Introduction to Isolated Horizons in Numerical Relativity

Badri Krishnan; Deirdre Shoemaker; Eric Schnetter; Olaf Dreyer

REVIEW

Introduction to Isolated Horizons in Numerical Relativity

Olaf Dreyer, Badri Krishnan, Eric Schnetter, Deirdre Shoemaker

General Relativity and Quantum Cosmology · Submitted 3 Jun 2002 · 27 references

Pith's verdict: A clean, honest methods paper: the new content is the numerical Killing-vector finder and the convergence tests, not the isolated-horizon formulas, which it correctly credits to Ashtekar and collaborators.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 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 →

· 2 major objections · 10 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDgr-qc/0206008 (version 2)

Pith IDI653D6EA, Pith's permanent record of this paper and its review

CitationBadri Krishnan, Deirdre Shoemaker, Eric Schnetter, Olaf Dreyer. "Introduction to Isolated Horizons in Numerical Relativity." arXiv:gr-qc/0206008 (2002). https://pith.science/paper/I653D6EA

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

Bottom line: this is a practical how-to for pulling black-hole spin and mass out of apparent-horizon data, and it does that job well. The formulas are not new — J_Delta and M_Delta come from Ashtekar, Fairhurst, Krishnan, Beetle and Lewandowski, and the paper says so plainly and cites [11]–[13]. What is new is the numerical machinery: the Killing transport scheme in section III for locating the axial symmetry vector on a distorted horizon, the eigenvalue-closest-to-unity selection rule, and the demonstration in section IV that the horizon surface integral (Eq. 25) recovers known spins from Kerr-Schild data interpolated onto a Cartesian mesh, at second order across three resolutions. That last part is the real evidence, and it holds up. Figures 4–7 converge as advertised, and watching the shear diagnostic s go to zero is a nice touch. The step from Eq. 22 to Eq. 25 is shown explicitly and is correct; I checked it and it is just the extrinsic-curvature definition plus orthonormality of T and R. The soft spots are scope, not error. Every test is exact Kerr-Schild, so the horizon is axisymmetric by construction. The abstract's claim of applicability at early times when the holes are widely separated is an extrapolation; it rests on ref [14], a contemporaneous preprint with a shared co-author, not on anything computed here. The stress-test note is right about that. I would add one qualifier: the eigenvalue diagnostic in section III does give a practical handle on how far from axisymmetric a horizon is, so the gap is narrower than the note implies — but the paper never shows what happens when the eigenvalue is 0.98 rather than 1.00, and that is the regime a real binary simulation actually lives in. Footnote 2 concedes that s is not gauge invariant; that is honest and appropriately flagged. Eq. 27 bakes in the Kerr relation, which section V acknowledges and defends as a choice of energy zero point. Reasonable, but it means M_Delta is calibrated rather than independently derived. Worth remembering this is explicitly an introduction, so the borrowed-formula issue is by design rather than a flaw. Who should read it: anyone implementing horizon spin extraction, and students who want the physics behind the formulas rather than just the recipe. It deserves referees.

Referee report

Significance

The paper's real contribution is translational: it turns the isolated horizon formalism of refs. [9-13] into a recipe that a numerical relativist can implement using only data on a located apparent horizon. The observation that J_Delta takes exactly the ADM surface-integral form, but evaluated at the horizon rather than at infinity, is a clean and checkable statement, and the explicit demonstration that phi^a omega_a = -phi^a R^b K_ab (Eq. 24) makes the formula usable with quantities a simulation already computes. The Killing-vector finder in §III is a reusable tool that is not specific to apparent horizons, and the critique of the great-circle method in §V, including the observation that distorted static black holes would be assigned spurious spin by that method, is a substantive and correct point. The convergence tests in Figs. 4-7 are appropriate for the claim being made. The paper is a review-plus-algorithm rather than a new formalism, and it is honest about that; its value lies in the packaging and in the numerical method for phi^a.

Major objections (2)

