on Pith 2006

[4] [4]

T. Nakamura, K. Oohara and Y. Kojima, Prog. Theor. Phys. Suppl. 90, 1 (1987)

View on Pith 1987

[5] [5]

M. Shibata and T. Nakamura, “Evolution of three- dimensional gravitational waves: Harmonic slicing case”, Phys. Rev. D52, 5428 (1995)

View on Pith 1995

[6] [6]

T. W. Baumgarte and S.L. Shapiro, “Numerical inte- gration of Einstein’s ﬁeld equations”, Phys. Rev. D59, 024007 (1999)

View on Pith 1999

[7] [7]

M. Campanelli, C.O. Lousto and Y. Zlochower, “The Last Orbit of Binary Black Holes”, Phys. Rev. D73, 061501 (2006)

View on Pith 2006

[8] [8]

J. G. Baker, J. Centrella, D. Choi, M. Koppitz and J. van Meter, “Binary Black Hole Merger Dynamics and Waveforms”, Phys. Rev. D73, 104002 (2006)

View on Pith 2006

[9] [9]

F. Herrmann, D. Shoemaker and P. Laguna, “Unequal- Mass Binary Black Hole Inspirals”, gr-qc/0601026 (2006)

View on Pith Pith review arXiv 2006

[10] [10]

J. G. Baker, J. Centrella, D. Choi, M. Koppitz, J. van Meter and M. Coleman Miller, “Getting a kick out of numerical relativity”, astro-ph/0603204 (2006)

View on Pith Pith review arXiv 2006

[11] [11]

M. Campanelli, C.O. Lousto and Y. Zlochower, “Gravi- tational radiation from spinning-black-hole binaries: Th e orbital hang up”, gr-qc/0604012 (2006)

View on Pith Pith review arXiv 2006

[12] [12]

B. Brugmann, “Binary Black Hole Mergers in 3d Numer- ical Relativity,” Int. J. Mod. Phys. D 8, 85 (1999)

View on Pith 1999

[13] [13]

B. Bruegmann, W. Tichy and N. Jansen “Numerical simulation of orbiting black holes”, Phys.Rev.Lett. 92 211101, (2004)

View on Pith 2004

[14] [14]

F. Pretorius, “Numerical Relativity Using a Generaliz ed Harmonic Decomposition”, Class. Quant. Grav. 22 425, (2005)

View on Pith 2005

[15] [15]

L. Lindblom, M. A. Scheel, L. E. Kidder, R. Owen and O. Rinne, “A New Generalized Harmonic Evolution Sys- tem”, gr-qc/0512093 (2005)

View on Pith Pith review arXiv 2005

[16] [16]

G. B. Cook and H. P. Pfeiﬀer, “Excision boundary condi- tions for black hole initial data,” Phys. Rev. D 70, 104016 (2004)

View on Pith 2004

[17] [17]

A. Buonanno, G. Cook and F. Pretorius, in preparation

View on Pith

[18] [18]

D. Garﬁnkle, “Harmonic coordinate method for simulat- ing generic singularities”, Phys.Rev. D65, 044029 (2002)

View on Pith 2002

[19] [19]

B. Szilagyi, B. G. Schmidt and J. Winicour, “Boundary conditions in linearized harmonic gravity,” Phys. Rev. D 65, 064015 (2002)

View on Pith 2002

[20] [20]

B. Szilagyi and J. Winicour, “Well-Posed Initial- Boundary Evolution in General Relativity”, Phys.Rev. D68, 041501 (2003)

View on Pith 2003

[21] [21]

M. C. Babiuc, B. Szilagyi and J. Winicour, “Test- 16 ing numerical relativity with the shifted gauge wave,” gr-qc/0511154 (2005)

View on Pith Pith review arXiv 2005

[22] [22]

M. C. Babiuc, B. Szilagyi and J. Winicour, “Har- monic Initial-Boundary Evolution in General Relativity,” Phys.Rev. D73, 064017 (2006)

View on Pith 2006

[23] [23]

C. Gundlach, J. M. Martin-Garcia, G. Calabrese and I. Hinder, “Constraint damping in the Z4 formulation and harmonic gauge,” Class. Quant. Grav. 22, 3767 (2005)

View on Pith 2005

[24] [24]

O. Brodbeck, S. Frittelli, P. Hubner and O. A. Reula, “Einstein’s equations with asymptotically stable con- straint propagation,” J. Math. Phys. 40, 909 (1999)

View on Pith 1999

[25] [25]

