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Sergey S. Kokarev

Publications and source records attributed to Sergey S. Kokarev.

At least 19 recordsLinked to original sources
arXiv2019

Dynamic general covariance of physical systems

One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations (optionally covariant) with respect to coordinate diffeomorphisms: the equations, in a sense, retain their form on their solutions. More precisely, non-covariant addends to the equations of such systems always exactly reduced in any order of perturbation theory by solutions of unperturbed (initial) equations. This property demonstrated by a set of simple illustrative examples. Various aspects of the dynamic covariance are discussed.

gr-qc↗
arXiv2010

Isometry classification of cubic homogeneous 3-dimensional forms

The problem of classification of cubic homogeneous Finslerian 3D metrics with respect to their isometries is considered. It is shown, that there are 6 different general affine types of such metrics. Algebras of isometries are presented in apparent kind together with their affine-invariant properties. Interrelation between symmetries and projective classifyings is discussed.

math-ph↗
arXiv2010

Complementarity of Kinematics and Geometry in General Relativity Theory

Relations between kinematics, geometry and law of reference frame motion are considered. We show, that kinematical tensors define geometry up to a space functional arbitrariness when integrability condition for spin tensor is satisfied. Some aspects of geometrization principle and geometrical conventionalism of Poincare are discussed in a light of the obtained results.

gr-qc↗
arXiv2009

Are different geometries really that different?

Here is presented a concept of centrogeometry which can be seen as a combination of the concept of point-like observer with an idea of Poincaré's that different geometries are principally equivalent. As it is to be shown later, all centrogeometries are obtained from each other by general deformation (i.e. active coordinate transformations). Isometries of centrogeometries are equivalent to those of the Euclidean centrogeometry as described by common diffeomorphisms of the Euclidean spheres. There are discussed physical aspects of centrogeometry in the context of chronogeometry, mechanics and cosmology.

gr-qc↗
arXiv2009

Plate-Universe in Multidimensional Elasticity Theory

A number of boundary problems in multidimensional elasticity theory are solved. The solutions can be treated as the simplest cosmological models. Some specific properties of the solutions and experimental consequences of the theory are discussed.

gr-qc↗
arXiv2009

Additive angles in H_3

Within the framework of Berwald-Moor Geometry in H_3, the paper studies the construction of additive poly-angles (bingles and tringles). It is shown that, considering additiveness in the large, there exist an infinity of such poly-angles.

math-ph↗
arXiv2009

Metric bingles and tringles in H_3

In the 3-dimensional Berwald-Moor space are bingles and tringles constructed, as additive characteristic objects associated to couples and triples of unit vectors - practically lengths and areas on the unit sphere. In analogy with the spherical angles, we build two types of bingles (reciprocal and relative). It is shown that reciprocal bingles are norms in the space of exponential angles (in the bi-space H^{\flat}, which exponentially define the representation of poly-numbers. It is shown that the metric of this space coincides with the Berwald-Moor metric of the original space. The relative bingles are connected to the elements of the second bi-space (angles, in the space of angles) H^{2\flat} and allow to provide the doble-exponential representation of poly-numbers. The explicit formulas for relative bingles and tringles contain integrals, which cannot be expressed by means of elementary functions.

math-ph↗
arXiv2009

Three lectures on Newton's laws

Three small lectures are devoted to three Newton's laws, lying in the foundation of classical mechanics. These laws are analyzed from the viewpoint of our contemporary knowledge about space, time and physical interactions. The lectures were delivered for students of YarGU in RSEC "Logos".

gr-qc↗
arXiv2008

Structural instability of Friedmann-Robertson-Walker cosmological models

Cosmological singularity and asymptotic behaviour of scale factor of generalized cosmological models are analyzed in respect of their structural stability. It is shown, that cosmological singularity is structurally unstable for the majority of models with barotropic perfect fluid with strong energy condition. Inclusion of Lambda-term extends the set of structurally stable cosmological models.

gr-qc↗
arXiv2006

Time-dependent Spherically-symmetric 5-D Vacuum Solutions

Vacuum 5-D Einstein equations with spherical symmetry and t-dependence are considered. For the case of separating variables several classes of exact solutions are obtained. Effective matter, induced by geometrical scalar field is analyzed.

gr-qc↗
arXiv2003

Nematic Structure of Space-Time and its Topological Defects in 5D Kaluza-Klein Theory

We show, that classical Kaluza-Klein theory possesses hidden nematic dynamics. It appears as a consequence of 1+4-decomposition procedure, involving 4D observers 1-form λ. After extracting of boundary terms the, so called, "effective matter" part of 5D geometrical action becomes proportional to square of anholonomicity 3-form λ\wedge dλ. It can be interpreted as twist nematic elastic energy, responsible for elastic reaction of 5D space-time on presence of anholonomic 4D submanifold, defined by λ. We derive both 5D covariant and 1+4 forms of 5D nematic equilibrium equations, consider simple examples and discuss some 4D physical aspects of generic 5D nematic topological defects.

gr-qc↗
arXiv2002

5-Dimensional Covariance and Generation of Solutions of Einstein Equations

A generation procedure, based on the 5-dimensional covariance of the Kaluza-Klein theory, is developed. The procedure allows one to obtain exact solutions of the 4-dimensional Einstein equations with electromagnetic and scalar fields from vacuum 5-dimensional solutions using special 5-dimensional coordinate transformations. Relations between the physical properties of the resulting solutions and invariant geometrical properties of the generating Killing vectors are found out.

gr-qc↗
arXiv2002

Deformational Structures on Smooth Manifolds

Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define motions and conformal motions together with deformational decomposition of manifolds, generalizing isometry of Riemannian spaces and consider some physical examples. In frame of dynamical deformational structures we formulate variational procedure for evolutional and static cases together with boundary conditions, derive dynamical (equilibrium in static case) equations, consider perturbative approach and perform deformational realization of the well known classical field-theoretical topics: strings and branes theories, classical mechanics of solids, gravity and Maxwell electrodynamics.

math-ph↗
arXiv2002

Geometrization of perfect fluid in 5-D Kaluza-Klein theory

General formulation of geometrization matter problem by scalar field $ϕ=\sqrt{-G_{55}}$ with the help of possibilities of classical 5-D Kaluza-Klein theory is given. Mathematical integrability conditions for such geometrization for the case of perfect fluid are derived.

gr-qc↗
arXiv2002

Gravity as a Bend of 4D Elastic Plate

Gravity is treated as manifestation of bending of 4D plate at the variational functionals level. Some estimates of elastic constants of space-time are made. Field lagrangians and Einstein equations are discussed in view point of the approach.

gr-qc↗
arXiv2002

d-objects kinematics on smooth manifolds

The kinematical part of general theory of deformational structures on smooth manifolds is developed. We introduce general concept of d-objects deformation, then within the set of all such deformations we develop some special algebra and investigate group and homotopical properties of the set. In case of proper deformations some propositions, generalizing isometry theory on Riemannian manifolds are formulated.

hep-th↗
arXiv2001

Clasical solids dynamics as 4D statics of elastic strings

Variational principle for a solid in classical mechanics is formulated in terms of a thin elastic 4D bar strain in Minkowsky events space of special relativity. It is shown, that the sum of elastic 4-energies of weak twist and bending under some identifications takes the form of classical non-relativistic action for a solids dynamics. The necessary conditions on 4D bar parameters and elastic constants, providing validity of Newton mechanics, are found.

gr-qc↗