Colliding Black Holes: The Close Limit

Jorge Pullin; Richard H. Price

REVIEW

Colliding Black Holes: The Close Limit

Richard H. Price, Jorge Pullin

General Relativity and Quantum Cosmology · Submitted 22 Feb 1994 · 11 references

Pith's verdict: The founding close-limit paper: the mu0 scaling is a genuine prediction, but the 'extends' in the abstract leans on an agreement the authors themselves call unexplained.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 13, 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 →

· 3 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDgr-qc/9402039 (version 1)

Pith IDEO4A62YL, Pith's permanent record of this paper and its review

CitationJorge Pullin, Richard H. Price. "Colliding Black Holes: The Close Limit." arXiv:gr-qc/9402039 (1994). https://pith.science/paper/EO4A62YL

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

This is the paper that started the close-limit approximation, and it holds up. The real content is not the perturbation machinery, which is borrowed from Cunningham-Price-Moncrief and Zerilli, but the observation that for Misner's two-throat data the entire mu0 dependence factors out into a single multiplicative function p(mu0). That means one Zerilli evolution gives the answer for all separations, and the shape of the energy curve is a prediction rather than a fit. The chain from Misner data through the Schwarzschild-coordinate form of F, the quadrupole extraction, and Eqs. (11)-(13) is written out explicitly enough to redo. They check the Q2 = 0 constraint, and the evolved wave reproduces the known quasinormal frequency and the -6 tail exponent. Those are real internal consistency checks, not decoration. The comparison to Anninos et al. is an external benchmark against independent code, which is the right way to make this case. The result Energy/2M = 3.07e-6 p(mu0)^2 is clean and useful, and the general recipe, feed any near-Schwarzschild initial data through this pipeline, is the part that outlived the specific numbers. On soft spots: the stress-test concern about the epsilon power counting is fair but narrower than it sounds. The selection-rule argument after Eq. (10), that nonlinear terms cannot generate a given multipole at the order where it first appears linearly, is sound as far as it goes. What is missing is any bound on the size of the neglected terms, since epsilon = 1/|ln mu0| is only logarithmically small. So the truncation to ell=2 is plausible, not controlled. The 'agrees with and extends' in the abstract is the sentence that overreaches: the agreement beyond small mu0 is empirical, and the authors say so themselves, calling it intriguing. That is an acknowledged limitation, not a hidden one, but the abstract should not get to claim it without the hedge the body supplies. Two smaller things: 3.07e-6 is quoted with no accuracy estimate, which matters for a paper whose selling point is being a benchmark, and Fig. 3 is a visual log-log comparison with no residuals. Neither is fatal. Who should read it: anyone doing binary black hole numerics who wants a cheap cross-check, and anyone thinking about perturbation theory as a tool for numerically known data. Worth a serious referee, and worth citing.

Referee report

Significance

The result is a genuinely parameter-free prediction of the shape of the energy curve: the entire mu0 dependence is analytic and factors out of the evolution, so only one numerical coefficient is computed and the rest is derived. The paper also ships two independent internal consistency checks that are not merely decorative: the constructed data explicitly satisfy the initial-value constraint Q2 = 0 of CPM, and the evolved waveform reproduces both the known quadrupolar quasinormal frequency and the predicted -6 power-law tail exponent. The prediction is falsifiable against full numerical relativity and, if it holds, provides both a cheap complement to nonlinear simulations in the close regime and a benchmark for code verification. The forward-looking remark that the method extends to numerically-known initial data is a useful and concrete program.

Major objections (3)

