arXiv subjects

S. A. Paston

Publications and source records attributed to S. A. Paston.

At least 37 records · Page 2Linked to original sources

arXiv2020

Explicit isometric embeddings of black holes geometry with non-singular matter distribution

The work is devoted to the construction of explicit embeddings for the metrics of the black holes, formed by nonsingular matter distribution. One of the possible examples of such type of solutions is regular black hole. Using the existing classification of minimal symmetric embeddings of the Schwarzschild metric as a base, we construct embeddings for regular black holes with de Sitter interior. Another simple example is black hole, formed by collapsing homogeneous spherically symmetric cloud of dustlike matter. We discuss embeddings for two variants of such black holes - the one with the eternally existing horizon, when dust ball never leaves the interior of the horizon, and another variant with the dynamically forming horizon.

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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.

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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.

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arXiv2020

Explicit isometric embeddings of collapsing dust ball

The work is devoted to the search for explicit isometric embeddings of a metric corresponding to the collapse of spherically symmetric matter with the formation of a black hole. Two approaches are considered: in the first, the embedding is constructed for the whole manifold at once; in the second, the idea of a junction of solutions, obtained separately for areas inside and outside the dust ball, is used. In the framework of the first approach, a global smooth embedding in 7D space with a signature (2 + 5) was constructed. It corresponds to the formation of the horizon as a result of matter falling from infinity. The second approach generally leads to an embedding in 7D space with the signature (1 + 6). This embedding corresponds to the case when matter flies out of a white hole with the disappearance of its horizon, after which the radius of the dust ball reaches its maximum, and then a collapse occurs with the formation of the horizon of a black hole. The embedding obtained is not smooth everywhere --- it contains a kink on the edge of the dust ball, and {also, it is} not quite global. In the particular case, when the maximum radius of the dust ball coincides with the radius of the horizon, it is possible to construct a global smooth embedding in a flat 6D space with a signature (1 + 5).

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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.

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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.

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arXiv2018

Noether and Belinfante stress-energy tensors for theories with arbitrary Lagrangians of tensor fields

We investigate the connection between stress-energy tensor (SET) arising from Noether's theorem and Belinfante SET which can be obtained as a right-hand side of the Einstein's equation in the flat metric limit. This question is studied in the wide class of Poincarè-invariant field theories with actions which depend on the tensor fields of arbitrary rank and their derivatives of arbitrary order. For this class we derive the relation between these SET and present the exact expression for the difference between them. We also show that the difference between corresponding integrals of motion can be expressed as a surface integral over 2-dimensinal infinitely remote surface.

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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.

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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.

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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.

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arXiv2018

Exact relation between canonical and metric energy-momentum tensors for higher derivative tensor field theories

We discuss the relation between canonical and metric energy-momentum tensors for field theories with actions that can depend on the higher derivatives of tensor fields in a flat spacetime. In order to obtain it we use a modification of the Noether's procedure for curved space-time. For considered case the difference between these two tensors turns out to have more general form than for theories with no more than first order derivatives. Despite this fact we prove that the difference between corresponding integrals of motion still has the form of integral over 2-dimensional surface that is infinitely remote in the spacelike directions.

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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.

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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.

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arXiv2017

Forms of action for perfect fluid in General Relativity and mimetic gravity

We consider various forms of action allowing us to describe a perfect fluid in the framework of General Relativity. First we consider a potential motion without pressure. Starting from an action in terms of the current density vector built similarly to the action of a single particle, we build a series of equivalent actions through various changes of variables. The results are then generalized to the cases of motion with vorticity and the presence of pressure. The obtained forms of action are compared to the previously known variants. We discuss the possibilities to use the obtained results to formulate the theories containing a description of a perfect fluid. A new form of action is proposed for mimetic gravity, which allows a motion with vorticity for mimetic matter as a perfect fluid.

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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.

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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.

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arXiv2017

Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory

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 imposed constraints, this theory can be viewed as an extension of GR. In the present paper we study the canonical description of the embedding theory in this general form. In this case, one of the natural constraints cannot be written explicitly, in contrast to the case where additional Einsteinian constraints are imposed. Nevertheless, it is possible to calculate all Poisson brackets with this constraint. We prove that the algebra of four emerging constraints is closed, i.e., all of them are first-class constraints. The explicit form of this algebra is also obtained.

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arXiv2017

Field-Theoretical Formulation of Regge-Teitelboim Gravity

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 a field theory in which the original pseudo-Rimannian space is defined by the field constant-value surfaces. The symmetry properties of the proposed theory are investigated, and possible structure of the field-theoretical Lagrangian is discussed.

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