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Dynamical Properties of Euclidean Solutions in a Multidimensional Cosmological Model

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Hirotaka Ochiai, Katsuhiko Sato

General Relativity and Quantum Cosmology · Submitted 22 Jul 2000

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

The authors' main claim In the case that both the curvatures of external and internal spaces are positive, and $\Lambda>0$, there exist Lorentzian solutions which start near the quasi-attractor, the internal space remains microscopic, and the external space evolves into our macroscopic universe.

how it is stated · asserted 0.96 read the record →

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arXiv IDgr-qc/0007059 (version 1)
Pith IDF6ERIXQR, Pith's permanent record of this paper and its review
CitationHirotaka Ochiai, Katsuhiko Sato. "Dynamical Properties of Euclidean Solutions in a Multidimensional Cosmological Model." arXiv:gr-qc/0007059 (2000). https://pith.science/paper/F6ERIXQR
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,760 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.38 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In the framework of the Hartle-Hawking no-boundary proposal, we investigated quantum creation of the multidimensional universe with a cosmological constant ($\Lambda$) but without matter fields. We have found that the classical solutions of the Euclidean Einstein equations in this model have ``quasi-attractors'', i.e., most trajectories on the a-b plane, where a and b are the scale factors of external and internal spaces, go around a point. It is presumed that the wave function of the universe has a hump near this quasi-attractor point. In the case that both the curvatures of external and internal spaces are positive, and $\Lambda>0$, there exist Lorentzian solutions which start near the quasi-attractor, the internal space remains microscopic, and the external space evolves into our macroscopic universe.

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 In the framework of the Hartle-Hawking no-boundary proposal, we investigated quantum creation of the multidimensional universe with a cosmological constant ($\Lambda$) but without matter fields. contribution 0.84 0.90 0.04 asserted 0.97
s1 We have found that the classical solutions of the Euclidean Einstein equations in this model have ``quasi-attractors'', i.e., most trajectories on the a-b plane, where a and b are the scale factors of external and internal spaces, go around a point. result 1.00 0.95 0.41 asserted 1.00
s2 It is presumed that the wave function of the universe has a hump near this quasi-attractor point. interpretation 0.99 0.17 0.14 speculative 0.69
s3 In the case that both the curvatures of external and internal spaces are positive, and $\Lambda>0$, there exist Lorentzian solutions which start near the quasi-attractor, the internal space remains microscopic, and the external space evolves into our macroscopic universe. result 0.98 0.75 0.58 asserted 0.96

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.95.

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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

In the framework of the Hartle-Hawking no-boundary proposal, we investigated quantum creation of the multidimensional universe with a cosmological constant ($\Lambda$) but without matter fields. We have found that the classical solutions of the Euclidean Einstein equations in this model have ``quasi-attractors'', i.e., most trajectories on the a-b plane, where a and b are the scale factors of external and internal spaces, go around a point. It is presumed that the wave function of the universe has a hump near this quasi-attractor point. In the case that both the curvatures of external and internal spaces are positive, and $\Lambda>0$, there exist Lorentzian solutions which start near the quasi-attractor, the internal space remains microscopic, and the external space evolves into our macroscopic universe.

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1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as background 1 paper
  • Specifically, we perform the analysis in $D=4+n$ dimensions using a standard and widely used asymptotic metric: [equation] a configuration extensively discussed in the literature (see, e.g., [ref] ), $n=1,2,...,$ is the number of extra dimensions.

    Multidimensional arrow of time · The multidimensional arrow of time · 0.94

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