[Abstract, sentence s3, and Fig. 3] The abstract states without qualification that the computed radiation 'agrees with and extends' the full numerical results, but the theoretical apparatus of the paper supports only the small-mu0 regime. The expansion parameter introduced after Eq. (10) is epsilon = 1/|ln mu0|, which is 0.43 at mu0 = 0.1 and divergent at mu0 = 1, and the authors themselves describe the agreement at larger mu0 as 'intriguing' because it lies 'considerably beyond the small-mu0 region in which our approximation is expected to be applicable.' The body of the paper is appropriately candid about this, but the abstract is not. Either the abstract claim should be scoped to the regime the derivation controls, or the paper should supply a quantitative justification for the extended agreement. As it stands the 'extends' half of the headline claim rests on an empirical coincidence the authors do not explain.
[Eqs. (6), (9), (11), and the paragraph following Eq. (10)] The truncation to l=2 is the load-bearing approximation, and the paper never estimates the size of the leading neglected multipole. From the paper's own Eq. (6), with coth^2 = 1 + csch^2, one finds kappa_4/kappa_2 = (1/(4 Sigma1))^2 (Sigma1 + 2 Sigma3 + Sigma5)/(Sigma1 + Sigma3), which is approximately 1/(16 Sigma1(mu0)^2). Evaluating Sigma1 from Eq. (7) gives a ratio of a few percent at mu0 = 1 but of order unity by mu0 approximately 2, which is precisely where Fig. 3 claims agreement. Since the l=4 channel contributes to the radiated energy at quadratic order and adds incoherently with l=2, this could be a tens-of-percent effect on the total energy in the region of the 'extends' claim. The paper should either compute the l=4 contribution explicitly or state the mu0 range over which it is demonstrably negligible, and this estimate would in any case sharpen the discussion of where the close-limit approximation breaks down.
[Eq. (16) and Fig. 2] The single number 3.07e-6 is the paper's entire quantitative output and enters the central result of Eq. (16), yet the manuscript gives no information about the numerical evolution that produced it: no grid or spectral resolution, no convergence study, no statement of the numerical error, and no discussion of the fact that the waveform is extracted at finite radius r* = 200 rather than at null infinity. Because the radiation amplitude falls as 1/r*, the finite-radius extraction requires a correction or an extrapolation before the energy can be quoted as radiated to infinity. A short paragraph reporting the resolution, an estimate of the discretization error, and the finite-r* correction (or a demonstration that it is below the quoted precision) is needed for the reader to attach an uncertainty to Eq. (16).

Minor objections (8)

[Eq. (3)] The definition of the Schwarzschild radial coordinate is printed as R = (r^{1/2} + sqrt(r - 2M))^2, which is dimensionally inconsistent since it adds a length^{1/2} to a length. Presumably the intended expression is R = (1/2)(sqrt(r) + sqrt(r - 2M))^2; please correct or clarify.
[Eqs. (4) and (5)] The prefactor (1 - M/2R)^{-4} in Eq. (4) and the factor (1 + M/2R)^{-1} in the summation of Eq. (5) should be reconciled explicitly, since a reader cannot immediately see that the two forms of F agree at the order retained.
[Eq. (9) and Eq. (11)] It would strengthen the paper to state explicitly that Eq. (9) is only the leading mu0 -> 0 asymptotic form, and that the p(mu0) actually used in Eq. (11) is the exact expression built from Eq. (7) rather than its asymptotic truncation. This is a genuine virtue of the construction and is currently left implicit.
[Fig. 3 caption] The figure caption attributes the numerical relativity points to reference [3], whereas the text attributes them to Anninos et al. [5]. Please make the citation consistent.
[Figs. 1 and 2 captions] The captions should quote the theoretical values alongside the measured ones: the predicted quasinormal period of 8.4 and the predicted tail exponent of -6 are mentioned in the text but the comparison is easier to assess if both numbers appear in the captions.
[Paragraph preceding Eq. (1)] The statement that an apparent horizon at R approximately 2M surrounds both throats for mu0 < 1.36 should carry an explicit attribution, since it is a quantitative input to the argument that the exterior geometry is nearly spherical.
[Eq. (15)] The coefficient 1/(348 pi) in the power formula should be accompanied by a one-line statement of the units and conventions used (G = c = 1, 2M = 1), so that the normalization can be checked against CPM (III-28).
[Fig. 1 and Fig. 2] The captions embedded in the text and the captions printed with the figures differ in wording and in the description of the r* coordinate; these should be made identical in the final version.

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

The paper

The paper claims

Two black holes that start out close enough to share one horizon can be treated as a small quadrupole distortion of a single black hole, and the energy they radiate is a fixed number times an analytic function of the initial separation.