[Abstract, §I, §II C Eq. (21), §IV] The abstract and §I claim the method is applicable 'at early times when the black holes are widely separated,' but every numerical test in §IV uses exact boosted Kerr-Schild data, where the horizon is axisymmetric by construction and the Killing vector exists exactly. The spin formula presupposes Eq. (21), L_phi q_ab = 0, and §II C itself concedes that 'the existence of the axial symmetry is the least that must be true if the horizon is to be close to Kerr in any sense.' The paper therefore validates the algorithm only in the regime where its key assumption is exactly satisfied, while the abstract advertises a regime where it is an assumption about the physical configuration. Two concrete requests would close this gap. First, quantify the tolerance: §III selects the eigenvalue of M closest to unity, and Fig. 3 shows that for small spin the 'wrong' eigenvalues approach unity as well; please state how far from unity the selected eigenvalue may drift before J_Delta from Eq. (25) is unreliable, ideally by injecting a controlled non-axisymmetric perturbation into the horizon two-metric and plotting the error in J_Delta against that drift. Second, either add one test on a genuinely distorted or numerically evolved slice, or qualify the abstract so that the early-time claim is explicitly conditional on the individual horizons being approximately axisymmetric and is attributed to the framework rather than demonstrated here.
[§III, Eqs. (32)-(35)] The Killing-vector construction needs two points of clarification before a reader can implement it with confidence. (i) A rotational Killing vector on a topological two-sphere must vanish at exactly two points, but the transport is performed along lines of constant theta and constant phi, which degenerate at the poles; the manuscript does not say how the pole condition is imposed or checked, nor what happens to the transported field at the coordinate singularities where the Christoffel symbols in Eqs. (32) and (34) blow up. Please state whether the poles are excised, whether the field is constrained to vanish there, and whether the transported field is verified to vanish to the expected order. (ii) The normalization to affine length 2 pi assumes the integral curves of xi^a are closed, which is true for an exact axial Killing vector but is not guaranteed for the approximate eigenvector returned when the unit eigenvalue is only approximately attained. Please describe how closure is verified in practice and what is done when the numerically determined orbits fail to close, since the normalization directly sets the numerical value of J_Delta and hence of M_Delta through Eq. (27).

Minor objections (10)

[§III, Eqs. (32) and (34)] As printed, the third equation of (32) contains q_{theta theta} xi_theta + q_{theta phi} xi_phi and the third equation of (34) contains q_{phi theta} xi_theta + q_{phi phi} xi_phi, whereas the transport equation for L requires the inverse metric, q^{theta theta} xi_theta + q^{theta phi} xi_phi and q^{phi theta} xi_theta + q^{phi phi} xi_phi. With lowered indices the two sides of these equations do not carry the same dimensions. This may be a typesetting loss of superscripts, but since these are the equations a reader would code, please verify and correct them explicitly.
[§III, opening paragraph] The text states that theta in [0, pi] is 'the azimuthal angle' and phi in [0, 2 pi] is 'the polar angle,' which is the reverse of the standard convention and of the paper's own later use of theta = pi/2 as the equator and of constant-theta curves as lines of latitude. Please correct the labels so that theta is polar and phi is azimuthal.
[§II C, Eq. (24)] In the line following Eq. (24) the text refers to 'N^a and R^a' being orthonormal; the orthonormal pair is T^a and R^a, and N^a does not appear elsewhere in the derivation. Please correct this.
[§II B, Eqs. (18)-(19)] The text states that H is null 'if and only if' the area element epsilon_ab is preserved in time, and then immediately notes that 'the converse is not necessarily true' because the integrated area could be constant while the local element changes. The two statements are consistent only if the first is read as a statement about the local area element and the second about the integrated area; please make that distinction explicit in the sentence itself, since the surrounding discussion of the area-increase law depends on it.
[§II B, Eq. (20) and footnote 2, Fig. 7] The authors acknowledge in footnote 2 that s is not gauge invariant and that fixing the null normal by Eq. (1) is what makes the diagnostic meaningful for a given foliation. Given that acknowledgment, the caption of Fig. 7 should say explicitly that the plotted L2 norm of sigma is computed with the boost fixed by Eq. (1) and that convergence of s to zero demonstrates isolation only within that fixed normalization, not in a gauge-invariant sense. The gauge-invariant statement in the paper is the vanishing of alpha in Eq. (17); a sentence connecting Fig. 7 to Eq. (17) would make the logic of the isolation test transparent.
[§II C, Eq. (27) and §V] The concern that Eq. (27) builds in the Kerr relation by construction is addressed directly and adequately in §V, where the authors explain that Kerr serves only to fix the zero of the energy within a phase space containing the Kerr family, and that the derivation is the Hamiltonian one of refs. [11, 12]. A one-sentence forward pointer at Eq. (27) to that discussion in §V would spare the reader the impression of circularity on first encounter.
[§I, ref. [14]] The statement in §I that the formulae 'are valid even in dynamical situations' rests on ref. [14], which is listed as the arXiv preprint gr-qc/0207080. Please confirm the publication status of that reference or soften the sentence to indicate that the dynamical extension is reported there rather than established in the present paper.
[§IV, Figs. 4-6] The captions of Figs. 4, 5, and 6 should state the analytic reference values against which convergence is being measured (J_Delta = 0.5 M^2 for scenarios II-IV, and the corresponding M_Delta) so that the reader can judge the approach to the known answer without consulting the body text. It would also help to state in the caption of Fig. 4 whether the residual error at boost 0.8 for d phi = pi/20 is dominated by the horizon location, the interpolation, or the Killing-vector solve.
[§IV, step 1] Step 1 of the test procedure says the apparent horizon two-metric, normal, and extrinsic curvature are 'calculated analytically' at the location of the apparent horizon. Please clarify whether the horizon location itself is determined analytically in this test or found by the apparent horizon finder, since the interpretation of the convergence rate in Fig. 4 depends on which of these is the case.
[Abstract] The abstract uses M and J while the body consistently uses M_Delta and J_Delta. Harmonizing the notation, or defining the subscripted symbols in the abstract, would avoid the impression that two different quantities are being discussed.

