Scientific Journal of KubSAU

The work discusses various examples of physical systems which state is determined by the logarithmic law - quantum and classical statistical systems and relativistic motion in multidimensional spaces. It was established that the Fermi-Dirac statistics and BoseEinstein-Maxwell-Boltzmann distribution could be described by a single equation, which follows from Einstein's equations for systems with central symmetry. We have built the rate of emergence of classical and quantum systems. The interrelation between statistical and dynamic parameters in supergravity theory in spaces of arbitrary dimension was established. It is shown that the description of the motion of a large number of particles can be reduced to the problem of motion on a hypersphere. Radial motion in this model is reduced to the known distributions of quantum and classical statistics. The model of angular movement is reduced to a system of nonlinear equations describing the interaction of a test particle with sources logarithmic type. The HamiltonJacobi equation was integrated under the most general assumptions in the case of centrally-symmetric metric. The dependence of actions on the system parameters and metrics was found out. It is shown that in the case of fermions the action reaches extremum in fourdimensional space. In the case of bosons there is a local extremum of action in spaces of any dimension

The article discusses various examples of dynamical systems in which the motion is determined by the logarithmic law - quark systems, hydrodynamic systems, galaxies. Set the general nature of angular motion on a hypersphere in a space of arbitrary dimension and radial movement 6D in the metric of a logarithmic potential. We investigate the 6D metric describing the case of motion with two centers of symmetry. It is shown that in such a metric exists a class of exact solutions, logarithmically dependent on the gravity center coordinates. It was established that in spiral galaxies the orbital motion is due to the logarithmic potential, which is the exact solution of the field equations of Einstein's theory of gravity. The most well-known and widespread in nature case is turbulent flow over a smooth or rough surface, in which the mean velocity depends logarithmically on the distance from the wall. We derivate the logarithmic velocity profile in turbulent flow from the NavierStokes equations. An analogy of the logarithmic velocity profile and the logarithmic law in the case of erosion of materials under impacts been proposed. In electrodynamics, Ampere's law, which describes the interaction of current-carrying conductors, is a consequence of the logarithmic dependence of the vector potential of the distance from the conductor axis. There is, however, an alternative derivation of Ampere law of the Riemann hypothesis about the currents due to the motion of charges

The question of extending the Lorentz electrodynamics to quantum theory is discussed. The system of equations of the Lorentz quantum electrodynamics was established

In this article we consider the many-body problem in general relativity in the case of the distribution of N singularities on the circle. It specifies the exact solution of the problem for an arbitrary distribution of singularities. It is shown that the static metric of N singularities corresponds to Newton's theory of N centers of gravity, moving around the central body in a circular orbit in a non-inertial frame of reference, rotating with a period of bodies revolving. We consider the statement of the problem of many bodies distributed at the initial time on the circle. In numerical calculations, we studied the properties of the gravitational potential in the problem of establishing a static condition in which multiple singularities retain the initial position on the circle. This is achieved due to relativistic effects, which have no analogues in Newton's theory of gravitation. Using the properties of relativistic potentials justified transition from the relativistic motion of the particles to the dynamic equations in the classical theory. A system of non-linear parabolic equations describing the evolution of the metric in the Ricci flow proposed. The problem of the calculation of the potentials in the Ricci flow formulated. The application of the theory to describe the ring galaxy, planetary rings and the asteroid belt considered

In this article, we investigate the problem of creation of matter in the collision of particles, presented by singularities of the gravitational field. A system of nonlinear parabolic equations describing the evolution of the axially symmetric metrics in the Ricci flow derived. A model describing the creation of matter in the collision and merger of the particles in the Ricci flow proposed. It is shown that the theory that describes the Ricci flow in the collision of black holes is consistent with EinsteinInfeld theory, which describes the dynamics of the material particles provided by the singularities of the gravitational field. As an example, we consider the metric having axial symmetry and which contains two singularities simulating particles of finite mass. It is shown that the static metric with two singularities corresponding to in Newton's theory of gravity two particles moving around the center of mass in circular orbits in a non-inertial frame of reference, rotating with a period of two-body system rotation. We have numerically investigated the change of the metric in the collision of particles with subsequent expansion. In numerical experiments, we have determined that the collision of the particles in the Ricci flow leads to the formation of two types of matter with positive and negative energy density, respectively. When moving singularities towards each other in the area between the particles the matter is formed with negative energy density, and in the region behind the particles - with positive density. In the recession of the singularities, the matter with positive energy density is formed in the area between the particles. The question of the nature of baryonic matter in the expanding universe is discussed

Metric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Maxwell's equations and Yang-Mills theory are converted to the moving axes in metric describes the acceleration and rotating reference frame in the general relativity in the case of an arbitrary dependence of acceleration and angular velocity of the system from time. The article discusses the known effects associated with acceleration and (or) the rotation of the reference frame - the Sagnac effect, the effect of the Stewart-Tolman and other similar effects. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It has been shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed

Metric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Consequently, there exist a metric in general relativity, in which the Coriolis theorem and classic velocity-addition formula are true. This means that classical mechanics is accurate rather than approximate model in general relativity. A theory of potential in non-inertial reference systems in general relativity is considered. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It is shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed

We investigate the hypothesis of a plurality of parallel and virtual worlds. It is assumed that sentient beings in each virtual world reach a stage of development that can create a virtual world to simulate the history of their own development. In this case, the virtual worlds are nested within each other, which put a severe restriction on the possible geometry of space-time. Discussed the draft geometry virtual worlds consistently displayed from one world to another. It is shown that in this case, the metric should be universal, depending only on the fundamental constants. There are examples of universal metrics obtained in Einstein's theory of gravitation and Yang-Mills theory

Movement of geographical and magnetic poles versus celestial bodies’ positions is examined on the basis of the special and general relativity theory.

Perturbed motion of a pole of the Earth caused by gravitational action of celestial bodies is explored in the article