The reading

The paper asks a narrow but practical question: how much gravitational radiation do two black holes emit when they begin so close together that a single horizon already encloses both? The authors' answer is that in this close limit the pair is a slight, non-spherical dimple on one Schwarzschild black hole, so linear perturbation theory applies, and the whole radiation problem collapses to evolving one quadrupole function with the Zerilli equation. Because the initial data are proportional to a single separation-dependent factor $p(μ_0)$, the evolved waveform scales with that factor and the radiated energy with its square, so one numerical evolution covers every separation. The payoff is a closed-form energy curve, $E/2M = 3.07×10^{-6}[p(μ_0)]^2$, that reproduces the full nonlinear numerical relativity results and predicts waveforms and ringing periods that codes can be checked against. The authors are explicit that the Misner data they use are chosen for mathematical convenience rather than because they are the most natural momentarily static configuration of two close holes.

What carries the argument

The load-bearing device is the reduction of Misner's two-throat data to a single quadrupole perturbation of Schwarzschild, plus the claim that this truncation is controlled. The authors argue order-by-order in $ε$ that the $ℓ=2$ piece of the vacuum equations is linear in $1-F$ (where $F$ is the conformal factor relating the Misner slice to Schwarzschild), that nonlinear terms cannot generate an $ℓ=6$ piece until higher order in $ε$, and that the argument generalizes to any $ℓ$. That lets them write the only nonvanishing metric perturbations as $H_2 = K = g(r)p(μ_0)$ with $g(r) = M^3/[8R^3(1+M/2R)]$, build the Cunningham–Price–Moncrief function $Q_1$, rescale it to $ψ = √(4π/5) Q_1/λ$ with $λ = 1 + 3M/2r$, and evolve $ψ$ from rest with the $ℓ=2$ Zerilli equation. The radiated power is then a fixed constant times $|∂ψ/∂t|^2$, as given by CPM (III-28). Separating the $μ_0$ dependence into the multiplicative factor $p(μ_0)$ is what makes a single numerical evolution sufficient.

Extended reading notes

Core claim

Starting from Misner's bispherical initial data for two momentarily static throats, the authors recast the geometry in Schwarzschild coordinates and expand in $ε ≡ 1/|ln μ_0|$. In that expansion the coefficient of each multipole is $κ_ℓ ≈ ζ(ℓ+1)/(4|ln μ_0|)^{ℓ+1}$, so at small separation the quadrupole dominates, and the deviation of the conformal factor from unity is a pure $ℓ=2$ perturbation of a single black hole. Feeding that perturbation into the gauge-invariant Cunningham–Price–Moncrief variables and evolving with the $ℓ=2$ Zerilli equation gives a radiated energy of $3.07×10^{-6}$ in units where $2M=1$, for the normalization $p(μ_0)=1$. The central claim is that the energy for any separation is therefore $E/2M = 3.07×10^{-6}[p(μ_0)]^2$ with $p(μ_0) = Σ_1(μ_0) + Σ_3(μ_0)/[Σ_1(μ_0)]^3$, and that this curve matches the full numerical relativity values of Anninos and collaborators, agreeing well beyond the small-$μ_0$ regime where the approximation was expected to hold.

Load-bearing premise

The argument that at small separation the quadrupole term alone matters, and that it can be treated by linear perturbation theory, rests on an order-by-order counting in $ε = 1/|ln μ_0|$ rather than on a controlled expansion with an error bound.

Editorial extensions

If this is right

The radiated energy from initially close black holes is predicted analytically as $E/2M = 3.07×10^{-6}[p(μ_0)]^2$, so no separate nonlinear simulation is needed for each starting separation.
The method predicts waveforms as well as energy: quasinormal ringing with period $8.4$ (in units $2M=1$) and a late-time power-law tail with exponent $-6$, both matching theoretical values, which gives numerical codes concrete targets to reproduce.
The close-limit result complements the quasi-Newtonian approximation that works at large separation, so the two together, bridged by full numerical relativity, cover the whole range of initial separations.
The same procedure can be applied to other momentarily static initial data, including data known only numerically, whenever those data represent a perturbation of a single black hole.
Because the $μ_0$ dependence factors out exactly, the shape of the energy curve is fixed in advance and only one overall coefficient has to be computed.

