arXiv subjects

A. A. Sheykin

Publications and source records attributed to A. A. Sheykin.

At least 19 recordsLinked to original sources

arXiv2024

Classification of ten-dimensional embeddings of spherically symmetric static metrics

The group-theoretic method for constructing symmetric isometric embeddings is used to describe all possible four-dimensional surfaces in flat $(1,9)$-dimensional space, whose induced metric is static and spherically symmetric. For such surfaces, we propose a classification related to the dimension of the elementary blocks forming the embedding function. All suitable 52 classes of embeddings are summarized in one table and analyzed for the unfolding property (wich means that the surface does not belong locally to some subspace of the ambient space), as well as for the presence of smooth embeddings of the Minkowski metric. The obtained results are useful for the analysis of the equations of motion in the Regge-Teitelboim embedding gravity, where the presence of unfolded embeddings of the Minkowski metric is essential.

gr-qc↗

arXiv2024

Yet another way from field theory to gravity

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 of these fields.

gr-qc↗

arXiv2022

Lower-dimensional Regge-Teitelboim gravity

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 corresponding to a central symmetric vacuum 2+1-dimensional spacetime. In contrast with GR, this vacuum spacetime is not flat, so it is possible for the gravitational field to exist even without matter or cosmological constant.

gr-qc↗

arXiv2021

Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction

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 embeddings of pseudo-Riemannian manifolds with symmetries into an ambient space of higher dimension. While most of the existing methods are based on Gauss-Codazzi-Mainardi-Peterson equations, we do not use them and instead concentrate on a system of equations which connects the metric on the manifold and the embedding function of the surface. Our algorithm is based on the group theoretical method of separation of variables that we developed earlier (arXiv:1202.1204). The algorithm makes this method more convenient and simple to use. It allowed us to simplify the construction of many known embeddings as well as obtain some new ones. In particular, we obtain explicit global embeddings of spinning BTZ black hole in 7-dimensional flat space.

gr-qc↗

arXiv2021

Universal Constants as Manifestations of Relativity

We study the possible interpretation of the "universal constants" by the classification of J.~M.~Lévy-Leblond. $\hbar$ and $c$ are the most common example of constants of this type. Using Fock's principle of the relativity w.r.t. observation means, we show that both $c$ and $\hbar$ can be viewed as manifestations of certain relativity. We also show that there is a possibility to interpret the Boltzmann's constant in a similar way, and make some comments about the relativistic interpretation of the constant spacetime curvature and gravitational constant $G$.

physics.hist-ph↗

arXiv2020

Explicit isometric embeddings of pseudo-Riemannian manifolds: ideas and applications

We study the problem of construction of explicit isometric embeddings of (pseudo)-Riemannian manifolds. We discuss the method which is based in the idea that the exterior symmetry of the embedded surface and the interior symmetry of the metric on it must be the same. In case of high enough symmetry of the metric such method allows to transform the metric inducedness condition, which is the one to be solved in order to construct an embedding, into a system of ODEs. It turns out that this method can be generalized to allow the surface to have lower symmetry as long as the above simplification occurs. This generalization can be of use in the construction of embeddings for metrics whose symmetry group is hard to analyze, as well for the construction of isometrically deformed (bended) surface. We give some examples of application of this method. In particular, we construct the embedding of spatially-flat Friedmann model and isometric bendings of sphere, 3-sphere and squashed AdS universe, which is connected to the Godel universe.

gr-qc↗

arXiv2020

Universal constants and natural systems of units in a spacetime of arbitrary dimension

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, etc.), constants of phenomena (coupling constants), and "universal constants" (such as $c$ and $\hbar$). We show that all of the known "natural" systems of units contain at least one non-universal constant. We discuss the possible consequences of such non-universality, e.g., the dependence of some of these systems on the number of spatial dimensions. In the search for a "fully universal" system of units, we propose a set of constants that consists of $c$, $\hbar$, and a length parameter and discuss its origins and the connection to the possible kinematic groups discovered by L{é}vy-Leblond and Bacry. Finally, we give some comments about the interpretation of these constants.

