{"arxiv_id":"astro-ph/0402403","incoming":{"papers":36,"sentences":75,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":6,"sentences":7,"quotes":[{"arxiv_id":"2607.16880","title":"Electromagnetic Emission from a Black Hole Evaporating in External Magnetic Field","url":"/paper/2607.16880","section":"Electromagnetic Emission from an Evaporating Black Hole: A Macroscopic Medium Perspective","sentence":"Using the vacuum constitutive equations derived by Komissarov [ref] , [equation] and setting $β^i = 0$, we obtain [equation] Thus the vacuum behaves as an isotropic effective medium with scalar permittivity and permeability: [equation] The distinction from the usual stationary optical-medium analogy is important: here $ϵ$ and $μ$ depend on time through $m(r,t)$.","intent_p":0.91,"contests_p":null},{"arxiv_id":"2504.15978","title":"Unveiling the electrodynamic nature of spacetime collisions","url":"/paper/2504.15978","section":"Introduction","sentence":"If we now interpret $𝒰^μν_α̂$ as a field strength tensor in its own right, we are led to introduce auxiliary electric and magnetic fields, [equation] which resemble electromagnetic fields in a medium, and are related to $B^α̂μ$ and $E^α̂μ$ via constitutive relations [ref] , [equation] We can recast Eqs. [ref], [ref] exactly in a more familiar vector calculus form [ref] , also following [ref] , [equation] where $√(γ) = √(-g)/α$, and $α$ and $β$ are the gravitational lapse and shift, respectively [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"2205.09643","title":"Electromagnetic precursor flares from the late inspiral of neutron star binaries","url":"/paper/2205.09643","section":"Force-free electrodynamics","sentence":"This amounts to imposing the force-free conditions [ref] [equation] We impose these conditions in the exterior of the neutron stars using the relaxation approach of [ref] , i.e. [equation] where $ν^-1= 1.25×10^-6 Ω^-1$ is a short relaxation time, $χ$ is the Heaviside function, and $Ω$ is the orbital angular speed, see Tab. [ref].","intent_p":1.0,"contests_p":null},{"arxiv_id":"1310.3274","title":"A new scheme for matching general relativistic ideal magnetohydrodynamics to its force-free limit","url":"/paper/1310.3274","section":"Magnetospheric Wald Problem","sentence":"Following [ref] , we perform this test setting $a_*=0.9$.","intent_p":0.82,"contests_p":null},{"arxiv_id":"2604.24846","title":"SN Ia Population Machine. I. A Unified Cosmological Simulation-Binary Synthesis Framework Establishing Non-universal Delay-time Distributions and Cosmic Progenitor-channel Dominance Crossover","url":"/paper/2604.24846","section":"Future Work","sentence":"In practice, this can be achieved by re-running the same end-to-end pipeline while replacing with other widely used BPS frameworks—e.g., [ref] , [ref] , [ref] , the Brussels code [ref] , [ref] , [ref] , and [ref] , and related codes.","intent_p":0.84,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":2,"quotes":[{"arxiv_id":"1310.3274","title":"A new scheme for matching general relativistic ideal magnetohydrodynamics to its force-free limit","url":"/paper/1310.3274","section":"Fast wave","sentence":"The initial configuration is defined by [Note that [ref] give the initial data for $^i$ and $^i$.","intent_p":0.93,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":4,"sentences":7,"quotes":[{"arxiv_id":"1310.3274","title":"A new scheme for matching general relativistic ideal magnetohydrodynamics to its force-free limit","url":"/paper/1310.3274","section":"Split monopole","sentence":"The results of this test without the resistivity prescription are shown in Fig. [ref], and are in good agreement with the ones obtained in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2606.19229","title":"Distinct Near-Horizon Trend of Synchrotron Polarization in Kerr Spacetime","url":"/paper/2606.19229","section":"Next-to-leading-order term","sentence":"If we further impose $∂_r ψ(r,π/2) = 0$, corresponding to field lines reaching a turning point at the equator—a configuration commonly realized in accretion systems [ref] —we obtain Z_1^eq(q_ψ=0) = η+(λ-a)^2/(λ-a)^2 ±_θ_s√(η) (1-aΩ_+)/2(H_+-aλ)(H_+Ω_+-a) , which reproduces the formula in [ref] .","intent_p":0.89,"contests_p":null},{"arxiv_id":"1805.05952","title":"Magnetosphere of a spinning black hole and the role of the current sheet","url":"/paper/1805.05952","section":"Introduction","sentence":"We confirm previous results regarding the structure of the electromagnetic fields, the angular velocity, and luminosity from these solutions [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"2604.11542","title":"Impact of Stochastic Pop~III X-ray Binaries on the Cosmological 21-cm Signal","url":"/paper/2604.11542","section":"Stochastic modeling of XRB luminosities","sentence":"These Monte Carlo results are compared with the results of BPS simulations (dotted lines) from [ref] , produced using the publicly available code [ref] considering their prescriptions for rotationally-driven mass transfer and critical spin-up (SR_CS) at $Z=10^-4$.","intent_p":0.97,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1908.07227","title":"Force-free electrodynamics near rotation axis of a Kerr black hole","url":"/paper/1908.07227","section":"Inner and outer light surfaces","sentence":"Numerical evidence for this also follows from [ref] since all the numerical simulations are seen to obey the conditions [ref] and [ref].","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":10,"sentences":12,"quotes":[{"arxiv_id":"1805.05952","title":"Magnetosphere of a spinning black hole and the role of the current sheet","url":"/paper/1805.05952","section":"Introduction","sentence":"Starting with [ref] , there have been a number of studies of this problem using numerical evolutions of the general-relativistic equations of FFE [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1310.3274","title":"A new scheme for matching general relativistic ideal magnetohydrodynamics to its force-free limit","url":"/paper/1310.3274","section":"Force-Free Electrodynamics (FFE)","sentence":"The first one uses the electric and magnetic fields as the fundamental dynamical variables [ref] , and the second one replaces the electric field by the Poynting vector [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2604.24846","title":"SN Ia Population Machine. I. A Unified Cosmological Simulation-Binary Synthesis Framework Establishing Non-universal Delay-time Distributions and Cosmic Progenitor-channel Dominance Crossover","url":"/paper/2604.24846","section":"Binary Population Synthesis: From Binaries to SNe Ia via Single- and Double-degenerate Channels","sentence":"Several BPS frameworks have been developed to study compact objects and SN progenitors, including [ref] , [ref] , [ref] , the Brussels code [ref] , [ref] , [ref] , and [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"2605.08597","title":"General Grad-Shafranov Equation","url":"/paper/2605.08597","section":"Introduction","sentence":"Via the covariant language in general relativity, stationary and axisymmetric fields near a rotating compact object were studied [ref] , including the preliminary form of the G-S equation in Kerr spacetime [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"2307.00478","title":"Harvesting energy driven by Comisso-Asenjo process from Kerr-MOG black holes","url":"/paper/2307.00478","section":"Introduction","sentence":"The most well-known are the Penrose process (PP) [ref] , the magnetic Penrose process (MPP) [ref] , superradiant scattering [ref] , and the Blandford–Znajek process (BZP) [ref] (see [ref] for more).","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":46},"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":"astro-ph/0402403","kind":"model","paper_version":2,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T19:14:18+00:00","loaded_at":"2026-10-28T01:03:24.443760+00:00","evidence":"substantial","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":5,"entries":[{"p":0.91,"quote":null,"citing":[{"self":false,"year":2026,"title":"Electromagnetic Emission from a Black Hole Evaporating in External Magnetic Field","arxiv_id":"2607.16880"}],"verified":true,"paraphrase":"Used the vacuum constitutive equations derived by this paper to obtain its own equations."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2026,"title":"Emergence of cyclic flux eruptions in kinetic simulations of magnetized spherical accretion onto a Schwarzschild black hole","arxiv_id":"2602.04519"}],"verified":true,"paraphrase":"Used a GRPIC code in which the fields and particle properties are derived in this paper's 3+1 formalism using spherical Kerr-Schild coordinates."},{"p":0.91,"quote":{"text":"We use the equations given by [ref] : [equation] which implies that $D^ϕ$ is nonzero and needs to be solved using Equation [ref].","citing":"2503.04558","section":"Vacuum Wald Solution"},"citing":[{"self":false,"year":2025,"title":"Introducing APERTURE: A GPU-based General Relativistic Particle-in-Cell Simulation Framework","arxiv_id":"2503.04558"}],"verified":true,"paraphrase":"Used the equations given by this paper."},{"p":0.99,"quote":null,"citing":[{"self":false,"year":2019,"title":"Instability of twisted magnetar magnetospheres","arxiv_id":"1908.00010"}],"verified":true,"paraphrase":"Solved Maxwell's equations in the force-free limit in analogy to this paper and another work."},{"p":0.89,"quote":null,"citing":[{"self":false,"year":2018,"title":"First-Principles Plasma Simulations of Black-Hole Jet Launching","arxiv_id":"1810.03613"}],"verified":true,"paraphrase":"Evolved the fields with Maxwell's equations, taking the auxiliary fields from this paper."}],"papers_all":14,"self_papers":0,"self_entries":[]},{"kind":"comparison","label":"Compares with it","papers":1,"entries":[{"p":1.0,"quote":null,"citing":[{"self":false,"year":2013,"title":"A new scheme for matching general relativistic ideal magnetohydrodynamics to its force-free limit","arxiv_id":"1310.3274"}],"verified":true,"paraphrase":"Compared its own steady-state poloidal magnetic field lines with this paper's, finding them very similar."}],"papers_all":4,"self_papers":0,"self_entries":[]}],"counts":{"by_kind":{"data_used":1,"comparison":4,"method_or_tool":14,"supports_this_paper":3},"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":15,"self_papers":0,"citing_papers":78,"sentences_read":18,"citing_sentences":159,"unambiguous_read":18,"typed_independent":18,"independent_papers":78,"by_kind_independent":{"data_used":1,"comparison":4,"method_or_tool":14,"supports_this_paper":3}},"input_sha256":"599188957f2dfdb236e19feb9fa2f3e58fbaa8780e18ecc02861def4565184bd","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":"6 later papers by other authors are listed below: 5 used its method or tool and 1 compared its own results with it."},"_links":{"html":"https://pith.science/paper/astro-ph/0402403"}}