{"arxiv_id":"gr-qc/0206008","incoming":{"papers":91,"sentences":124,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":70,"sentences":83,"quotes":[{"arxiv_id":"1608.02810","title":"Modeling Mergers of Known Galactic Systems of Binary Neutron Stars","url":"/paper/1608.02810","section":"Results","sentence":"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] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2312.01136","title":"The Shear at the Common Dynamical Horizon in Binary Black Hole Mergers and its Imprint in their Gravitational Radiation","url":"/paper/2312.01136","section":"Numerical Simulations","sentence":"General quasi-local physical quantities are computed on the horizons following [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1711.09041","title":"Evolutions of unequal mass, highly spinning black hole binaries","url":"/paper/1711.09041","section":"Evolution","sentence":"We locate the apparent horizons using the AHFinderDirect code [ref] and measure the horizon spins using the isolated horizon algorithm [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2106.02595","title":"Tidal deformation of dynamical horizons in binary black hole mergers","url":"/paper/2106.02595","section":"Numerical simulations of binary black hole mergers","sentence":"Since this work is focused on the study of individual horizon geometry of the black holes in the inspiral phase, we track the individual horizons up to merger and compute quasi-local quantities [ref] using the isolated and dynamical horizon formalism [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"1903.01036","title":"Initial data for general relativistic simulations of multiple electrically charged black holes with linear and angular momenta","url":"/paper/1903.01036","section":"Numerical implementation","sentence":"We implement the formalism outlined in the previous Sections by modifying the [ref] and open-source codes [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1703.07785","title":"Gravitational Wave Oscillations in Bigravity","url":"/paper/1703.07785","section":"Phenomenology","sentence":"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] .","intent_p":0.95,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2608.07985","title":"Conformal-Mapping Method for Horizon Multipoles in Numerical Relativity: Implementation, Kerr Validation, and Applications Beyond Axisymmetry","url":"/paper/2608.07985","section":"Theoretical Framework","sentence":"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] .","intent_p":0.83,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1310.4771","title":"Astrophysical black holes may radiate, but they do not evaporate","url":"/paper/1310.4771","section":"Astrophysical implications","sentence":"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.","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":4,"sentences":5,"quotes":[{"arxiv_id":"1310.4771","title":"Astrophysical black holes may radiate, but they do not evaporate","url":"/paper/1310.4771","section":"The overall view","sentence":"The geometry of such dynamic horizons is very nicely discussed by Ashtekar and Krishnan [ref] and by Dreyer et al [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"2104.06978","title":"Numerical-relativity simulations of the quasi-circular inspiral and merger of non-spinning, charged black holes: methods and comparison with approximate approaches","url":"/paper/2104.06978","section":"Contribution of the electromagnetic fields to the spin of a black hole","sentence":"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] .","intent_p":0.89,"contests_p":null},{"arxiv_id":"1907.00683","title":"Self-intersecting marginally outer trapped surfaces","url":"/paper/1907.00683","section":"Marginally outer trapped surfaces","sentence":"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.","intent_p":0.99,"contests_p":null},{"arxiv_id":"0809.3850","title":"Black holes and black hole thermodynamics without event horizons","url":"/paper/0809.3850","section":"Introduction","sentence":"This area has already been covered in [ref] and [ref] .","intent_p":0.98,"contests_p":null}]}],"unlabelled_sentences":33},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":{"arxiv_id":"gr-qc/0206008","kind":"model","paper_version":2,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T16:09:55+00:00","loaded_at":"2026-10-28T01:02:37.181185+00:00","evidence":"substantial","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":13,"entries":[{"p":1.0,"quote":null,"citing":[{"self":false,"year":2017,"title":"Evolutions of unequal mass, highly spinning black hole binaries","arxiv_id":"1711.09041"}],"verified":true,"paraphrase":"Measured the horizon spins using the isolated horizon algorithm from this paper."},{"p":0.99,"quote":null,"citing":[{"self":false,"year":2019,"title":"Initial data for general relativistic simulations of multiple electrically charged black holes with linear and angular momenta","arxiv_id":"1903.01036"}],"verified":true,"paraphrase":"Implemented its formalism by modifying the open-source codes from this paper and another work."