Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction

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Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction. / Шейкин, Антон Андреевич ; Марков, Михаил Викторович ; Пастон, Сергей Александрович.

In: Journal of Mathematical Physics, Vol. 62, No. 10, 102502, 01.10.2021.

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

BibTeX

@article{b2d20d9d16964d32b7c2c66cedd41832,

title = "Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction",

abstract = "It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an ambient space of higher dimension. While most of the existing methods are based on Gauss-Codazzi-Mainardi-Peterson equations, we do not use them and instead concentrate on a system of equations that connects the metric on the manifold and the embedding function of the surface. Our algorithm is based on the group theoretical method of separation of variables that we developed earlier. The algorithm makes this method more convenient and simple to use. It allowed us to simplify the construction of many known embeddings as well as obtain some new ones. In particular, we obtain explicit global (i.e., smooth at all values of radius) embeddings of spinning the BTZ black hole in seven-dimensional flat space.",

keywords = "FIELD-THEORY, GRAVITY, RIEMANNIAN MANIFOLDS",

author = "Шейкин, {Антон Андреевич} and Марков, {Михаил Викторович} and Пастон, {Сергей Александрович}",

note = "Publisher Copyright: {\textcopyright} 2021 Author(s).",

year = "2021",

month = oct,

day = "1",

doi = "10.1063/5.0062060",

language = "English",

volume = "62",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics",

number = "10",

}

RIS

TY - JOUR

T1 - Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction

AU - Шейкин, Антон Андреевич

AU - Марков, Михаил Викторович

AU - Пастон, Сергей Александрович

PY - 2021/10/1

Y1 - 2021/10/1

N2 - It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an ambient space of higher dimension. While most of the existing methods are based on Gauss-Codazzi-Mainardi-Peterson equations, we do not use them and instead concentrate on a system of equations that connects the metric on the manifold and the embedding function of the surface. Our algorithm is based on the group theoretical method of separation of variables that we developed earlier. The algorithm makes this method more convenient and simple to use. It allowed us to simplify the construction of many known embeddings as well as obtain some new ones. In particular, we obtain explicit global (i.e., smooth at all values of radius) embeddings of spinning the BTZ black hole in seven-dimensional flat space.

AB - It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an ambient space of higher dimension. While most of the existing methods are based on Gauss-Codazzi-Mainardi-Peterson equations, we do not use them and instead concentrate on a system of equations that connects the metric on the manifold and the embedding function of the surface. Our algorithm is based on the group theoretical method of separation of variables that we developed earlier. The algorithm makes this method more convenient and simple to use. It allowed us to simplify the construction of many known embeddings as well as obtain some new ones. In particular, we obtain explicit global (i.e., smooth at all values of radius) embeddings of spinning the BTZ black hole in seven-dimensional flat space.

KW - FIELD-THEORY

KW - GRAVITY

KW - RIEMANNIAN MANIFOLDS

UR - http://www.scopus.com/inward/record.url?scp=85117732824&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/cb971ac0-bcf5-3fb6-b77d-88ec84787ded/

U2 - 10.1063/5.0062060

DO - 10.1063/5.0062060

M3 - Article

VL - 62

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 10

M1 - 102502

ER -

ID: 87304389