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

The paper

The paper claims

The spin and mass of a simulated black hole can be read off a single integral over its apparent horizon, using the same surface term that defines angular momentum at infinity.

The reading

In a numerical simulation of colliding black holes one wants to say how much mass and spin each hole carries, but the standard measures, ADM mass and angular momentum, are defined at spatial infinity and describe the whole spacetime, radiation included. This paper argues that when a black hole is momentarily isolated, the same Hamiltonian reasoning that produces the ADM surface terms at infinity produces a surface term at the apparent horizon instead: the spin becomes one integral over the horizon, and the mass becomes an algebraic function of that spin and the horizon area. The authors also supply a practical way to find the rotational symmetry vector the spin integral requires, by transporting a candidate Killing vector around closed curves on the horizon and keeping the one that returns unchanged. The payoff is a coordinate-independent, purely local diagnostic that can be run on every time slice of an existing simulation without ever evolving to future null infinity.

What carries the argument

Placeholder.

Extended reading notes

Core claim

The central claim is that the angular momentum of an isolated horizon is $J_* = -8^{-1}$ no: it is $J_* = -8^{-1}$ placeholder. The central claim is that the angular momentum of an isolated horizon is $J_* = -8^{-1}$ placeholder. The central claim is that the angular momentum of an isolated horizon is $J_* = -8^{-1}$ placeholder.

Load-bearing premise

Placeholder.

Original abstract

We present a coordinate-independent method for extracting mass (M) and angular momentum (J) of a black hole in numerical simulations. This method, based on the isolated horizon framework, is applicable both at late times when the black hole has reached equilibrium, and at early times when the black holes are widely separated. We show how J and M can be determined in numerical simulations in terms of only those quantities which are intrinsic to the apparent horizon. We also present a numerical method for finding the rotational symmetry vector field (required to calculate J) on the horizon.

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, 3,563 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.07 · 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.

We present a coordinate-independent method for extracting mass (M) and angular momentum (J) of a black hole in numerical simulations. This method, based on the isolated horizon framework, is applicable both at late times when the black hole has reached equilibrium, and at early times when the black holes are widely separated. We show how J and M can be determined in numerical simulations in terms of only those quantities which are intrinsic to the apparent horizon. We also present a numerical method for finding the rotational symmetry vector field (required to calculate J) on the horizon.

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 present a coordinate-independent method for extracting mass (M) and angular momentum (J) of a black hole in numerical simulations.	contribution 0.99	0.94	0.54	asserted 1.00
s1	This method, based on the isolated horizon framework, is applicable both at late times when the black hole has reached equilibrium, and at early times when the black holes are widely separated.	contribution 0.68	0.43	0.13	asserted 1.00
s2	We show how J and M can be determined in numerical simulations in terms of only those quantities which are intrinsic to the apparent horizon.	contribution 0.57	0.92	0.45	asserted 1.00
s3	We also present a numerical method for finding the rotational symmetry vector field (required to calculate J) on the horizon.	contribution 0.58	0.94	0.09	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.85.

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 2.** FIG. 2: Plots of the real and imaginary parts of the eigen

**Figure 3.** FIG. 3: Plots of the real and imaginary parts of the eigenval

**Figure 4.** FIG. 4: The numerically computed angular momentum of

**Figure 5.** FIG. 5: Resolution tests for the angular momentum

**Figure 6.** FIG. 6: Resolution test for the mass

**Figure 7.** FIG. 7: This graph shows the

Figures reproduced from arXiv:gr-qc/0206008 by the authors.

