The ADM Lagrangian in extrinsic gravity

Franke, V. A.; Tapia, Víctor

doi:10.1007/bf02723170

Cited by 18 publications

(31 citation statements)

References 15 publications

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“…A further analysis of this result on the constraints surface does not require dealing with implicitly specified expressions and can be performed by a direct calculation. As a result of this analysis, it becomes possible to prove that if the constraints (16) and (17) the expression (33), and hence the expression (24) turn to zero, i.e., the Poisson brackets Φ 4 γ , Φ 4 σ turn out to be proportional to the constraints.…”

Section: The Constraints Algebramentioning

confidence: 99%

Algebra of implicitly defined constraints for gravity as the general form of embedding theory

Paston¹,

Semenova²,

Franke³

et al. 2017

Gravit. Cosmol.

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We consider the embedding theory, the approach to gravity proposed by Regge and Teitelboim, in which 4D space-time is treated as a surface in high-dimensional flat ambient space. In its general form, which does not contain artificially imposed constraints, this theory can be viewed as an extension of GR. In the present paper we study the canonical description of the embedding theory in this general form. In this case, one of the natural constraints cannot be written explicitly, in contrast to the case where additional Einsteinian constraints are imposed. Nevertheless, it is possible to calculate all Poisson brackets with this constraint. We prove that the algebra of four emerging constraints is closed, i.e., all of them are first-class constraints. The explicit form of this algebra is also obtained. *

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Section: The Constraints Algebramentioning

confidence: 99%

Algebra of implicitly defined constraints for gravity as the general form of embedding theory

Paston¹,

Semenova²,

Franke³

et al. 2017

Gravit. Cosmol.

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“…If we suppose that (aρ τ )/(ρ τȧ ) is limited by a constant (as we will see in the following, it is true for any epoch after the inflation), then we can easily obtain from (21) that the absolute value of p τ cannot strongly exceed ρ τ . This is why, if β ≪ 1, it means that the Einstein equations (in the framework of FRW symmetry) are satisfied with a good precision, since in the equation (7) the contribution τ µν is small compared to T µν . Using the known dependencies ρ(a) for the epochs where different kinds of matter play a major role, we easily to obtain, using (37), the dependence of the values ρ τ and β on a for these epochs, assuming that the relation ρ τ ≪ ρ remains valid.…”

Section: Expansion After Inflationmentioning

confidence: 99%

“…Since the embedding theory is formulated in a flat ambient space, the role of the "physical" time can be played by a time-like coordinate. Note that this problem needs a separate consideration, since a canonical formalism for the embedding theory appears to be very complicated [6,7,8,9], as it contains the second class constraints.…”

Section: Introductionmentioning

confidence: 99%

From the Embedding Theory to General Relativity in a Result of Inflation

Paston

Sheykin

2012

Int. J. Mod. Phys. D

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We study the embedding theory being a formulation of the gravitation theory where the independent variable is the embedding function for the four-dimensional space-time in a flat ambient space. We do not impose additional constraints which are usually used to remove from the theory the extra solutions not being the solutions of Einstein equations. In order to show the possibility of automatic removal of these extra solutions we analyze the equations of the theory, assuming an inflation period during the expansion of the Universe. In the framework of FRW symmetry we study the initial conditions for the inflation, and we show that after its termination the Einstein equations begin to satisfy with a very high precision. The properties of the theory equations allow us to suppose with confidence that the Einstein equations will satisfy with enough precision out of the framework of FRW symmetry as well. Thus the embedding theory can be considered as a theory of gravity which explains observed facts without any additional modification of it and we can use this theory in a flat space when we try to develop a quantum theory of

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“…We note that it is extremely difficult to write this constraint as an algebraic expression (this problem was studied in [10]). But instead of studying the general case, we assume that Einstein's constraints (42) are additionally imposed when constructing the canonical formalism.…”

Section: Canonical Formalism With Additionally Imposed Einstein's Conmentioning

confidence: 99%

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

2007

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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.

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The ADM Lagrangian in extrinsic gravity

Cited by 18 publications

References 15 publications

Algebra of implicitly defined constraints for gravity as the general form of embedding theory

Algebra of implicitly defined constraints for gravity as the general form of embedding theory

From the Embedding Theory to General Relativity in a Result of Inflation

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

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