Reading between the lines

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

The factorization of $μ_0$ gives a coefficient-free test of any numerical relativity code: the ratio of radiated energies at two different starting separations is fixed analytically, so a code can be checked without ever matching an absolute amplitude.
The suppression of the next multipole is only logarithmic. The $ℓ=4$ amplitude scales as $(4|ln μ_0|)^{-5}$ against $(4|ln μ_0|)^{-3}$ for $ℓ=2$, a relative factor of order $ε^2$, so including $ℓ=4$ would be a sharp probe of whether the $ε$ power counting really controls the expansion.
The agreement persisting past the point where a common horizon forms suggests the radiation is set by how nearly spherical the exterior geometry is, rather than by the detailed shape of the merged horizon, which would make the close-limit result insensitive to the choice of initial data family.
A practical extension is a hybrid pipeline: take any numerically constructed close-hole initial data, project out its quadrupole piece, and evolve that single function to get an inexpensive estimate of the waveform before committing to a full nonlinear run.

Original abstract

The problem of the mutual attraction and joining of two black holes is of importance as both a source of gravitational waves and as a testbed of numerical relativity. If the holes start out close enough that they are initially surrounded by a common horizon, the problem can be viewed as a perturbation of a single black hole. We take initial data due to Misner for close black holes, apply perturbation theory and evolve the data with the Zerilli equation. The computed gravitational radiation agrees with and extends the results of full numerical computations.

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, 3,552 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The problem of the mutual attraction and joining of two black holes is of importance as both a source of gravitational waves and as a testbed of numerical relativity. If the holes start out close enough that they are initially surrounded by a common horizon, the problem can be viewed as a perturbation of a single black hole. We take initial data due to Misner for close black holes, apply perturbation theory and evolve the data with the Zerilli equation. The computed gravitational radiation agrees with and extends the results of full numerical computations.

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	The problem of the mutual attraction and joining of two black holes is of importance as both a source of gravitational waves and as a testbed of numerical relativity.	background 1.00	0.05	0.04	asserted 1.00
s1	If the holes start out close enough that they are initially surrounded by a common horizon, the problem can be viewed as a perturbation of a single black hole.	background 0.62	0.08	0.05	asserted 0.77
s2	We take initial data due to Misner for close black holes, apply perturbation theory and evolve the data with the Zerilli equation.	method 0.98	0.95	0.05	asserted 0.96
s3	The computed gravitational radiation agrees with and extends the results of full numerical computations.	result 0.98	0.89	0.81	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.79 · 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

Showing 1 of the paper's 3 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:gr-qc/9402039 by the authors.

References

Works cited (11)

[1]

A. A. Abramovici et al. , Science 256, 325 (1992), and references therein

View on Pith 1992
[2]

C. Cutler et al. , Phys. Rev. Lett. 70, 2984 (1993)

View on Pith 1993
[3]

L. L. Smarr, Ph.D. dissertation, University of Texas at A ustin, unpublished (1975); K. R. Eppley, Ph.D. dissertatio n, Princeton University, unpublished (1977)

View on Pith 1975
[4]

L. L. Smarr, in Sources of Gravitational Radiation, ed. L. L. Smarr (Cambridge University Press, Cambridge, 197 9)

View on Pith
[5]

P. Anninos, D. Hobill, E. Seidel, L. Smarr, W.-M. Suen, Ph ys. Rev. Lett. 71, 2851 (1993)

View on Pith 1993
[6]

C. Misner, Phys. Rev. 118, 1110 (1960)

View on Pith 1960
[7]

C. Cunningham, R. Price, V. Moncrief, Ap. J. 230, 870 (1979)

View on Pith 1979
[8]

V. Moncrief, Ann. Phys. (NY), 88, 323 (1974)

View on Pith 1974
[9]

F. Zerilli, Phys. Rev. Lett. 24, 737 (1970)

View on Pith 1970
[10]

E. W. Leaver, Proc. R. Soc. London A402, 285 (1985)

View on Pith 1985
[11]

C. Gundlach, R. H. Price and J. Pullin, Phys. Rev. D49, 883 (1994). FIG. 1. The function ψ of the Cunningham-Price-Moncrief perturbation scheme for Misner’s initial data. The values shown are for p(µ0) = 1, and for units in which 2 M = 1. For the r∗ coordinate the horizon is at r∗ = −∞ andr∗ ∼r for large positive values. FIG. 2. Time evolution of the Misn...

