Related papers: The approach to gravity as a theory of embedded su…
We study modified gravity theory known as Regge-Teitelboim approach, in which the gravity is represented by dynamics of a surface isometrically embedded in a flat bulk. We obtain some particular solutions of Regge-Teitelboim equations…
Regge-Teitelboim embedding gravity is the modified gravity based on a simple string-inspired geometrical principle: our spacetime is considered here as a 4-dimensional surface in a flat bulk. This theory is similar to the recently popular…
The description of gravity in the form of an embedding theory is based on the hypothesis that our space-time is a four-dimensional surface in a flat ten-dimensional space. The choice of standard Einstein-Hilbert action leads in this case to…
In the Regge-Teitelboim model, gravity is described by embedding the space-time manifold in a (usually flat) fixed higher-dimensional background, where the embedding coordinates, rather than the metric tensor, are the dynamical degrees of…
We propose a formulation of gravity theory in the form of a field theory in a flat space-time with a number of dimensions greater than four. Configurations of the field under consideration describe the splitting of this space-time into a…
This paper is devoted to the approach to gravity as a theory of a surface embedded in a flat ambient space. After the brief review of the properties of original theory by Regge and Teitelboim we concentrate on its field-theoretic…
We study the possibility to explain the mystery of the dark matter through the transition from General Relativity to embedding gravity. This modification of gravity, which was proposed by Regge and Teitelboim, is based on a simple…
We consider the embedding theory, the approach to gravity proposed by Regge and Teitelboim, in which 4D space-time is treated as a surface in high-dimensional flat ambient space. In its general form, which does not contain artificially…
Theory of gravity is considered in the Regge-Teitelboim approach in which the pseudo-Riemannian space is treated as a surface isometrically embedded in an ambient Minkowski space of higher dimension. This approach is formulated in terms of…
We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…
We discuss the possibility of explaining observations usually related to the existence of dark matter by passing from the general relativity (GR) theory to a modified theory of gravity, the embedding theory proposed by Regge and Teitelboim.…
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…
We discuss Exterior Differential Systems (EDS) for the vacuum gravitational field. These EDS are derived by varying the Hilbert-Einstein Lagrangian, given most elegantly as a Cartan 4-forrm calibrating 4-spaces embedded in ten flat…
We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the…
We suggest a method to search the embeddings of Riemannian spaces with a high enough symmetry in a flat ambient space. It is based on a procedure of construction surfaces with a given symmetry. The method is used to classify the embeddings…
It is proved in the manuscript that as long as the proper coordinate transformation is introduced,, the equations of geodetic lines described in curved space-time can be transformed into the dynamic equations in flat space-time, that is to…
We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the…
The formulation of General Relativity in which the 4-dimensional space-time is embedded in a flat host space of higher dimension is reconsidered. New classes of embeddings (modeled after Nash's classical free embeddings) are introduced.…
A number of recent observations have suggested that the Einstein's theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to…
In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a…