C. Bona, T. Ledvinka, C. Palenzuela and M. Zacek, “General-covariant evolution formalism for Numerical Relativity”, Phys. Rev. D67, 104005 (2003)

View on Pith 2003

[26] [26]

H. Friedrich, “Hyperbolic reductions for Einstein’s e qua- tions”, Class. Quant. Grav. 13, 1451 (1996)

View on Pith 1996

[27] [27]

J. Balakrishna, G. Daues, E. Seidel, W. Suen, M. Tobias, E. Wang, “Coordinate Conditions and Their Implemen- tation in 3D Numerical Relativity”, Class. Quant. Grav. 13, L135 (1996)

View on Pith 1996

[28] [28]

M. Alcubierre, B. Bruegmann, P. Diener, M. Koppitz, D. Pollney, E. Seidel, R. Takahashi, “Gauge conditions for long-term numerical black hole evolutions without exci- sion”, Phys. Rev. D67, 084023 (2003)

View on Pith 2003

[29] [29]

L. Lindblom and M.A. Scheel, “Dynamical Gauge Condi- tions for the Einstein Evolution Equations”, Phys. Rev. D67, 124005 (2003)

View on Pith 2003

[30] [30]

M. Alcubierre, A. Corichi, J. A. Gonzalez, D. Nunez, FIG. 14: Gravitational waveforms from the two simulations depicted in Fig. 13. What is shown here are the two po- larizations of one of the dominant spin weight − 2 spherical harmonic components of Ψ 4 (32), calculated over a coordinate sphere a distance r = 50 M0 from the origin, and normalized by rM0....

View on Pith 2005

[31] [31]

C. Bona, J. Carot and C. Palenzuela-Luque, “Almost- stationary motions and gauge conditions in general rela- tivity,” Phys. Rev. D 72, 124010 (2005)

View on Pith 2005

[32] [32]

C. Bona, L. Lehner and C. Palenzuela-Luque, “Geomet- rically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementa- tions,” Phys. Rev. D 72, 104009 (2005)

View on Pith 2005

[33] [33]

G. B. Cook, “Initial Data for Numerical Relativity”, Liv- ing Rev.Rel. 3, 5 (2000)

View on Pith 2000

[34] [34]

R. Arnowitt, S. Deser and C.W. Misner, in Gravitation: An Introduction to Current Research, ed. L. Witten, New York, Wiley (1962)

View on Pith 1962

[35] [35]

H. Friedrich, “On the Hyperbolicity of Einstein’s and Other Gauge Field Equations”, Commun. Math. Phys 100, 525 (1985)

View on Pith 1985

[36] [36]

PAMR (Parallel Adaptive Mesh Reﬁnement) and AMRD (Adaptive Mesh Reﬁnement Driver) libraries (http://laplace.physics.ubc.ca/Group/Software.html)

View on Pith

[37] [37]

G. Calabrese, “Finite diﬀerencing second order system s describing black hole spacetimes”, Phys. Rev. D 71, 027501 (2005)

View on Pith 2005

[38] [38]

A. Ashtekar and B. Krishnan “Isolated and dynamical horizons and their applications,” Living Rev. Rel. 7, 10 (2004)

View on Pith 2004

[39] [39]

S.R. Brandt and E. Seidel, “The Evolution of Dis- torted Rotating Black Holes II: Dynamics and Analysis”, Phys.Rev. D52, 870 (1995)

View on Pith 1995

[40] [40]

A. Nerozzi, C. Beetle, M. Bruni, L. M. Burko and D. Poll- ney, “Towards wave extraction in numerical relativity: The quasi-Kinnersley frame,” Phys. Rev. D 72, 024014 (2005)

View on Pith 2005

[41] [41]

L. Smarr, in Sources of Gravitational Radiation , ed. L. Smarr, Seattle, Cambridge University Press (1978)

View on Pith 1978

[42] [42]

J. Thornburg, “Finding Apparent Horizons in Numerical Relativity”, Phys. Rev. D54, 4899 (1996)

View on Pith 1996

[43] [43]

J. Thornburg, “Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity,” gr-qc/0512169 (2005)

View on Pith Pith review arXiv 2005

[44] [44]

C. Cutler, D. Kenneﬁck and E. Poisson, “Gravita- tional radiation reaction for bound motion around a Schwarzschild black hole,” Phys. Rev. D 50, 3816 (1994)

View on Pith 1994

[45] [45]

K. Glampedakis and D. Kenneﬁck, “Zoom and whirl: Ec- centric equatorial orbits around spinning black holes and their evolution under gravitational radiation reaction,” Phys. Rev. D 66, 044002 (2002)

View on Pith 2002