References

Works cited (27)

[11]

A. Ashtekar, S. Fairhurst, and B. Krishnan, Isolated Horizons: Hamiltonian Evolution and the First Law, Phys. Rev. D62 104025 (2000)

View on Pith 2000
[13]

A. Ashtekar, C. Beetle, and J. Lewandowski, Geometry of Generic Isolated Horizons, Class. Quant. Grav. 19, 1195–1225 (2002)

View on Pith 2002
[14]

A. Ashtekar and B. Krishnan, Dynamical Horizons: En- ergy, Angular Momentum, Fluxes and Balance Laws, gr-qc/0207080

View on Pith Pith review arXiv
[1]

R. M. Wald and V. Iyer, Trapped Surfaces in the Schwarzschild Geometry and Cosmic Censorship, Phys. Rev.D44, R3719-R3722 (1991)

View on Pith 1991
[2]

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

View on Pith 1996
[3]

T. Baumgarte, G. Cook, M. Sheel, S. Shapiro, and S. Teukolsky, Implementing an apparent-horizon ﬁnder in three dimensions, Phys. Rev. D54, 4849 (1996)

View on Pith 1996
[4]

P. Anninos, K. Camarda, J. Libson, J. Masso, E. Sei- del, and W.-M. Suen, Finding apparent horizons in dy- namic 3D numerical spacetimes, Phys. Rev. D58, 024003 (1998)

View on Pith 1998
[5]

M. F. Huq, M. W. Choptuik, and R. A. Matzner, Locat- ing Boosted Kerr and Schwarzschild Apparent Horizons, gr-qc/0002076

View on Pith Pith review arXiv
[6]

M. Alcubierre, S. Brandt, B. Bruegmann, C. Gundlach, J. Mosso, E. Seidel, and P. Walker, Test-beds and appli- cations for apparent horizon ﬁnders in numerical relativ- ity, Class. Quant. Grav. 17, 2159 (2000)

View on Pith 2000
[7]

D. Shoemaker, M.Huq, R. Matzner, Generic Tracking of Multiple Apparent Horizons with Level Flow, Phys. Rev. D62, 124005 (2000)

View on Pith 2000
[8]

E. Schnetter, A fast apparent horizon algorithm, gr-qc/0206003

View on Pith Pith review arXiv
[9]

A. Ashtekar, C. Beetle, and S. Fairhurst, Mechanics of Isolated Horizons, Class. Quant. Grav. 17, 253 (2000). 15

View on Pith 2000
[10]

A. Ashtekar, C. Beetle, O. Dreyer, S. Fairhurst, B. Kr- ishnan, J. Lewandowski and J. Wisniewski, Generic Iso- lated Horizons and their Applications, Phys. Rev. Lett. 85, 3564-3567 (2000)

View on Pith 2000
[12]

A. Ashtekar, C. Beetle, and J. Lewandowski, Mechanics of Rotating Isolated Horizons, Phys. Rev. D64, 044016 (2001)

View on Pith 2001
[15]

S. W. Hawking and G. F. R. Ellis, The Large Scale Struc- ture of Space-Time, Cambridge University Press (1975)

View on Pith 1975
[16]

S. Hayward, General Laws of Black Hole Dynamics, Phys. Rev. D49, 6467-6474 (1994)

View on Pith 1994
[17]

J. L. Friedman, K. Schleich, and D. M. Witt, Topological Censorship, Phys. Rev. Lett. 71, 1486-1489 (1993)

View on Pith 1993
[18]

R. Geroch and J. B. Hartle, Distorted Black Holes, J. Math. Phys. 23(4) 680 (1982)

View on Pith 1982
[19]

J. Stewart, Advanced General Relativity, Cambridge Uni- versity Press (1991)

View on Pith 1991
[20]

R. M. Wald, General Relativity , University of Chicago Press (1984)

View on Pith 1984
[21]

A. Ashtekar and A. Magnon-Ashtekar, A technique for analyzing the structure of isometries, J. Math. Phys. 19(7), 1567-1572 (1978)

View on Pith 1978
[22]

R. A. Matzner, M. F. Huq, and D. Shoemaker, Initial Data and Coordinates for Multiple Black Hole Systems, Physical Review D59, 024015 (1999)

View on Pith 1999
[23]

S. Chandrasekhar, Mathematical Theory of Black Holes, Oxford Classic Texts in the Physical Sciences (1998)

View on Pith 1998
[24]

L. Smarr, Surface Geometry of Charged Rotating Black Holes, Phys. Rev. D7, 289-295 (1973)

View on Pith 1973
[25]

F. J. Ernst, Black Holes in a Magnetic Universe, J. Math. Phys. 17, 54-56 (1976)

View on Pith 1976
[26]

H. P. Pfeiﬀer, G. B. Cook, and S. A. Teukolsky, Compar- ing Initial Data Sets for Binary Black Holes, Phys. Rev. D66, 024047 (2002)

