Embeddings for solutions of Einstein equations

Several time dependent backgrounds, with perfect fluid matter, can be used to construct solutions of Einstein equations in the presence of a negative cosmological constant along with some matter sources. In this work we focus on the non-vacuum Kasner-AdS geometry and its solitonic generalization. To characterize these space-times, we provide ways to embed them in higher dimensional flat space-times. General space-like geodesics are then studied and used to compute the two point boundary correlators within the geodesic approximation.

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“…for an arbitrary future directed timelike vector field v a , where T = 3 2 T dz 2 part. Introducing new coordinates [30],…”

Section: Ads-frw Embeddingmentioning

confidence: 99%

Nonvacuum AdS cosmology and comments on gauge theory correlator

et al. 2017

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“…Let us suppose that there are no event horisons in the region of our interest, so in this region P (r), Q(r) < 1. The embeddings of the metric (18), which have the SO(3) ⊗ T 1 symmetry and which are smooth in the whole considered region, can be constructed using the method described in [26,27]. The embeddings of the metric satisfying the condition (19) belong to the one out of the six following types.…”

Section: The Absence Of the Extra Solutions For 6-dimensional Symmetrmentioning

confidence: 99%

The approach to gravity as a theory of embedded surface

Sheykin¹,

Paston²

2014

AIP Conference Proceedings

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We study the approach to gravity in which our curved spacetime is considered as a surface in a flat ambient space of higher dimension (the embedding theory). The dynamical variable in this theory is not a metric but an embedding function. The Euler-Lagrange equations for this theory (Regge-Teitelboim equations) are more general than the Einstein equations, and admit "extra solutions" which do not correspond to any Einsteinian metric. The Regge-Teitelboim equations can be explicitly analyzed for the solutions with high symmetry. We show that symmetric embeddings of a static spherically symmetric asymptotically flat metrics in a 6-dimensional ambient space do not admit extra solutions of the vacuum Regge-Teitelboim equations. Therefore in the embedding theory the solutions with such properties correspond to the exterior Schwarzchild metric.Comment: LaTeX, 10 pages. Proceedings of "II Russian-Spanish Congress Particle and Nuclear Physics at all Scales and Cosmology", Saint-Petersburg, October 1-4, 201

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“…For example, N ≥ 48 in the case of generic compact four-dimensional spacetime embedded in a flat ambient spacetime and N ≥ 89 in the case of a non-compact one [24]. However, most symmetric spacetimes can be embedded (even globally) in the spacetimes with a relatively small N; e.g., for a Friedmann-Robertson-Walker (FRW) model N = 5 (see, e.g., [25]) and for a spherically symmetric spacetime N = 6 [26].…”

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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Embeddings for solutions of Einstein equations

Cited by 19 publications

References 31 publications

Nonvacuum AdS cosmology and comments on gauge theory correlator

Nonvacuum AdS cosmology and comments on gauge theory correlator

The approach to gravity as a theory of embedded surface

Modifications of Gravity Via Differential Transformations of Field Variables

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