The approach to gravity as a theory of embedded surface

Sheykin, A. A.; Paston, S. A.

doi:10.1063/1.4891157

Cited by 18 publications

(44 citation statements)

References 34 publications

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“…We see that, in this case, which is analogous to the one considered in Section 2.2, the extension of dynamics occurs as a result of the DFT in Equation (29). Furthermore, as in Section 2.2, the dynamics coincides with the original one if τ µν = 0 in an arbitrary moment of time (or at arbitrary value of any coordinate, see [15]). However, it was shown in [35] that the conservation of dynamics can be achieved (with certain technical assumptions) by imposing a much weaker condition…”

Section: Isometric Embeddings and Regge-teitelboim Gravitysupporting

confidence: 58%

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 Gravitysupporting

confidence: 58%

Modifications of Gravity Via Differential Transformations of Field Variables

et al. 2020

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“…We consider this model as an intermediate stage before formulating a consistent field theory that 250 takes into account the approaches of local isometric embedding's methods. These methods were considered in [44][45][46][47]. From these researches it follows that each manifold requires a separate study on "embedding" , which makes it difficult to develop a general theory used for comparison with the observed data.…”

Section: Introduction To the Original Theorymentioning

confidence: 99%

The Ambiguity in the Definition and Behavior of the Gravitational and Cosmological ‘Coupling Constants’ in the Theory of Induced Gravity

Zaripov¹

2019

Symmetry

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This work is the extension of author's research, where the modified theory of induced gravity (MTIG) is proposed. The theory describes two systems (stages): Einstein (ES) and "restructuring" (RS). We consider equations with quadratic potential that are symmetric with respect to scale transformations. The solutions of the equations obtained for the case of spaces defined by the Friedman-Robertson-Walker metric, as well as for a centrally symmetric space are investigated. In our model arise effective gravitational and cosmological "constants" , which are defined by the "mean square" of the scalar fields. In obtained solutions the values of such parameters as "Hubble parameter", gravitational and cosmological "constants" in the RS stage fluctuate near monotonically evolving mean values. These parameters are matched with observational data, described as phenomena of dark energy and dark matter. The MTIG equations for the case of a centrally symmetric gravitational field, in addition to the Schwarzschild-de Sitter solutions, contain solutions that lead to the new physical effects at large distances from the center. The Schwarzschild-Sitter solution becomes unstable and enters the oscillatory regime. For distances greater than a certain critical value, the following effects can appear: deviation from General relativity and Newton's law of gravitational interaction, antigravity. Telescope (HST) and Planck observatory [5]. The Hubble Space Telescope is tuned to measure the parallax Milky Way Cepheid variables and the distances are 1.7-3.6 kpc (the modern Universe). The measurements of the Planck spacecraft correspond to distant galaxies (the early Universe is about 375,000 years old). In 2018, the accuracy of the measurement of H 0 is increased to 2.3 percent, which gives H 0 = 73.48 ± 1.66 km · s −1 Mpc −1 . In the early Universe, based on the data received from the "Planck" spacecraft and ΛCDM theory, the predicted value is H 0 = 67.0 ± 1.2 km · s −1 Mpc −1 . The difference is about 9 percent. The accuracy of the measurements is about 4.5 percent. There is also a variance in the observations made at different times and different methods. For example, as indicated in the work [6], the local and direct definition of H 0 gives H 0 = 73.24 ± 1.74 km · s −1 Mpc −1 , and the most recent value from [7] in consent with ΛCDM is 66.93 ± 0.62 km · s −1 Mpc −1 . In our opinion, the problem can be reduced to a strong binding of calculations of the Hubble parameter H 0 to the ΛCDM model. In our work we present a model where, due to the oscillatory regime in the solutions of equations, the Hubble parameter also fluctuates with respect to the mean value-which is also a function of time.3. The problems of so-called "dark energy" (DE) and "dark matter" (DM). The first of them can be reduced to the problem of existence and smallness of the "cosmological constant" (par. 1). The challenge posed by the cosmological constant problem [1] has spurred many attempts at directly modifying Einstein's gravity at large distances [8]. As example of s...

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“…Note that without loss of generality one can assume that a, b ≥ 0. The polynomial (25) is positive at r → ∞ if al < 1, so we assume it. Let us consider the quotient of (25) and the positive quantity b 2 (1 − a 2 l 2 )(l 2 + r 2 ):…”

Section: Appendix B Non-negativity Of the Polynomial (25)mentioning

confidence: 99%

Global Embeddings of BTZ and Schwarzschild-ADS Type Black Holes in a Flat Space

2019

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We study the problem of construction of global isometric embedding for spherically symmetric black holes with negative cosmological constant in various dimensions. Firstly, we show that there is no such embedding for 4D RN-AdS black hole in 6D flat ambient space, completing the classification which we started earlier. Then we construct an explicit embedding of non-spinning BTZ black hole in 6D flat ambient space. Using this embedding as an anzats, we then construct a global explicit embedding of (d)-dimensional Schwarzschild-AdS black hole in a flat (d + 3)-dimensional ambient space. *

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The approach to gravity as a theory of embedded surface

Cited by 18 publications

References 34 publications

Modifications of Gravity Via Differential Transformations of Field Variables

Modifications of Gravity Via Differential Transformations of Field Variables

The Ambiguity in the Definition and Behavior of the Gravitational and Cosmological ‘Coupling Constants’ in the Theory of Induced Gravity

Global Embeddings of BTZ and Schwarzschild-ADS Type Black Holes in a Flat Space

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