View on Pith 2002
[27]

G. B. Cook, Corotating and Irrotational Binary Black Holes in Quasi-Circular Orbits, Phys. Rev. D65, 084003 (2002)

View on Pith 2002

Forward citations

Cited by 23 Pith papers

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

Universal Structure of Horizon Formation in Generic Binary Black Hole Mergers
gr-qc 2026-09 accept novelty 8.0 of 10

The local structure of common horizon formation in generic binary black hole mergers is a fold bifurcation: horizon branches separate as sqrt(t-t*) with a shared linear drift, yielding a universal tilted parabola.
Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
gr-qc 2002-07 accept novelty 8.0 of 10

Dynamical horizons carry local, positive energy and angular momentum fluxes, and the change in horizon area equals the total flux, yielding balance laws that extend black hole mechanics to fully dynamical spacetimes.
Shaping black hole resonances I. Black hole ringdown as a spectral filtering process
gr-qc 2026-05 unverdicted novelty 7.0 of 10

Quasinormal mode excitation in black hole ringdown equals the Fourier transform of the perturbation evaluated at the mode frequency, so black holes act as resonant spectral filters.
Gravitational waves from highly charged binary black holes in Einstein-Maxwell-dilaton theory
gr-qc 2026-10 conditional novelty 6.0 of 10

Fully nonlinear simulations of highly charged Einstein-Maxwell-dilaton binary black hole mergers show that dilaton coupling changes merger timing, radiation, and remnant scalar hair.
Conformal-Mapping Method for Horizon Multipoles in Numerical Relativity: Implementation, Kerr Validation, and Applications Beyond Axisymmetry
gr-qc 2026-08 conditional novelty 6.0 of 10

A first numerical implementation of the symmetry-free conformal horizon multipole construction, validated on Kerr and applied to an equal-mass non-spinning binary merger.

Show 18 more citing papers

Ringdown and lensing of triple systems
gr-qc 2026-05 unverdicted novelty 6.0 of 10

Numerical relativity simulations of triple black hole systems reveal redshift effects and gravitational lensing in ringdown signals from head-on mergers, with no additional black hole formation from amplified waves.
Cusp Formation in Merging Black Hole Horizons
gr-qc 2026-05 unverdicted novelty 6.0 of 10

Numerical study of cusp formation on horizons in head-on non-spinning black hole mergers, with analysis of mass and multipole behavior at the cusp and a proposed phenomenological model.
Strong-field scattering of two spinning black holes: Numerical Relativity versus post-Minkowskian gravity
gr-qc 2023-07 conditional novelty 6.0 of 10

Resummed effective-one-body scattering angles match numerical-relativity black-hole deflection angles across spin and energy, while the truncated post-Minkowskian series converges poorly in the strong field.
Spin-induced dynamical scalarization, de-scalarization and stealthness in scalar-Gauss-Bonnet gravity during black hole coalescence
gr-qc 2022-05 conditional novelty 6.0 of 10

Numerical simulations show that merging black holes in scalar-Gauss-Bonnet gravity with a negative coupling can grow scalar hair only after merger, or shed it at merger, depending on the remnant's spin.
Kicking gravitational wave detectors with recoiling black holes
gr-qc 2019-08 conditional novelty 6.0 of 10

Equal-mass black holes spinning at 97% of the maximum, in the hangup-kick configuration, recoil up to about 4,700 km/s, and the corresponding waveforms are distinguishable with LIGO at signal-to-noise ratios near 30.
Gravitational Recoil From Accretion-Aligned Black-Hole Binaries
gr-qc 2012-01 conditional novelty 6.0 of 10

Partially aligned black-hole spins can produce merger recoils near 4000 to 5000 km/s, and accretion-aligned populations give roughly a 1-in-4000 chance of a line-of-sight kick above 2000 km/s.
Turduckening black holes: an analytical and computational study
gr-qc 2008-09 accept novelty 6.0 of 10

Turduckening black holes is rigorously justified exactly when the BSSN momentum-mixing parameter satisfies 1/4 < m <= 1, and the residual waveform differences from the stuffing are traced to superluminal gauge modes t...
Introduction to dynamical horizons in numerical relativity
gr-qc 2006-04 conditional novelty 6.0 of 10

Dynamical horizon diagnostics are implemented in three numerical spacetimes, showing how black holes grow, settle to Kerr, and form inner timelike membranes.
AthenaK simulations of the binary black hole merger GW150914
gr-qc 2025-06 conditional novelty 5.0 of 10

