Gravitational energy in the framework of embedding and splitting theories

Grad, D. A.; Ilin, R. V.; Paston, S. A.; Sheykin, A. A.

doi:10.1142/s0218271817501887

Cited by 8 publications

(11 citation statements)

References 29 publications

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“…The area of applications of isometric embeddings is quite large and includes the study of the geometric structure of the Riemannian manifolds [27], the classification of solutions of the Einstein equations [1], the calculation of the thermodynamic properties of the spacetimes with a horizon [28,29], the definition of energy in various theories of gravity [30,31], and so on.…”

Section: Isometric Embeddings and Regge-teitelboim Gravitymentioning

confidence: 99%

Modifications of Gravity Via Differential Transformations of Field Variables

et al. 2020

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We discuss field theories appearing as a result of applying field transformations with derivatives (differential field transformations, DFT) to a known theory. We begin with some simple examples of DFTs to see the basic properties of the procedure. In this process the dynamics of the theory might either change or conserve. After that we concentrate on the theories of gravity which appear as a result of various DFT applied to general relativity, namely the mimetic gravity and Regge-Teitelboim embedding theory. We review main results related to the extension of dynamics in these theories, as well as the possibility to write down the action of a theory after DFT as the action of the original theory before DFT plus an additional term. Such a term usually contains some constraints with Lagrange multipliers and can be interpreted as an action of additional matter, which might be of use in cosmological applications, e.g. for the explanation of the effects of dark matter. action, which often turns out very helpful, and addresses many other issues in the theory of gravity, e.g., its quantization [3] and unification with other theories (for a historical survey, see [4] and the references therein; see also [5]).Another early attempt to reformulate GR in terms of alternate variables was made by Cartan [6] and later by Einstein himself (possibly independently, see [7]). They introduced the notion of the tetrad (or vierbein), which has been extensively used in the GR since then. In particular, it allowed V. A. Fock to generalize the Dirac equation to the case of curved spacetime [8]. Moreover, the tetrad approach provides a very convenient way to study torsion in the so-called Einstein-Cartan theory (see, e.g. [9]). Later, Newman and Penrose proposed another kind of tetrad approach to the GR, which was named after them and proved itself very powerful in the analysis of the geometrical structure of GR [10].Probably the most frequently used variables in GR besides the metric are canonical variables of some kind. Indeed, almost any attempt of quantization requires a Hamiltonian and the corresponding canonical formulation. Since the appearance of the pioneering work of Arnowitt, Deser and Misner [11], many other canonical formulations of gravity have been developed [12]. Of course, the canonical approach to GR can be combined with those above [13], leading, e.g., to the loop variables. Besides quantization, Hamiltonian formulation of GR can be of use, e.g., in the analysis of compact sources [14].It must be stressed that all these approaches (at least in their simplest forms) in general do not necessarily lead to the modification of dynamics. However, there are some redefinition procedures of the field variables in gravity, which are by default altering the dynamics of the theory. Many of these are characterized by the presence of additional derivatives of new field variables in the relation between old and new ones.The main purpose of this paper is to put together the results and methods related to the extended dynamics of Lagran...

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Section: Isometric Embeddings and Regge-teitelboim Gravitymentioning

confidence: 99%

Modifications of Gravity Via Differential Transformations of Field Variables

et al. 2020

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“…Now let us substitute (14) and (15) forδϕ A andδg µν into it and then set the spacetime metric equal to flat one g µν → η µν . Note that in this limitL becomes equal to L andT µν becomes equal to T µν (see (2)) and hence for any ξ µ (x) one has the following equation:…”

Section: Search For the Relation Between Canonical And Metric Emtmentioning

confidence: 99%

Exact relation between canonical and metric energy-momentum tensors for higher derivative tensor field theories

Ilin

Paston

2019

Eur. Phys. J. Plus

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We discuss the relation between canonical and metric energy-momentum tensors for field theories with actions that can depend on the higher derivatives of tensor fields in a flat spacetime. In order to obtain it we use a modification of the Noether's procedure for curved space-time. For considered case the difference between these two tensors turns out to have more general form than for theories with no more than first order derivatives. Despite this fact we prove that the difference between corresponding integrals of motion still has the form of integral over 2-dimensional surface that is infinitely remote in the spacelike directions. *

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“…As the splitting theory has the form of a some field theory in a flat spacetime, it is possible to define the metric EMT, namely to vary the action with respect to ambient space metric. For the action (9) this procedure gives [10] the EMT as the sum of gravitational and matter parts:…”

Section: The Metric Emtmentioning

confidence: 99%

“…Let us pick out a contribution of a single surface as it was done in the previous section. Rewriting (22) in the curvilinear coordinates {x µ , z A } in a bulk and assume that x 0 = y 0 , we obtain (see details in [10])…”

Section: The Metric Emtmentioning

confidence: 99%

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Definitions of energy for the description of gravity as the splitting theory

Grad

Paston

Sheykin

2018

J. Phys.: Conf. Ser.

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We study the definitions of energy, naturally arising in the splitting theory, which is the field theoretic formulation of the Regge-Teitelboim gravity. The latter regards our spacetime as a surface embedded in a flat bulk. The splitting theory describes embedded spacetime in the language of the some field theory in a flat bulk. We consider the Noether energy-momentum tensor (EMT) and the metric EMT defined by the variation with respect to the metric of a flat bulk. We discuss a localizability of energy. Then using these EMTs we calculate the full energy of an isolated massive body. We compare the results with the standard general relativity results obtained from the Einstein energy-momentum pseudotensor (pEMT) and from the Møller pEMT. Finally, we propose the several ways of correction of the definitions of the energy in the splitting theory.

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Gravitational energy in the framework of embedding and splitting theories

Cited by 8 publications

References 29 publications

Modifications of Gravity Via Differential Transformations of Field Variables

Modifications of Gravity Via Differential Transformations of Field Variables

Exact relation between canonical and metric energy-momentum tensors for higher derivative tensor field theories

Definitions of energy for the description of gravity as the splitting theory

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