{"arxiv_id":"1012.0595","incoming":{"papers":14,"sentences":20,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":5,"sentences":6,"quotes":[{"arxiv_id":"1012.1853","title":"Dynamics and Gravitational Wave Signature of Collapsar Formation","url":"/paper/1012.1853","section":"Introduction","sentence":"We extract GWs directly from the spacetime fields using the fully gauge-invariant Cauchy-Characteristic Extraction method of [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1801.08362","title":"Numerical Relativity Investigation of the Effects of Gravitational Waves on the Inhomogeneity of the Universe","url":"/paper/1801.08362","section":"Introduction","sentence":"Here, our work is based on: a new thorn (a language counterpart of ) which takes the tensor perturbation into consideration and initializes an almost FLRW Universe with saclar and tensor perturbations; a self-developing thorn which calculates several derived varivables including the comoving time, scale factor, the tensor component of perturbation and the distribution of overdensity at the end of each evolution step; the thorn [ref] which evolves spacetime using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism [ref] and the thorn which evolves the hydrodynamical system [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1901.07392","title":"A Gravitational Wave Background from Primordial Black Hole Lattices in Matter Dominated Era","url":"/paper/1901.07392","section":"Introduction","sentence":"More precisely: the thorn (and ) [ref] gets the initial data of PBHLs; the thorn [ref] evolves spacetime using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism [ref] ; the thorn evolves the hydrodynamical system [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2404.01395","title":"Numerical relativity surrogate models for exotic compact objects: the case of head-on mergers of equal-mass Proca stars","url":"/paper/2404.01395","section":"The Proca Merger Catalog","sentence":"The simulations were performed in the [ref] , which uses the framework [ref] , under the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation using the [ref] and [ref] thorns.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1606.02532","title":"Extraction of Gravitational Waves in Numerical Relativity","url":"/paper/1606.02532","section":"Numerical Implementations of the Characteristic Approach","sentence":"Work that uses, rather than develops, characteristic extraction includes [ref] .","intent_p":0.86,"contests_p":null}]}],"unlabelled_sentences":14},"outgoing":{"papers":7,"sentences":15,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":3,"sentences":6,"quotes":[{"arxiv_id":"1011.4223","title":"A Characteristic Extraction Tool for Gravitational Waveforms","url":"/paper/1011.4223","section":"Introduction","sentence":"In addition, and also for the first time in the present context, we utilize the Cauchy-Characteristic Extraction (CCE) approach [ref] that propagates the GW information to $^+$ for completely gauge independent and unambiguous GW extraction.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1006.1632","title":"Notes on the integration of numerical relativity waveforms","url":"/paper/1006.1632","section":"Computing the Strain","sentence":"In order to reduce the contribution of these artificial low-frequency components, we first transform to the Fourier domain, multiply by $f$ in order to take the first time derivative, and then apply fixed FFI [ref] to obtain $h_+,e$.","intent_p":1.0,"contests_p":null},{"arxiv_id":"0910.3803","title":"High accuracy binary black hole simulations with an extended wave zone","url":"/paper/0910.3803","section":"Newman-Penrose Scalars","sentence":"In our construction of an approximate tetrad, we follow common practice (e.g. [ref] ) and use a triad of spatial vectors $u, v, w$ obtained via a Gram-Schmidt orthonormalization starting from","intent_p":0.94,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1011.4223","title":"A Characteristic Extraction Tool for Gravitational Waveforms","url":"/paper/1011.4223","section":"Cauchy-Characteristic Extraction","sentence":"The numerical implementation of CCE including results from binary black hole mergers is discussed in [ref] .","intent_p":0.9,"contests_p":null}]}],"unlabelled_sentences":8},"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":null,"_links":{"html":"https://pith.science/paper/1012.0595"}}