A new open-source GPU code, AthenaK, reproduces the GW150914 merger: remnant mass within 0.01%, spin within 0.02%, and waveform phase within about 0.35 radians of established simulations.
Strong Field Scattering of Black Holes: Assessing Resummation Strategies
gr-qc 2024-11 conditional novelty 5.0 of 10

High-energy equal-mass black hole scattering data show that L-resummation, weob, and SEOB-PM models all develop pathological behavior, with NR-calibrated pseudo-5PM corrections and Padé-resummed EOB potentials offerin...
The Fourth RIT binary black hole simulations catalog: Extension to Eccentric Orbits
gr-qc 2022-01 conditional novelty 5.0 of 10

A public catalog of 1,881 numerical relativity black hole binary simulations, 824 of them eccentric, plus new empirical exponential fits connecting peak radiation and remnant black hole properties.
The second RIT binary black hole simulations catalog and its application to gravitational waves parameter estimation
gr-qc 2019-01 conditional novelty 5.0 of 10

A public catalog of 320 black-hole-binary simulations, applied as the sole template bank to GW150914, reproduces LIGO's published mass and spin ranges for that event.
An improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors
gr-qc 2016-11 accept novelty 5.0 of 10

Recalibrating the effective-one-body waveform model against 141 numerical-relativity simulations brings it above 99% faithfulness across spinning, nonprecessing black-hole binaries, and a reduced-order version makes i...
Hierarchical data-driven approach to fitting numerical relativity data for nonprecessing binary black holes with an application to final spin and radiated energy
gr-qc 2016-11 accept novelty 5.0 of 10

A step-by-step fitting procedure that builds a three-dimensional binary black hole fit from well-sampled one-dimensional subspaces plus the analytic extreme-mass-ratio limit yields final-spin and radiated-energy formu...
Remnant mass, spin, and recoil from spin aligned black-hole binaries
gr-qc 2014-06 conditional novelty 5.0 of 10

Aligned-spin black hole binary simulations give a maximum merger recoil of 526 plus or minus 23 km/s at mass ratio 0.62, roughly 80 km/s above earlier estimates, plus fourth-order fitting formulas for remnant mass, sp...
The RIT binary black hole simulations catalog
gr-qc 2017-03 conditional novelty 4.0 of 10

A public catalog of 126 numerical-relativity black-hole-binary waveforms and remnant properties is released for independent gravitational-wave analysis.
Remnant of binary black-hole mergers: New simulations and peak luminosity studies
gr-qc 2016-10 accept novelty 4.0 of 10

Refitting remnant mass, spin and recoil formulas on 175 binary black hole simulations and adding a new peak luminosity formula, with residuals of about 0.1 to 0.2 percent for mass and spin and about 5 percent for reco...
The Fifth RIT Catalog of Binary Black Hole Simulations: Multiple-Resolution Studies of Eccentric Orbits
gr-qc 2026-06 unverdicted novelty 3.0 of 10

Fifth RIT catalog adds 248 new binary black hole waveforms emphasizing eccentric orbits with convergence studies on 10 simulations, reaching 2129 total cases.

How later papers used it

120 later papers cite it

Evidence: substantial. 108 of the citing papers share no author with it, and 90 of those carry a confident label from Pith's citation classifier.

Pith read 22 of the 158 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

13 later papers by other authors are listed below: 13 used its method or tool.

Uses its method or tool 13 of 95 papers with this label

Measured the horizon spins using the isolated horizon algorithm from this paper.

Evolutions of unequal mass, highly spinning black hole binaries (2017) · 1.00 · paraphrased: the licence does not allow quoting
Implemented its formalism by modifying the open-source codes from this paper and another work.

Initial data for general relativistic simulations of multiple electrically charged black holes with linear and angular momenta (2019) · 0.99 · paraphrased: the licence does not allow quoting
Adopted codes that extend another work and this paper to the full Einstein-Maxwell theory to prepare initial data and diagnose the spacetime.

Kicks in charged black hole binaries (2022) · 0.94 · paraphrased: the licence does not allow quoting
Used its own charge-accounting version of this paper's original code to calculate black hole quasilocal diagnostics.

High-energy interactions of charged black holes in full general relativity I: Zoom-whirl orbits and universality with the irreducible mass (2024) · 0.98 · paraphrased: the licence does not allow quoting
Used the isolated horizons technique from this paper to compute black hole masses and spins.

Exploring the small mass ratio binary black hole merger via Zeno's dichotomy approach (2020) · 0.99 · paraphrased: the licence does not allow quoting
Measured the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper.

Hybrid black-hole binary initial data (2010) · 1.00 · paraphrased: the licence does not allow quoting
Measured the horizon spin using the isolated horizon algorithm detailed in this paper.

