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Embeddings for Schwarzschild metric: classification and new results. / Paston, S.A.; Sheykin, A.A.

In: Classical and Quantum Gravity, Vol. 29, No. 9, 2012, p. 095022_1-17.

Research output: Contribution to journal › Article

Harvard

Paston, SA & Sheykin, AA 2012, 'Embeddings for Schwarzschild metric: classification and new results', Classical and Quantum Gravity, vol. 29, no. 9, pp. 095022_1-17. https://doi.org/10.1088/0264-9381/29/9/095022

APA

Paston, S. A., & Sheykin, A. A. (2012). Embeddings for Schwarzschild metric: classification and new results. Classical and Quantum Gravity, 29(9), 095022_1-17. https://doi.org/10.1088/0264-9381/29/9/095022

Vancouver

Paston SA, Sheykin AA. Embeddings for Schwarzschild metric: classification and new results. Classical and Quantum Gravity. 2012;29(9):095022_1-17. https://doi.org/10.1088/0264-9381/29/9/095022

Author

Paston, S.A. ; Sheykin, A.A. / Embeddings for Schwarzschild metric: classification and new results. In: Classical and Quantum Gravity. 2012 ; Vol. 29, No. 9. pp. 095022_1-17.

BibTeX

@article{2ea2748b821e462f891659a85a51d779,
title = "Embeddings for Schwarzschild metric: classification and new results",
abstract = "We suggest a method to search the embeddings of Riemannian spaces with a high enough symmetry in a flat ambient space. It is based on a procedure of construction surfaces with a given symmetry. The method is used to classify the embeddings of the Schwarzschild metric which have the symmetry of this solution, and all such embeddings in a six-dimensional ambient space (i.~e. a space with a minimal possible dimension) are constructed. Four of the six possible embeddings are already known, while the two others are new. One of the new embeddings is asymptotically flat, while the other embeddings in a six-dimensional ambient space do not have this property. The asymptotically flat embedding can be of use in the analysis of the many-body problem, as well as for the development of gravity description as a theory of a surface in a flat ambient space.",
author = "S.A. Paston and A.A. Sheykin",
year = "2012",
doi = "10.1088/0264-9381/29/9/095022",
language = "English",
volume = "29",
pages = "095022_1--17",
journal = "Classical and Quantum Gravity",
issn = "0264-9381",
publisher = "IOP Publishing Ltd.",
number = "9",

}

RIS

TY - JOUR

T1 - Embeddings for Schwarzschild metric: classification and new results

AU - Paston, S.A.

AU - Sheykin, A.A.

PY - 2012

Y1 - 2012

N2 - We suggest a method to search the embeddings of Riemannian spaces with a high enough symmetry in a flat ambient space. It is based on a procedure of construction surfaces with a given symmetry. The method is used to classify the embeddings of the Schwarzschild metric which have the symmetry of this solution, and all such embeddings in a six-dimensional ambient space (i.~e. a space with a minimal possible dimension) are constructed. Four of the six possible embeddings are already known, while the two others are new. One of the new embeddings is asymptotically flat, while the other embeddings in a six-dimensional ambient space do not have this property. The asymptotically flat embedding can be of use in the analysis of the many-body problem, as well as for the development of gravity description as a theory of a surface in a flat ambient space.

AB - We suggest a method to search the embeddings of Riemannian spaces with a high enough symmetry in a flat ambient space. It is based on a procedure of construction surfaces with a given symmetry. The method is used to classify the embeddings of the Schwarzschild metric which have the symmetry of this solution, and all such embeddings in a six-dimensional ambient space (i.~e. a space with a minimal possible dimension) are constructed. Four of the six possible embeddings are already known, while the two others are new. One of the new embeddings is asymptotically flat, while the other embeddings in a six-dimensional ambient space do not have this property. The asymptotically flat embedding can be of use in the analysis of the many-body problem, as well as for the development of gravity description as a theory of a surface in a flat ambient space.

U2 - 10.1088/0264-9381/29/9/095022

DO - 10.1088/0264-9381/29/9/095022

M3 - Article

VL - 29

SP - 095022_1-17

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 9

ER -

ID: 5327348