Forms of action for perfect fluid in general relativity and mimetic gravity

Paston, S. A.

doi:10.1103/physrevd.96.084059

Cited by 27 publications

(38 citation statements)

References 27 publications

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“…For the description of such a matter one can choose a current J µ (x) as an independent variable, which is a vector density and satisfies the continuity equation ∂ µ J µ = 0. Various forms of the action of the ideal fluid based on this choice are examined in [28]. The part of the action S 3 describing the interaction of the ideal fluid with the connection Γ µ βα can be written by analogy with (26) in the following form:…”

Section: Resultsmentioning

confidence: 99%

Classical Electromagnetic Potential as a Part of Gravitational Connection: Ideas and History

2018

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We consider a natural form of unified theory of gravity and electromagnetism which was somehow missed at the time of intense search for such an unification, and was noticed only in 1978 but remained quite unknown. The basic idea of this unification is to use the metric and non-symmetric connection as independent variables, which generalizes the socalled Palatini formalism. The certain components of connection in the appearing theory can be naturally identified with electromagnetic potential, and with the proper choice of action the Einstein-Maxwell equations are reproducing. In this paper we compare such an approach with the known ideas of unification. Also we propose the more consistent way of including matter (in the form of classical particles) in the theory and briefly discuss the perspectives of further development of this approach. *

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Section: Resultsmentioning

confidence: 99%

Classical Electromagnetic Potential as a Part of Gravitational Connection: Ideas and History

2018

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“…can be used in the description of an perfect fluid with no vorticity [3]. The similarity between the action of embedding matter (13) and potentially moving perfect fluid (22) is not confined to the presence of Lagrange multipliers.…”

Section: Forms Of Action For Embedding Mattermentioning

confidence: 99%

“…By analogy with the possibility to write the perfect fluid action (22) in many equivalent ways [3], there are several ways to write an action equivalent (possibly up to certain special solutions) to (13) without the use of matrix root. In this case, however, the number of independent variables increases.…”

Section: Forms Of Action For Embedding Mattermentioning

confidence: 99%

“…In the latter case the description of mimetic matter contains two more fields in addition to n and λ. Moreover, one can return to the original formulation of mimetic gravity with the auxiliary metricg µν and three scalar fields that are present in the expression for physical metric g µν analogous to (1), see details in [3]. For the current status of mimetic gravity framework see the review [10] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Embedding theory as new geometrical mimetic gravity

Paston

Sheykin

2018

Eur. Phys. J. C

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It is known that recently proposed model of mimetic gravity can be presented as general relativity with an additional mimetic matter. We discuss a possibility to analogously reformulate the embedding theory, which is the geometrical description of gravity proposed by Regge and Teitelboim, treating it also as general relativity with some additional matter. We propose a form of action which allows to describe this matter in terms of conserved currents. This action turns out to be a generalization of the perfect fluid action, which can be useful in the analysis of the properties of the additional matter. On the other side, the action contains a trace of the root of the matrix product, which is similar to the constructions appearing in bimetric theories of gravity. The action is completely equivalent to the original embedding theory, so it is not just some artificial model, but has a clear geometric sense. We discuss the possible equivalent forms of the theory and ways of study of the appearing equations of motion. *

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“…Then it was immediately noticed [7] that the action of the theory can be rewritten in the form of GR plus an additional mimetic matter term which simplifies the analysis of its behavior. Later this action was generalized to the case of mimetic matter with arbitrary motion [8], for other generalizations see [9].…”

Section: Introductionmentioning

confidence: 99%

Polyakov-like approach to the modified gravity and other geometric theories

Sheykin

Ioffe

Manida

et al. 2020

Int. J. Geom. Methods Mod. Phys.

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We study the procedure that allows to rewrite the actions of some modified gravity theories like mimetic gravity and Regge-Teitelboim embedding theory as Einstein-Hilbert actions with additional matter contributions. It turns out that this procedure can be applied to brane action, which lead to a polynomial brane action. We also examine the connection between this procedure and Polyakov trick in string theory.

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Forms of action for perfect fluid in general relativity and mimetic gravity

Cited by 27 publications

References 27 publications

Classical Electromagnetic Potential as a Part of Gravitational Connection: Ideas and History

Classical Electromagnetic Potential as a Part of Gravitational Connection: Ideas and History

Embedding theory as new geometrical mimetic gravity

Polyakov-like approach to the modified gravity and other geometric theories

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