arXiv subjects

Sergey G. Fedosin

Publications and source records attributed to Sergey G. Fedosin.

13 recordsLinked to original sources

arXiv2025

Lagrangian formalism in the theory of relativistic vector fields

The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its derivatives are directly involved. The obtained results, including equation for metric, equation of motion, equations for fields, are applied to purely vector fields. As a consequence, formulas are determined for calculating the basic quantities necessary to describe physical systems. In this case, not only the pressure field and the acceleration field are taken into account, but also the electromagnetic and gravitational fields outside the matter, which contribute to the four-momentum and to the four-dimensional angular momentum pseudotensor of each system. It is shown that the canonical representation of the angular momentum pseudotensor is its representation with covariant indices. The radius-vector of the center of momentum of a physical system is determined in covariant form.

physics.gen-ph↗

arXiv2024

The potentials of the acceleration field and pressure field in rotating relativistic uniform system

The scalar and vector potentials of the acceleration field and the pressure field are calculated for the first time for a rotating relativistic uniform system, and the dependence of the potentials on the angular velocity is found. These potentials are compared with the potentials for the non-rotating uniform system that have been found previously. The rotation leads to the appearance of vector potentials, which at each point turn out to be directed along the corresponding linear velocity of rotation. The calculation shows that for rotating stellar objects the contribution to the fields vector potentials from the proper random motion of particles is small compared to the contribution from rotation and may not be taken into account. From the expression for the pressure field potential a relativistic formula follows that relates the pressure, mass density, and mean square velocity of the particles. This formula in the limit of low speeds corresponds to the expression for the pressure in molecular kinetic theory. When calculating the potentials, a new method is used that takes into account the potentials of two different bodies, a cylinder and a sphere, for solving the wave equation of rotating system.

physics.gen-ph↗

arXiv2024

Electron-ion model of ball and bead lightning

Based on the electron-ion model, parameters of ball and bead lightning are calculated. The model allows us to estimate maximum size of ball lightning, its energy content, electric charge and magnetic field, to determine equilibrium conditions between positively charged ions located inside and outer shell containing rapidly moving electrons. An explanation is given to the fact that shells are observed inside ball lightning that differ from each other in color of glow. The model describes structure of not only ball lightning, but also bead lightning. The long-term stability of bead lightning is associated with the balance of neighboring beads under action of magnetic force of their attraction and electric force of repulsion, which exceed in magnitude the force of wind pressure.

physics.plasm-ph↗

arXiv2024

What should we understand by the four-momentum of physical system?

It is shown that in curved spacetime none of the known definitions of four-momentum correspond to the definition, in which all the system particles and fields, including fields outside matter, make an explicit contribution to the four-momentum. This drawback can be eliminated under the assumption that the primary representation of four-momentum is the sum of two nonlocal four-vectors of the integral type with covariant indices. The first of these four-vectors is the generalized four-momentum, found with the help of Lagrangian density. The second four-vector is the four-momentum of fields themselves, and its time component is related to the energy given by tensor invariants. The standard approach makes it possible to find the four-momentum in covariant form only for a free point particle. In contrast, the obtained formulas for calculating the four-momentum components are applied to a stationary and moving relativistic uniform system, consisting of many particles. In this case, the main fields of the system under consideration are taken into account, including the electromagnetic and gravitational fields, the acceleration field and the pressure field. The formalism used includes the principle of least action, charged and neutral four-currents, corresponding four-potentials and field tensors, which ensures unification and the possibility of combining fields into a single interaction. The calculation of the integral vector components shows that the so-called integral vector is not equal to four-momentum and is not a four-vector at all, although it is conserved in a closed system. Thus, the four-momentum cannot be found with the help of an integral vector and components of the system stress-energy tensor, in contrast to how it is assumed in the general theory of relativity.