gr-qc↗

arXiv2020

Canonical description for formulation of embedding gravity as a field theory in a flat spacetime

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 the ideas and results of such an approach we concentrate on the study of the so-called splitting gravity, a form of this description in which constant value surface of a set of scalar fields in the ambient flat space-time defines the embedded surface. We construct a form of action which is invariant w.r.t. all symmetries of this theory. We construct the canonical formalism for splitting gravity. The resulting theory turns out to be free of constraints. However, the Hamiltonian of this theory is an implicit function of canonical variables. Finally, we discuss the path integral quantization of such a theory.

gr-qc↗

arXiv2020

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

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.

gr-qc↗

arXiv2020

Modifications of gravity via differential transformations of field variables

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.

gr-qc↗

arXiv2019

Global embeddings of BTZ and Schwarzschild-AdS type black holes in a flat space

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 that there is no such embedding for 4D RN-AdS black hole in 6D flat ambient space, completing the classification which we started earlier. Then we construct an explicit embedding of non-spinning BTZ black hole in 6D flat ambient space. Using this embedding as an anzats, we then construct a global explicit embedding of (d)-dimensional Schwarzschild-AdS black hole in a flat (d+3)-dimensional ambient space.

gr-qc↗

arXiv2018

Global Embedding of the Reissner-Nordström Metric in the Flat Ambient Space

We study isometric embeddings of non-extremal Reissner-Nordström metric describing a charged black hole. We obtain three new embeddings in the flat ambient space with minimal possible dimension. These embeddings are global, i.e. corresponding surfaces are smooth at all values of radius, including horizons. Each of the given embeddings covers one instance of the regions outside the horizon, one instance between the horizons and one instance inside the internal horizon. The lines of time for these embeddings turn out to be more complicated than circles or hyperbolas. The obtained embeddings are also smooth at all values of radius for extremal and hyperextremal black holes.

gr-qc↗

arXiv2018

Embedding theory as new geometrical mimetic gravity

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.

gr-qc↗

arXiv2018

Modifying the theory of gravity by changing independent variables

We study some particular modifications of gravity in search for a natural way to unify the gravitational and electromagnetic interaction. The certain components of connection in the appearing variants of the theory can be identified with electromagnetic potential. The methods of adding matter in the form of scalar and spinor fields are studied. In particular, the expansion of the local symmetry group up to $GL(2,C)$ is explored, in which equations of Einstein, Maxwell and Dirac are reproduced for the theory with Weyl spinor.

gr-qc↗

arXiv2018

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

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.

gr-qc↗

arXiv2018

Description of gravity in the model with independent nonsymmetric connection

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 variables, and the connection is not symmetric. As a result of variation with respect to the metric Einstein equations are obtained. A variation with respect to the connection leads to an arbitrariness in the determination of connection, i.e. the presence of gauge invariance. Then a matter in a form of point particle which interacts with field of connection is introduced. Also the action is complemented by a kinetic term for field of the connection to avoid incompatible equation of motion. Thus after the variation procedures we obtain the Einstein equations, the geodesic equation and the Maxwell`s equations for electromagnetism, where some components of the connection play the role of the electromagnetic potential. Thereby the electromagnetic potential is obtained from the geometry of space-time.

gr-qc↗

arXiv2017

Gravitational energy in the framework of embedding and splitting theories

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 coordinate translations on the surface as well as the coordinate translations in the flat bulk. In the latter case the independent definition of gravitational energy-momentum tensor appears as a Noether current corresponding to global inner symmetry. In the field-theoretic form of this approach (splitting theory) we consider Noether procedure and the alternative method of energy-momentum tensor defining by varying the action of the theory with respect to flat bulk metric. As a result we obtain energy definition in field-theoretic form of embedding theory which, among the other features, gives a nontrivial result for the solutions of embedding theory which are also solutions of Einstein equations. The question of energy localization is also discussed.

gr-qc↗

arXiv2017

Classical electromagnetic potential as a part of gravitational connection: ideas and history

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 so-called 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.

gr-qc↗