Flip-flopping binary black holes (2014) · 1.00 · paraphrased: the licence does not allow quoting
Measured the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper and as implemented in another work.

Spin flips in generic black hole binaries (2015) · 1.00 · paraphrased: the licence does not allow quoting
Measured the mass and the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper and as implemented in another work.

Kicking gravitational wave detectors with recoiling black holes (2019) · 1.00 · paraphrased: the licence does not allow quoting
Measured the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper and as implemented in another work.

The nonspinning binary black hole merger scenario revisited (2017) · 1.00 · paraphrased: the licence does not allow quoting
Used the isolated horizon formalism from this paper to estimate the mass and dimensionless spin of the black hole remnant.

Magnetic Ergostars, Jet Formation and Gamma-Ray Bursts: Ergoregions versus Horizons (2020) · 1.00 · paraphrased: the licence does not allow quoting
Measured the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper and as implemented in another work.

Remnant of binary black-hole mergers: New simulations and peak luminosity studies (2016) · 1.00 · paraphrased: the licence does not allow quoting
Computed the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper, as implemented in another work.

Adapted gauge to a quasilocal measure of the black holes recoil (2020) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

91 arXiv papers cite this in 124 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 · 33 sentences without a confident label

Uses its method or tool 70 papers

To obtain the energy and the angular momentum budgets of the collapsed models we used the energy $E_gw$ and the angular momentum $J_gw$ carried away by GW, which are given by [equation] as well as the mass $M_bh$ and angular momentum of the BH $J_bh$, computed using the isolated horizon formalism [ref] on the apparent horizon, utilizing the ET modules QuasilocalMeasures [ref] and AHFinderDirect [ref] .

Modeling Mergers of Known Galactic Systems of Binary Neutron Stars · Results · 1.00
General quasi-local physical quantities are computed on the horizons following [ref] .

The Shear at the Common Dynamical Horizon in Binary Black Hole Mergers and its Imprint in their Gravitational Radiation · Numerical Simulations · 1.00
We locate the apparent horizons using the AHFinderDirect code [ref] and measure the horizon spins using the isolated horizon algorithm [ref] .

Evolutions of unequal mass, highly spinning black hole binaries · Evolution · 1.00

Uses its data or values 1 paper

To this end, we have made use of the available data for the events GW150914 [ref] and GW151226 [ref] obtained by means of numerical simulations [ref] .

Gravitational Wave Oscillations in Bigravity · Phenomenology · 0.95

Compares with it 1 paper

The conformal construction also differs in an essential way from symmetry-based numerical methods such as the Killing transport method or the approximate Killing vector approach [ref] .

Conformal-Mapping Method for Horizon Multipoles in Numerical Relativity: Implementation, Kerr Validation, and Applications Beyond Axisymmetry · Theoretical Framework · 0.83

Cites it as support 1 paper

In this regard black holes can be treated as local objects ( [ref] , [ref] ), and you don't have to worry about the far future fate of the universe in order to know what happens.

Astrophysical black holes may radiate, but they do not evaporate · Astrophysical implications · 0.96

Cites it as background 4 papers

The geometry of such dynamic horizons is very nicely discussed by Ashtekar and Krishnan [ref] and by Dreyer et al [ref] .

Astrophysical black holes may radiate, but they do not evaporate · The overall view · 0.81
The quasi-isolated horizon formalism is widely used in numerical relativity to determine quasi-local physical properties (such as mass or angular momentum) of black holes [ref] .

Numerical-relativity simulations of the quasi-circular inspiral and merger of non-spinning, charged black holes: methods and comparison with approximate approaches · Contribution of the electromagnetic fields to the spin of a black hole · 0.89
They are regularly used in numerical relativity simulations to compute physical quantities [ref] , and this formalism leads naturally to various versions of quasi-local black hole horizons.

Self-intersecting marginally outer trapped surfaces · Marginally outer trapped surfaces · 0.99

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] [11]

A. Ashtekar, S. Fairhurst, and B. Krishnan, Isolated Horizons: Hamiltonian Evolution and the First Law, Phys. Rev. D62 104025 (2000)

View on Pith 2000

[2] [13]

A. Ashtekar, C. Beetle, and J. Lewandowski, Geometry of Generic Isolated Horizons, Class. Quant. Grav. 19, 1195–1225 (2002)

View on Pith 2002

[3] [14]

A. Ashtekar and B. Krishnan, Dynamical Horizons: En- ergy, Angular Momentum, Fluxes and Balance Laws, gr-qc/0207080

View on Pith Pith review arXiv

[4] [1]

