{"arxiv_id":"gr-qc/9712077","incoming":{"papers":76,"sentences":131,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1504.00360","title":"Black hole jet power from impedance matching","url":"/paper/1504.00360","section":"Introduction","sentence":"Recently, we have given an action principle formulation of the membrane at infinity [ref] , extending an earlier action principle formulation of the membrane at the horizon [ref] .","intent_p":0.95,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":8,"sentences":8,"quotes":[{"arxiv_id":"1110.4277","title":"Transport coefficients of D1-D5-P system and the membrane paradigm","url":"/paper/1110.4277","section":"Membrane transport coefficients induced by minimal scalars","sentence":"Let us calculate the membrane transport coefficient of the near extremal black hole induced by $h_ij$ [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1306.1263","title":"Conductivity in the gravity dual to massive ABJM and the membrane paradigm","url":"/paper/1306.1263","section":"Scalar field calculation","sentence":"Following [ref] , we need to add a boundary term at the horizon to the one that arises from variations of this action.","intent_p":0.91,"contests_p":null},{"arxiv_id":"2104.14582","title":"Direct photons emission rate and electric conductivity in twice anisotropic QGP holographic model with first-order phase transition","url":"/paper/2104.14582","section":"Perturbation","sentence":"To obtain equations of motion we use the so-called 'membrane paradigm' [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1111.1242","title":"Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity","url":"/paper/1111.1242","section":"Introduction","sentence":"We follow the standard route of evaluating the surface stress tensor of the perturbed horizon surface, and then comparing it with the structure of the stress tensor for a viscous fluid [ref] to read off the pressure, transport co-efficients, etc.","intent_p":0.85,"contests_p":null},{"arxiv_id":"1504.07616","title":"Effective actions for relativistic fluids from holography","url":"/paper/1504.07616","section":"Introduction and summary","sentence":"Instead, we will couple the effective theory to a simple membrane paradigm boundary condition [ref] a small distance away from the horizon and then take the membrane to the horizon.","intent_p":0.92,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":8,"sentences":11,"quotes":[{"arxiv_id":"2502.18199","title":"Viscosity, entanglement and acceleration","url":"/paper/2502.18199","section":"Unruh effect and KSS bound: resume","sentence":"Moreover, the derivation [ref] and ours differs significantly from the well-known membrane derivation [ref] briefly discussed in Section [ref], in which it is essential that viscosity appears as a quantity visible to an infinitely distant observer.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1206.6924","title":"The Incompressible Rindler fluid versus the Schwarzschild-AdS fluid","url":"/paper/1206.6924","section":"Thermodynamic quantities","sentence":"When $c_1=0$, $$ agrees with the membrane paradigm result [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1503.00728","title":"Energy extraction from boosted black holes: Penrose process, jets, and the membrane at infinity","url":"/paper/1503.00728","section":"Membrane stress-energy tensor","sentence":"This is the same stress-energy tensor that appears in the original black hole membrane paradigm [ref] but with an overall minus sign.","intent_p":0.99,"contests_p":null},{"arxiv_id":"0806.3165","title":"Hydrodynamics of spacetime and vacuum viscosity","url":"/paper/0806.3165","section":"Entropy balance law and vacuum viscosity","sentence":"This result agrees with the equation for the “long-time\" evolution of black hole entropy in the membrane paradigm [ref] , if we identify $ħ/2$ as a Hawking temperature.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1108.5577","title":"RG flow of transport quantities","url":"/paper/1108.5577","section":"Flow equation: Fixed geometry","sentence":"For $g^2_YM=4π$, it reproduces the result of the conductivity found using membrane paradigm [ref] .","intent_p":0.97,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":3,"sentences":3,"quotes":[{"arxiv_id":"0911.0557","title":"Near-Horizon Analysis of $\\eta/s$","url":"/paper/0911.0557","section":"Introduction and Summary","sentence":"There are enough hints [ref] which seems to point to an affirmative answer to this question.","intent_p":0.97,"contests_p":null},{"arxiv_id":"2606.11984","title":"Modular quantization and black holes","url":"/paper/2606.11984","section":"Discussion","sentence":"These include membrane paradigm [ref] - [ref] , as well as related fluid/gravity correspondence in AdS/CFT [ref] , [ref] , the near horizon conformal symmetry with analogous structure of a single copy of the “near-horizon Virasoro algebra” [ref] - [ref] , as noticed in [ref] , Kerr/CFT correspondence [ref] , Carrolian