View on Pith Pith review arXiv 1994

Forward citations

Cited by 21 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Foundations of Direct Waves in Schwarzschild Ringdown
gr-qc 2026-07 accept novelty 7.0 of 10

Direct waves in filtered Schwarzschild ringdown are the anti-causal filter-pole contribution sourced by near-horizon trajectory dynamics and do not vanish.
Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
gr-qc 2009-10 conditional novelty 7.0 of 10

Renormalizing a published self-force result to physical units and mapping it onto the Effective One Body Hamiltonian yields a tentative constraint on two EOB parameters that numerical relativity alone left degenerate.
Black Hole Ringdown Nonlinearities in the Large-D Limit
gr-qc 2026-06 unverdicted novelty 6.0 of 10

In the large-D limit, analytic third-order nonlinear corrections to quasinormal modes improve ringdown modeling accuracy by several orders of magnitude for head-on black hole collisions.
Nonlinearities of Schwarzschild Black Hole Head-on Collisions
gr-qc 2025-08 unverdicted novelty 6.0 of 10

Quadratic quasi-normal mode amplitudes in Schwarzschild head-on collisions can be derived analytically via second-order perturbation theory bootstrapping.
Nonlinear Effects In Black Hole Ringdown From Scattering Experiments I: spin and initial data dependence of quadratic mode coupling
gr-qc 2024-01 conditional novelty 6.0 of 10

The quadratic coupling coefficient of the l=m=2 black hole ringdown mode is governed by the Kerr background, falling by about a factor of two from spin 0 to 0.99 and staying nearly fixed under large changes in initial data.

Show 16 more citing papers

Challenges in Quasinormal Mode Extraction: Perspectives from Numerical solutions to the Teukolsky Equation
gr-qc 2023-09 accept novelty 6.0 of 10

Fitting black hole ringdown with the full spatial profile of quasinormal eigenfunctions, rather than time series alone, stably recovers the fundamental mode and first two overtones but not n>=3 overtones when a transi...
Non-linear Black Hole Ringdowns: an Analytical Approach
gr-qc 2023-08 conditional novelty 6.0 of 10

Second-order black hole ringdown modes can be computed analytically from a light-ring-localized quadratic source, and the ratio of second-order to squared first-order amplitude is nearly independent of initial conditions.
Numerical computation of second order vacuum perturbations of Kerr black holes
gr-qc 2020-10 conditional novelty 6.0 of 10

A pseudo-spectral time-domain code evolves second-order vacuum perturbations of Kerr black holes, showing that a linear m=2 wave drives second-order m=0 and m=4 waves that ring down at the expected quasinormal frequencies.
Second Order Perturbations of Kerr Black Holes: Reconstruction of the Metric
gr-qc 2020-08 conditional novelty 6.0 of 10

The authors give an explicit chain of Newman-Penrose transport equations that reconstructs the first-order Kerr metric perturbation from the Teukolsky solution alone, and demonstrate it at leading order in a large-dis...
Equilibration rates in a strongly coupled nonconformal quark-gluon plasma
hep-th 2015-03 conditional novelty 6.0 of 10

Quasinormal mode frequencies in the nonconformal N=2* holographic plasma stay within a factor of about two of the conformal value, so equilibration is set by temperature rather than by the symmetry-breaking scale.
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...
Boundary Conditions for Kerr-AdS Perturbations
hep-th 2013-02 accept novelty 6.0 of 10

Two Robin boundary conditions on the Teukolsky master variables are derived that yield asymptotically global AdS gravitational perturbations of Kerr-AdS, and they map onto the scalar and vector sectors of the Kodama-I...
Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms
gr-qc 2012-02 conditional novelty 6.0 of 10

A calibrated effective-one-body model reproduces numerical-relativity waveforms of non-precessing spinning black-hole binaries with mismatch below 0.003 in the Advanced LIGO band for total masses of 20 to 200 solar masses.
A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole
gr-qc 2009-03 conditional novelty 6.0 of 10

