Canonical formulation of the embedded theory of gravity equivalent to Einstein’s general relativity

We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form that requires imposing additional constraints, which are a part of Einstein’s equati...

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Bibliographic Details
Published inTheoretical and mathematical physics Vol. 153; no. 2; pp. 1582 - 1596
Main Authors Paston, S. A., Franke, V. A.
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.11.2007
Subjects
Embedding
Equivalence
Gravitation theory
Independent variables
Mathematical analysis
Relativity
Symmetry
Theory of relativity
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Summary:We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form that requires imposing additional constraints, which are a part of Einstein’s equations. As a result, we obtain a theory with an eight-parameter gauge symmetry. This theory becomes equivalent to Einstein’s general relativity either after partial gauge fixing or after rewriting the metric in the form that is invariant under the additional gauge transformations. We write the action for such a theory.
ISSN:0040-5779
1573-9333
DOI:10.1007/s11232-007-0134-9