Nontrivial isometric embeddings for flat spaces

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Nontrivial isometric embeddings for flat spaces. / Paston, Sergey ; Zaitseva, Taisiia.

In: Universe, Vol. 7, No. 12, 477, 04.12.2021.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{89a1e197e5d14685a46a80bfc88ea7e4,

title = "Nontrivial isometric embeddings for flat spaces",

abstract = "Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be required to have the same symmetry as the metric. On the other hand, it is possible to require the embedding to be unfolded so that the surface in the ambient space would occupy the subspace of the maximum possible dimension. In the weak gravitational field limit, such a requirement together with a large enough dimension of the ambient space makes embedding gravity equivalent to general relativity, while at lower dimensions it guarantees the linearizability of the equations of motion. We discuss symmetric embeddings for the metrics of flat Euclidean three-dimensional space and Minkowski space. We propose the method of sequential surface deformations for the construction of unfolded embeddings. We use it to construct such embeddings of flat Euclidean three-dimensional space and Minkowski space, which can be used to analyze the equations of motion of embedding gravity.",

keywords = "Embedding theory, Free embedding, Isometric embeddings, Regge–Teitelboim gravity, Symmetrical surfaces, Unfolded embedding",

author = "Sergey Paston and Taisiia Zaitseva",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = dec,

day = "4",

doi = "10.3390/universe7120477",

language = "English",

volume = "7",

journal = "Universe",

issn = "2218-1997",

publisher = "MDPI AG",

number = "12",

}

RIS

TY - JOUR

T1 - Nontrivial isometric embeddings for flat spaces

AU - Paston, Sergey

AU - Zaitseva, Taisiia

PY - 2021/12/4

Y1 - 2021/12/4

N2 - Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be required to have the same symmetry as the metric. On the other hand, it is possible to require the embedding to be unfolded so that the surface in the ambient space would occupy the subspace of the maximum possible dimension. In the weak gravitational field limit, such a requirement together with a large enough dimension of the ambient space makes embedding gravity equivalent to general relativity, while at lower dimensions it guarantees the linearizability of the equations of motion. We discuss symmetric embeddings for the metrics of flat Euclidean three-dimensional space and Minkowski space. We propose the method of sequential surface deformations for the construction of unfolded embeddings. We use it to construct such embeddings of flat Euclidean three-dimensional space and Minkowski space, which can be used to analyze the equations of motion of embedding gravity.

AB - Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be required to have the same symmetry as the metric. On the other hand, it is possible to require the embedding to be unfolded so that the surface in the ambient space would occupy the subspace of the maximum possible dimension. In the weak gravitational field limit, such a requirement together with a large enough dimension of the ambient space makes embedding gravity equivalent to general relativity, while at lower dimensions it guarantees the linearizability of the equations of motion. We discuss symmetric embeddings for the metrics of flat Euclidean three-dimensional space and Minkowski space. We propose the method of sequential surface deformations for the construction of unfolded embeddings. We use it to construct such embeddings of flat Euclidean three-dimensional space and Minkowski space, which can be used to analyze the equations of motion of embedding gravity.

KW - Embedding theory

KW - Free embedding

KW - Isometric embeddings

KW - Regge–Teitelboim gravity

KW - Symmetrical surfaces

KW - Unfolded embedding

UR - http://www.scopus.com/inward/record.url?scp=85121380413&partnerID=8YFLogxK

U2 - 10.3390/universe7120477

DO - 10.3390/universe7120477

M3 - Article

AN - SCOPUS:85121380413

VL - 7

JO - Universe

JF - Universe

SN - 2218-1997

IS - 12

M1 - 477

ER -

ID: 90310225