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On the existence of initial data containing isolated black holes

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Sergio Dain, Jose Luis Jaramillo, Badri Krishnan

General Relativity and Quantum Cosmology · Submitted 13 Dec 2004

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show rigorously that with these choices, the resulting non-linear elliptic system always admits solutions.

how it is stated · asserted 1.00 read the record →

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arXiv IDgr-qc/0412061 (version 1)
Pith IDSCBS6Q4M, Pith's permanent record of this paper and its review
CitationBadri Krishnan, Jose Luis Jaramillo, Sergio Dain. "On the existence of initial data containing isolated black holes." arXiv:gr-qc/0412061 (2004). https://pith.science/paper/SCBS6Q4M
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The paper's own sentences, arranged. 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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,261 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary conditions that must be imposed there. We show rigorously that with these choices, the resulting non-linear elliptic system always admits solutions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. contribution 0.99 0.95 0.72 asserted 1.00
s1 Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. method 0.83 0.65 0.05 asserted 0.99
s2 The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. background 0.70 0.20 0.04 asserted 0.98
s3 Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary conditions that must be imposed there. method 0.97 0.92 0.06 asserted 0.98
s4 We show rigorously that with these choices, the resulting non-linear elliptic system always admits solutions. result 0.99 0.95 0.70 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.73 · evidence from proof or derivation 1.00.

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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

The paper
Original abstract

We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary conditions that must be imposed there. We show rigorously that with these choices, the resulting non-linear elliptic system always admits solutions.

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