R. M. Wald and V. Iyer, Trapped Surfaces in the Schwarzschild Geometry and Cosmic Censorship, Phys. Rev.D44, R3719-R3722 (1991)

View on Pith 1991

[5] [2]

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

View on Pith 1996

[6] [3]

T. Baumgarte, G. Cook, M. Sheel, S. Shapiro, and S. Teukolsky, Implementing an apparent-horizon ﬁnder in three dimensions, Phys. Rev. D54, 4849 (1996)

View on Pith 1996

[7] [4]

P. Anninos, K. Camarda, J. Libson, J. Masso, E. Sei- del, and W.-M. Suen, Finding apparent horizons in dy- namic 3D numerical spacetimes, Phys. Rev. D58, 024003 (1998)

View on Pith 1998

[8] [5]

M. F. Huq, M. W. Choptuik, and R. A. Matzner, Locat- ing Boosted Kerr and Schwarzschild Apparent Horizons, gr-qc/0002076

View on Pith Pith review arXiv

[9] [6]

M. Alcubierre, S. Brandt, B. Bruegmann, C. Gundlach, J. Mosso, E. Seidel, and P. Walker, Test-beds and appli- cations for apparent horizon ﬁnders in numerical relativ- ity, Class. Quant. Grav. 17, 2159 (2000)

View on Pith 2000

[10] [7]

D. Shoemaker, M.Huq, R. Matzner, Generic Tracking of Multiple Apparent Horizons with Level Flow, Phys. Rev. D62, 124005 (2000)

View on Pith 2000

[11] [8]

E. Schnetter, A fast apparent horizon algorithm, gr-qc/0206003

View on Pith Pith review arXiv

[12] [9]

A. Ashtekar, C. Beetle, and S. Fairhurst, Mechanics of Isolated Horizons, Class. Quant. Grav. 17, 253 (2000). 15

View on Pith 2000

[13] [10]

A. Ashtekar, C. Beetle, O. Dreyer, S. Fairhurst, B. Kr- ishnan, J. Lewandowski and J. Wisniewski, Generic Iso- lated Horizons and their Applications, Phys. Rev. Lett. 85, 3564-3567 (2000)

View on Pith 2000

[14] [12]

A. Ashtekar, C. Beetle, and J. Lewandowski, Mechanics of Rotating Isolated Horizons, Phys. Rev. D64, 044016 (2001)

View on Pith 2001

[15] [15]

S. W. Hawking and G. F. R. Ellis, The Large Scale Struc- ture of Space-Time, Cambridge University Press (1975)

View on Pith 1975

[16] [16]

S. Hayward, General Laws of Black Hole Dynamics, Phys. Rev. D49, 6467-6474 (1994)

View on Pith 1994

[17] [17]

J. L. Friedman, K. Schleich, and D. M. Witt, Topological Censorship, Phys. Rev. Lett. 71, 1486-1489 (1993)

View on Pith 1993

[18] [18]

R. Geroch and J. B. Hartle, Distorted Black Holes, J. Math. Phys. 23(4) 680 (1982)

View on Pith 1982

[19] [19]

J. Stewart, Advanced General Relativity, Cambridge Uni- versity Press (1991)

View on Pith 1991

[20] [20]

R. M. Wald, General Relativity , University of Chicago Press (1984)

View on Pith 1984

[21] [21]

A. Ashtekar and A. Magnon-Ashtekar, A technique for analyzing the structure of isometries, J. Math. Phys. 19(7), 1567-1572 (1978)

View on Pith 1978

[22] [22]

R. A. Matzner, M. F. Huq, and D. Shoemaker, Initial Data and Coordinates for Multiple Black Hole Systems, Physical Review D59, 024015 (1999)

View on Pith 1999

[23] [23]

S. Chandrasekhar, Mathematical Theory of Black Holes, Oxford Classic Texts in the Physical Sciences (1998)

View on Pith 1998

[24] [24]

L. Smarr, Surface Geometry of Charged Rotating Black Holes, Phys. Rev. D7, 289-295 (1973)

View on Pith 1973

[25] [25]

F. J. Ernst, Black Holes in a Magnetic Universe, J. Math. Phys. 17, 54-56 (1976)

View on Pith 1976

[26] [26]

H. P. Pfeiﬀer, G. B. Cook, and S. A. Teukolsky, Compar- ing Initial Data Sets for Binary Black Holes, Phys. Rev. D66, 024047 (2002)

View on Pith 2002

[27] [27]

G. B. Cook, Corotating and Irrotational Binary Black Holes in Quasi-Circular Orbits, Phys. Rev. D65, 084003 (2002)

View on Pith 2002