},{"p":0.94,"quote":null,"citing":[{"self":false,"year":2022,"title":"Kicks in charged black hole binaries","arxiv_id":"2207.06429"}],"verified":true,"paraphrase":"Adopted codes that extend another work and this paper to the full Einstein-Maxwell theory to prepare initial data and diagnose the spacetime."},{"p":0.98,"quote":null,"citing":[{"self":false,"year":2024,"title":"High-energy interactions of charged black holes in full general relativity I: Zoom-whirl orbits and universality with the irreducible mass","arxiv_id":"2411.11960"}],"verified":true,"paraphrase":"Used its own charge-accounting version of this paper's original code to calculate black hole quasilocal diagnostics."},{"p":0.99,"quote":null,"citing":[{"self":false,"year":2020,"title":"Exploring the small mass ratio binary black hole merger via Zeno's dichotomy approach","arxiv_id":"2006.04818"}],"verified":true,"paraphrase":"Used the isolated horizons technique from this paper to compute black hole masses and spins."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2010,"title":"Hybrid black-hole binary initial data","arxiv_id":"1012.0886"}],"verified":true,"paraphrase":"Measured the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2014,"title":"Flip-flopping binary black holes","arxiv_id":"1410.3830"}],"verified":true,"paraphrase":"Measured the horizon spin using the isolated horizon algorithm detailed in this paper."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2015,"title":"Spin flips in generic black hole binaries","arxiv_id":"1506.04768"}],"verified":true,"paraphrase":"Measured the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper and as implemented in another work."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2019,"title":"Kicking gravitational wave detectors with recoiling black holes","arxiv_id":"1908.04382"}],"verified":true,"paraphrase":"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."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2017,"title":"The nonspinning binary black hole merger scenario revisited","arxiv_id":"1705.07034"}],"verified":true,"paraphrase":"Measured the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper and as implemented in another work."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2020,"title":"Magnetic Ergostars, Jet Formation and Gamma-Ray Bursts: Ergoregions versus Horizons","arxiv_id":"2009.08982"}],"verified":true,"paraphrase":"Used the isolated horizon formalism from this paper to estimate the mass and dimensionless spin of the black hole remnant."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2016,"title":"Remnant of binary black-hole mergers: New simulations and peak luminosity studies","arxiv_id":"1610.09713"}],"verified":true,"paraphrase":"Measured the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper and as implemented in another work."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2020,"title":"Adapted gauge to a quasilocal measure of the black holes recoil","arxiv_id":"2003.02286"}],"verified":true,"paraphrase":"Computed the magnitude of the horizon spin using the isolated horizon algorithm detailed in this paper, as implemented in another work."}],"papers_all":95,"self_papers":0,"self_entries":[]}],"counts":{"by_kind":{"data_used":1,"comparison":1,"method_or_tool":95,"supports_this_paper":1},"dropped":{"relied_on":0,"unknown_ids":0,"account_lines":0,"contest_vetoed":0,"below_threshold":0,"contest_drawback":0,"contest_without_basis":0,"contest_not_one_sentence":0,"contest_on_group_citation":0},"papers_read":18,"self_papers":12,"citing_papers":120,"sentences_read":22,"citing_sentences":158,"unambiguous_read":22,"typed_independent":90,"independent_papers":108,"by_kind_independent":{"data_used":1,"comparison":1,"method_or_tool":89,"supports_this_paper":1}},"input_sha256":"a04333915384995468563fc23326524471315f68230b800d4f13a722cf0b1102","method":"For a paper with five or more citing arXiv papers, Pith selected up to 40 citing sentences its citation classifier typed, read those whose citation markers point at this paper alone, and wrote one paraphrase for each later paper in each group, each resting on one sentence. A later paper is listed under a label only when the classifier gives one of its sentences that label at intent probability 0.8 or more (0.95 for support), Pith's reading of the sentence finds that the citing paper itself did it, and a second check of the paraphrase against the sentence passes. The section lists uses only: building on the paper, using its method, tool, data or values, comparing with it and citing it as support. It does not list criticism or disagreement, so their absence says nothing about how the paper has been received. Code counted the papers, wrote the summary from the listed entries, set the evidence level and linked each entry to its citing paper. Quotes are copied from the citing sentence and shown only when the citing paper's licence is CC BY, CC BY-SA or CC0; otherwise the paraphrase is shown. Papers that share an author with this one are listed apart. A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"13 later papers by other authors are listed below: 13 used its method or tool."},"_links":{"html":"https://pith.science/paper/gr-qc/0206008"}}