physics.gen-ph↗

arXiv2024

Generalized Four-momentum for Continuously Distributed Materials

A four-dimensional differential Euler-Lagrange equation for continuously distributed materials is derived based on the principle of least action, and instead of Lagrangian, this equation contains the Lagrangian density. This makes it possible to determine the density of generalized four-momentum in covariant form as derivative of the Lagrangian density with respect to four-velocity of typical particles of a system taken with opposite sign, and then calculate the generalized four-momentum itself. It is shown that the generalized four-momentum of all typical particles of a system is an integral four-vector and therefore should be considered as a special type of four-vectors. The presented expression for generalized four-momentum exactly corresponds to the Legendre transformation connecting the Lagrangian and Hamiltonian. The obtained formulas are used to calculate generalized four-momentum of stationary and moving relativistic uniform systems for the Lagrangian with particles and vector fields, including electromagnetic and gravitational fields, acceleration field and pressure field. It turns out that the generalized four-momentum of a moving system depends on the total mass of particles, on the Lorentz factor and on the velocity of the systems center of momentum. Besides, an additional contribution is made by the scalar potentials of the acceleration field and the pressure field at the center of system. The direction of the generalized four-momentum coincides with the direction of four-velocity of the system under consideration, while the generalized four-momentum is part of the relativistic four-momentum of the system.

physics.gen-ph↗

arXiv2021

The electromagnetic field outside the steadily rotating relativistic uniform system

Using the method of retarded potentials approximate formulas are obtained that describe the electromagnetic field outside the relativistic uniform system in the form of a charged sphere rotating at a constant speed. For the near, middle and far zones the corresponding expressions are found for the scalar and vector potentials, as well as for the electric and magnetic fields. Then these expressions are assessed for correspondence to the Laplace equations for potentials and fields. One of the purposes is to test the truth of the assumption that the scalar potential and the electric field depend neither on the value of the angular velocity of rotation of the sphere nor on the direction to the point where the field is measured. However, calculations show that potentials and fields increase as the observation point gets closer to the sphere's equator and to the sphere's surface, compared with the case for a stationary sphere. In this case, additions are proportional to the square of the angular velocity of rotation, the square of the sphere's radius and inversely proportional to the square of the speed of light. The largest found relative increase in potentials and fields could reach the value of 4% for the rapidly rotating neutron star PSR J1614-2230, if the star were charged. For a proton, a similar increase in fields on its surface near the equator reaches 54%.

physics.class-ph↗

arXiv2021

The relativistic uniform model: the metric of the covariant theory of gravitation inside a body

It is shown that the sum of stress-energy tensors of the electromagnetic and gravitational fields, the acceleration field and the pressure field inside a stationary uniform spherical body within the framework of relativistic uniform model vanishes. This fact significantly simplifies solution of equation for the metric in covariant theory of gravitation (CTG). The metric tensor components are calculated inside the body, and on its surface they are combined with the components of external metric tensor. This also allows us to exactly determine one of the two unknown coefficients in the metric outside the body. Comparing the CTG metric and the Reissner-Nordström metric in general theory of relativity shows their difference, which is a consequence of difference between equations for the metric and different understanding of essence of cosmological constant.

physics.gen-ph↗

arXiv2021

The theorem on the magnetic field of rotating charged bodies

The method of retarded potentials is used to derive the Biot-Savart law, taking into account the correction that describes the chaotic motion of charged particles in rectilinear currents. Then this method is used for circular currents and the following theorem is proved: The magnetic field on the rotation axis of an axisymmetric charged body or charge distribution has only one component directed along the rotation axis, and the magnetic field is expressed through the surface integral, which does not require integration over the azimuthal angle . In the general case, for arbitrary charge distribution and for any location of the rotation axis, the magnetic field is expressed through the volume integral, in which the integrand does not depend on the angle . The obtained simple formulas in cylindrical and spherical coordinates allow us to quickly find the external and central magnetic field of rotating bodies on the rotation axis.

physics.class-ph↗

arXiv2019

The integral theorem of generalized virial in the relativistic uniform model

In the relativistic uniform model for continuous medium the integral theorem of generalized virial is derived, in which generalized momenta are used as particles momenta. This allows us to find exact formulas for the radial component of the velocity of typical particles of the system and for their root-mean-square speed, without using the notion of temperature. The relation between the theorem and the cosmological constant, characterizing the physical system under consideration, is shown. The difference is explained between the kinetic energy and the energy of motion, the value of which is equal to half the sum of the Lagrangian and the Hamiltonian. This difference is due to the fact that the proper fields of each particle have mass-energy, which makes an additional contribution into the kinetic energy. As a result, the total energy of motion of particles and fields is obtained.