The authors construct gauge-invariant second-order Zerilli and Regge-Wheeler equations for arbitrary pairs of first-order modes on Schwarzschild, with sources regularized at the horizon and at null infinity, plus a fo...
Ringdown Signatures of Dehnen Dark Matter Halos: Fluid Modes and Detectability with Space-Based Detectors
gr-qc 2026-05 unverdicted novelty 5.0 of 10

Numerical ringdown waveforms for black holes in Dehnen dark matter profiles are generated and analyzed for detectability and parameter inference using second-generation TDI in space-based detectors such as LISA, Taiji...
Estimating False Alarm Rates of Sub-Dominant Quasi-normal Modes in GW190521
gr-qc 2022-09 conditional novelty 5.0 of 10

Injection studies of 500 simulated GW190521-like signals without a (3,3,0) ringdown mode show that only about 2% produce Bayes factors as large as the 56 measured for the real event, supporting the claimed detection.
Holographic isotropization linearized
hep-th 2013-04 conditional novelty 5.0 of 10

Linearizing Einstein's equations around the final black brane reproduces event-horizon entropy production to roughly 20 percent across hundreds of far-from-equilibrium states, and adding higher-order corrections makes...
Accuracy of the Post-Newtonian Approximation: Optimal Asymptotic Expansion for Quasi-Circular, Extreme-Mass Ratio Inspirals
gr-qc 2008-03 conditional novelty 5.0 of 10

For quasi-circular extreme-mass-ratio inspirals, the post-Newtonian energy flux has its widest region of validity near 3PN order and appears to diverge at higher orders, likely because of logarithmic terms.
Perturbations of Black Holes Surrounded by Anisotropic Matter Field
gr-qc 2024-11 conditional novelty 4.0 of 10

For a black hole with anisotropic matter hair, quasinormal mode frequencies shift monotonically with the matter strength K, and the shift also appears in shadow radius and grey-body factors.
The Effective One Body description of the Two-Body problem
gr-qc 2009-06 accept novelty 3.0 of 10

The Effective One Body formalism, using a parameter-free resummation of the radiation reaction and only two adjustable strong-field coefficients, reproduces numerical relativity binary black hole waveforms to within t...
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.

How later papers used it

48 later papers cite it

Evidence: substantial. 48 of the citing papers share no author with it, and 11 of those carry a confident label from Pith's citation classifier.

Pith read 15 of the 82 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

2 later papers by other authors are listed below: 2 compared their own results with it.

Compares with it 2 of 4 papers with this label

Solved an equation with two approaches, reproducing in both cases the literature results for head-on black hole collisions with the close limit approach.

Applications of the close-limit approximation: horizonless compact objects and scalar fields (2021) · 0.90 · paraphrased: the licence does not allow quoting
Found that its total energy agrees with this paper's within one percent.

Challenging theories of gravitation: dark matter, compact objects and gravitational waves (2021) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

41 arXiv papers cite this in 72 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 · 48 sentences without a confident label

Builds on it 1 paper

It is important to restress that we want to use the linearized approximation without necessarily restricting to the initial data being small perturbations of the AdS-Schwarzschild black brane, precisely in the spirit of the original close-limit approximation [ref] but now in the context of AdS spacetime.

Holographic isotropization linearized · Leading order correction to the pressure anisotropy · 0.86

Uses its method or tool 4 papers

In order to model BBH configurations, we use results from the Close Limit Approximation (CLAP) of binary BHs [ref] .

CLAP for modified gravity: scalar instabilities in binary black hole spacetimes · Introduction · 1.00
A possible way to circumvent the above problem is to use an alternative approach, in particular the close-limit approximation (CLAP) [ref] .

Applications of the close-limit approximation: horizonless compact objects and scalar fields · Introduction · 0.87
The CLAP formalism of BBHs in GR succeeded to consistently describe such configurations [ref] , and we will use this approximation in what follows.

Challenging theories of gravitation: dark matter, compact objects and gravitational waves · Binary black hole background · 0.90

Compares with it 3 papers

We have solved Eq. [ref] using two different approaches (see Appendix [ref] for details), reproducing in both cases the results in the literature for head-on BBH collisions with the CLAP approach [ref] .

