35 citations · 143 across the 21 of their papers we have counts for
21 papers
Classification of ten-dimensional embeddings of spherically symmetric static metrics
S. S. Kuptsov, S. A. Paston, A. A. Sheykin
The group-theoretic method for constructing symmetric isometric embeddings is used to describe all possible four-dimensional surfaces in flat -dimensional space, whose induc…
Yet another way from field theory to gravity
A. A. Sheykin
It is shown that target space diffeomorphism invariance of a generic Lagrangian for a set of scalar fields leads to an analog of Einstein equations for the geometry of a level set…
Lower-dimensional Regge-Teitelboim gravity
A. A. Sheykin, A. A. Grechko
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 s…
Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction
A. A. Sheykin, M. V. Markov, S. A. Paston
It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddi…
Universal Constants as Manifestations of Relativity
A. A. Sheykin
We study the possible interpretation of the "universal constants" by the classification of J.~M.~Lévy-Leblond. and are the most common example of constants of this type…
Canonical description for formulation of embedding gravity as a field theory in a flat spacetime
S. A. Paston, E. N. Semenova, A. A. Sheykin
We consider the approach to gravity in which four-dimensional curved spacetime is represented by a surface in a flat Minkowski space of higher dimension. After a short overview of…
Universal constants and natural systems of units in a spacetime of arbitrary dimension
A. A. Sheykin, S. N. Manida
We study the properties of fundamental physical constants using the threefold classification of dimensional constants proposed by J.-M. L{é}vy-Leblond: constants of objects (masses…
Modifications of gravity via differential transformations of field variables
A. A. Sheykin, D. P. Solovyev, V. V. Sukhanov +1
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 s…
Polyakov-like approach to the modified gravity and other geometric theories
A. A. Sheykin, M. V. Ioffe, S. N. Manida +1
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 w…
Global embeddings of BTZ and Schwarzschild-AdS type black holes in a flat space
A. A. Sheykin, D. P. Solovyev, S. A. Paston
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…
Definitions of energy for the description of gravity as the splitting theory
D. A. Grad, S. A. Paston, A. A. Sheykin
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 spac…
Embedding theory as new geometrical mimetic gravity
S. A. Paston, A. A. Sheykin
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 reform…
Description of gravity in the model with independent nonsymmetric connection
N. V. Kharuk, S. A. Paston, A. A. Sheykin
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent…
Classical electromagnetic potential as a part of gravitational connection: ideas and history
N. V. Kharuk, S. A. Paston, A. A. Sheykin
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…
Gravitational energy in the framework of embedding and splitting theories
D. A. Grad, R. V. Ilin, S. A. Paston +1
We study various definitions of the gravitational field energy based on the usage of isometric embeddings in the Regge-Teitelboim approach. For the embedding theory we consider the…
Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory
S. A. Paston, E. N. Semenova, V. A. Franke +1
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. I…
Field-Theoretical Formulation of Regge-Teitelboim Gravity
A. A. Sheykin, S. A. Paston
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 o…
Friedmann cosmology in Regge-Teitelboim gravity
A. A. Sheykin, S. A. Paston
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…
The approach to gravity as a theory of embedded surface
A. A. Sheykin, S. A. Paston
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…
Embeddings for solutions of Einstein equations
S. A. Paston, A. A. Sheykin
We study isometric embeddings of some solutions of the Einstein equations with suffciently high symmetries into a flat ambient space. We briefly describe a method for constructing…
From the Embedding Theory to General Relativity in a result of inflation
S. A. Paston, A. A. Sheykin
We study the embedding theory being a formulation of the gravitation theory where the independent variable is the embedding function for the four-dimensional space-time in a flat a…