physics.class-ph↗

arXiv2019

On the covariant representation of integral equations of the electromagnetic field

Gauss integral theorems for electric and magnetic fields, Faradays law of electromagnetic induction, magnetic field circulation theorem, theorems on the flux and circulation of vector potential, which are valid in curved spacetime, are presented in a covariant form. Covariant formulas for magnetic and electric fluxes, for electromotive force and circulation of the vector potential are provided. In particular, the electromotive force is expressed by a line integral over a closed curve, while in the integral, in addition to the vortex electric field strength, a determinant of the metric tensor also appears. Similarly, the magnetic flux is expressed by a surface integral from the product of magnetic field induction by the determinant of the metric tensor. A new physical quantity is introduced - the integral scalar potential, the rate of change of which over time determines the flux of vector potential through a closed surface. It is shown that the commonly used four-dimensional Kelvin-Stokes theorem does not allow one to deduce fully the integral laws of the electromagnetic field and in the covariant notation requires the addition of determinant of the metric tensor, besides the validity of the Kelvin-Stokes theorem is limited to the cases when determinant of metric tensor and the contour area are independent from time. This disadvantage is not present in the approach that uses the divergence theorem and equation for the dual electromagnetic field tensor. A new effect is predicted, according to which the circulation of magnetic field can appear even in the absence of electric current and with a constant electric field through the contour, if the area of this contour would change. By analogy with electromagnetic induction, for the magnetic field circulation to appear it is important that electric field flux that passes through the area of the contour would change over time.

physics.gen-ph↗

arXiv2017

Two components of the macroscopic general field

The general field, containing all the macroscopic fields in it, is divided into the mass component, the source of which is the mass four-current, and the charge component, the source of which is the charge four-current. The mass component includes the gravitational field, acceleration field, pressure field, dissipation field, strong interaction and weak interaction fields, other vector fields. The charge component of the general field represents the electromagnetic field. With the help of the principle of least action we derived the field equations, the equation of the matter's motion in the general field, the equation for the metric, the energy and momentum of the system of matter and its fields, and calibrated the cosmological constant. The general field components are related to the corresponding vacuum field components so that the vacuum field generates the general field at the macroscopic level.

physics.gen-ph↗

arXiv2017

The virial theorem and the kinetic energy of particles of a macroscopic system in the general field concept

The virial theorem is considered for a system of randomly moving particles that are tightly bound to each other by the gravitational and electromagnetic fields, acceleration field and pressure field. The kinetic energy of the particles of this system is estimated by three methods, and the ratio of the kinetic energy to the absolute value of the energy of forces, binding the particles, is determined, which is approximately equal to 0.6 . For simple systems in classical mechanics, this ratio equals 0.5 . The difference between these ratios arises by the consideration of the pressure field and acceleration field inside the bodies, which make additional contribution to the acceleration of the particles. It is found that the total time derivative of the system's virial is not equal to zero, as is assumed in classical mechanics for systems with potential fields. This is due to the fact that although the partial time derivative of the virial for stationary systems tends to zero, but in real bodies the virial also depends on the coordinates and the convective derivative of the virial, as part of the total time derivative inside the body, is not equal to zero. It is shown that the convective derivative is also necessary for correct description of the equations of motion of particles.

physics.gen-ph↗

arXiv2016

Four-dimensional equation of motion for viscous compressible and charged fluid with regard to the acceleration field, pressure field and dissipation field

From the principle of least action the equation of motion for viscous compressible and charged fluid is derived. The viscosity effect is described by the 4-potential of the energy dissipation field, dissipation tensor and dissipation stress-energy tensor. In the weak field limit it is shown that the obtained equation is equivalent to the Navier-Stokes equation. The equation for the power of the kinetic energy loss is provided, the equation of motion is integrated, and the dependence of the velocity magnitude is determined. A complete set of equations is presented, which suffices to solve the problem of motion of viscous compressible and charged fluid in the gravitational and electromagnetic fields.

physics.flu-dyn↗