Gravity as a field theory in flat space-time

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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“…The polynomial action (25) is no more than quadratic w.r.t. j µ a as well as β µν , moreover, there are no derivatives of these variables.…”

Section: Forms Of Action For Embedding Mattermentioning

confidence: 99%

“…e.g. [17][18][19][20][21][22][23][24][25][26]. A detailed bibliography of embedding theory and close topics can be found in [27].…”

Section: Introductionmentioning

confidence: 99%

Embedding theory as new geometrical mimetic gravity

Paston

Sheykin

2018

Eur. Phys. J. C

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“…The splitting theory [4] describes gravity as a field theory in a flat bulk of higher dimensions. This theory considers N − 4 real fields z A (y), A, B, · · · = 1, .…”

Section: The Splitting Theorymentioning

confidence: 99%

“…Thus, the action (9) is not invariant under the renumeration of the surfaces, but the equations of motion (10) are, nevertheless, possess such an invariance. For the detailed construction of the splitting theory see [4].…”

Section: Any Surface Can Be Viewed As Our Spacetimementioning

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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When does the Hawking into Unruh mapping for global embeddings work?

Paston

2014

J. High Energ. Phys.

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Abstract:We discuss for which smooth global embeddings of a metric into a Minkowskian spacetime the Hawking into Unruh mapping takes place. There is a series of examples of global embeddings into the Minkowskian spacetime (GEMS) with such mapping for physically interesting metrics. These examples use Fronsdal-type embeddings for which timelines are hyperbolas. In the present work we show that for some new embeddings (non Fronsdal-type) of the Schwarzschild and Reissner-Nordström metrics there is no mapping. We give also the examples of hyperbolic and non hyperbolic type embeddings for the de Sitter metric for which there is no mapping. For the Minkowski metric where there is no Hawking radiation we consider a non trivial embedding with hyperbolic timelines, hence in the ambient space the Unruh effect takes place, and it follows that there is no mapping too. The considered examples show that the meaning of the Hawking into Unruh mapping for global embeddings remains still insufficiently clear and requires further investigations.

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Gravity as a field theory in flat space-time

Cited by 43 publications

References 4 publications

Embedding theory as new geometrical mimetic gravity

Embedding theory as new geometrical mimetic gravity

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

When does the Hawking into Unruh mapping for global embeddings work?

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