description of near horizon physics [ref] - [ref] , which may provide a natural holographic framework for non-extremal black holes, even beyond the AdS setting.","intent_p":0.99,"contests_p":null},{"arxiv_id":"2006.13106","title":"Emergence of Spacetime: From Entanglement to Einstein","url":"/paper/2006.13106","section":"Stretched Lightcone Thermodynamics","sentence":"This is consistent with the black hole membrane paradigm in which the timelike stretched horizon can also be thought of as having thermodynamic properties [ref] .","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":31,"sentences":34,"quotes":[{"arxiv_id":"1508.06577","title":"BMS invariance and the membrane paradigm","url":"/paper/1508.06577","section":"Introduction","sentence":"According to the membrane paradigm, black hole event horizons behave like 2+1 dimensional fluids [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"1010.5380","title":"Shear viscosity of a highly excited string and the black hole membrane paradigm","url":"/paper/1010.5380","section":"Introduction","sentence":"One of them is the membrane paradigm [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1110.4277","title":"Transport coefficients of D1-D5-P system and the membrane paradigm","url":"/paper/1110.4277","section":"Introduction","sentence":"The membrane paradigm states that a distant observer sees a fictitious membrane or fluid with some transport coefficients such as viscosities and conductivities on a stretched horizon of a black hole [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"0901.2338","title":"Thermal Noise and Stochastic Strings in AdS/CFT","url":"/paper/0901.2338","section":"Introduction","sentence":"When analyzing dissipation in the context of black holes, the notion of a stretched horizon plays a central role [ref] and this surface is shown in string1fig at $r=r_h = 1 + ϵ$.","intent_p":0.88,"contests_p":null},{"arxiv_id":"2502.18199","title":"Viscosity, entanglement and acceleration","url":"/paper/2502.18199","section":"Introduction","sentence":"Initially, the relation for viscosity was obtained for the black hole membrane (see [ref] and references therein), the viscosity of which is at the lower limit of ([ref]) [equation]","intent_p":0.8,"contests_p":null}]}],"unlabelled_sentences":74},"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/9712077","kind":"model","paper_version":2,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T18:56:27+00:00","loaded_at":"2026-10-28T01:03:19.402890+00:00","evidence":"substantial","account":[],"groups":[{"kind":"extends","label":"Builds on it","papers":1,"entries":[{"p":0.95,"quote":null,"citing":[{"self":false,"year":2015,"title":"Black hole jet power from impedance matching","arxiv_id":"1504.00360"}],"verified":true,"paraphrase":"Extended an earlier action principle formulation of the membrane at the horizon given by this paper."}],"papers_all":1,"self_papers":0,"self_entries":[]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":2,"entries":[{"p":0.91,"quote":null,"citing":[{"self":false,"year":2013,"title":"Conductivity in the gravity dual to massive ABJM and the membrane paradigm","arxiv_id":"1306.1263"}],"verified":true,"paraphrase":"Followed this paper in adding a boundary term at the horizon to the one arising from variations of its action."},{"p":0.96,"quote":null,"citing":[{"self":false,"year":2022,"title":"Asymptotic symmetries and memories of gauge theories in FLRW spacetimes","arxiv_id":"2207.13726"}],"verified":true,"paraphrase":"Followed an approach similar to this paper's, approaching a null hypersurface by a timelike hypersurface on which the computation is performed before taking the limit."}],"papers_all":8,"self_papers":0,"self_entries":[]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"entries":[{"p":0.97,"quote":null,"citing":[{"self":false,"year":2020,"title":"Emergence of Spacetime: From Entanglement to Einstein","arxiv_id":"2006.13106"}],"verified":true,"paraphrase":"Said its attribution of entropy to sections of its timelike stretched horizon is consistent with the black hole membrane paradigm, in which this paper holds that the timelike stretched horizon can also be thought of as having thermodynamic properties."}],"papers_all":4,"self_papers":0,"self_entries":[]}],"counts":{"by_kind":{"extends":1,"comparison":8,"method_or_tool":8,"supports_this_paper":4},"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":1,"citing_papers":81,"sentences_read":20,"citing_sentences":142,"unambiguous_read":20,"typed_independent":20,"independent_papers":80,"by_kind_independent":{"extends":1,"comparison":8,"method_or_tool":8,"supports_this_paper":4}},"input_sha256":"ce18672350f1115a5d22a3a26ec49a98e7d2aa40534251b9d1d3f7de3e21fd6b","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":"4 later papers by other authors are listed below: 1 built on it, 2 used its method or tool and 1 cited it as support."},"_links":{"html":"https://pith.science/paper/gr-qc/9712077"}}