Applications of the close-limit approximation: horizonless compact objects and scalar fields · Perturbations and their time evolution · 0.90
The total energy obtained with our computation agrees with that of Ref. [ref] within one percent.

Challenging theories of gravitation: dark matter, compact objects and gravitational waves · Perturbations and their time evolution · 1.00
* Using the Misner initial data [ref] as given by Price & Pullin [ref] , we reproduced in the case of head-on collision the waveform of their Fig. 2 and the associated radiated energy; cf. Eq. (16) in [ref] .

The Close-Limit Approximation for Black Hole Binaries with Post-Newtonian Initial Conditions · Numerical evolution · 0.93

Cites it as support 3 papers

A second notable support to Simplicity and Universality is the Close-Limit approximation due to Pullin, Price, Gleiser, Khanna and collaborators [ref] .

Airy-function approach to binary black hole merger waveforms: The fold-caustic diffraction model · Asymptotic Reasoning and Structural Stability · 1.00
Once a common horizon has formed, the geometry on a suitable Cauchy slice and in its future domain of dependence can be viewed as a perturbed remnant BH — a picture supported by the successes of the close-limit approximation [ref] , the Lazarus project [ref] , and the hybrid approach [ref] , which treat suitable post-merger regions perturbatively while retaining agreement with NR.

Foundations of Direct Waves in Schwarzschild Ringdown · Discussion · 0.96
Additional motivation for the EOB treatment of the transition from plunge to ring-down came from work on the, so-called, “close limit approximation” [ref] .

The general relativistic two body problem · EOB description of the conservative dynamics of two body systems · 0.96

Cites it as background 6 papers

0.5cm The Close limit approximation – The CLA was originally introduced in Ref. [ref] (see also Ref. [ref] for further analytical developments).

Nonlinearities of Schwarzschild Black Hole Head-on Collisions · Introduction · 0.83
On the other hand, the close-limit approximation consists of an expansion in powers of the dimensionless ratio considered small[In the works [ref] , the CL parameter is defined as $c^2 r_12/ (G M)$.

The Close-Limit Approximation for Black Hole Binaries with Post-Newtonian Initial Conditions · Introduction · 0.87
In the last stage the oscillation ceases with a power-law tail [ref] .

Black hole spectroscopy: prospects for testing the nature of black holes with gravitational wave observations · Black hole perturbation theory · 0.87

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]

A. A. Abramovici et al. , Science 256, 325 (1992), and references therein

View on Pith 1992

[2] [2]

C. Cutler et al. , Phys. Rev. Lett. 70, 2984 (1993)

View on Pith 1993

[3] [3]

L. L. Smarr, Ph.D. dissertation, University of Texas at A ustin, unpublished (1975); K. R. Eppley, Ph.D. dissertatio n, Princeton University, unpublished (1977)

View on Pith 1975

[4] [4]

L. L. Smarr, in Sources of Gravitational Radiation, ed. L. L. Smarr (Cambridge University Press, Cambridge, 197 9)

View on Pith

[5] [5]

P. Anninos, D. Hobill, E. Seidel, L. Smarr, W.-M. Suen, Ph ys. Rev. Lett. 71, 2851 (1993)

View on Pith 1993

[6] [6]

C. Misner, Phys. Rev. 118, 1110 (1960)

View on Pith 1960

[7] [7]

C. Cunningham, R. Price, V. Moncrief, Ap. J. 230, 870 (1979)

View on Pith 1979

[8] [8]

V. Moncrief, Ann. Phys. (NY), 88, 323 (1974)

View on Pith 1974

[9] [9]

F. Zerilli, Phys. Rev. Lett. 24, 737 (1970)

View on Pith 1970

[10] [10]

E. W. Leaver, Proc. R. Soc. London A402, 285 (1985)

View on Pith 1985

[11] [11]

C. Gundlach, R. H. Price and J. Pullin, Phys. Rev. D49, 883 (1994). FIG. 1. The function ψ of the Cunningham-Price-Moncrief perturbation scheme for Misner’s initial data. The values shown are for p(µ0) = 1, and for units in which 2 M = 1. For the r∗ coordinate the horizon is at r∗ = −∞ andr∗ ∼r for large positive values. FIG. 2. Time evolution of the Misn...

View on Pith Pith review arXiv 1994