Electrodynamics in Curvilinear Coordinates and the Equation of a Geodesic Line

The creation of the theory of relativity, which discovered the equivalence of mass and energy, showed that the concept of a point charge, used in the formulation of Coulomb’s law, one of the basic laws of classical electrodynamics, contradicts the famous formula establishing the equivalence of mass and energy. But the discovery of quarks makes it possible to present classical electrodynamics in a form free from the indicated contradiction. In the article, having considered the electromagnetic field in a curvilinear coordinate system, a theory has been created that expands our understanding of the electromagnetic field, the nature of quarks, the nature of strong interaction, and the connection between strong interaction and electromagnetic interaction. This theory is based on the principle of equivalence of an electromagnetic field to a free material particle formulated in the article and the law of formation of elementary particles from an electromagnetic field that follows from it.

Tidal effects based on a GUP-induced effective metric

In this paper,we study tidal forces in the Schwarzschild black hole,whose metric explicitly includes a generalized uncertainty principle(GUP)effect.We also investigate interesting features of the geodesic equations and tidal effects that are dependent on the GUP parameterαrelated to a minimum length.Then,by solving the geodesic deviation equations explicitly with appropriate boundary conditions,we show thatαin the effective metric affects both the radial and angular components of the geodesic equation,particularly near the singularities.

On Light-Like Extremal Surfaces in Curved Spacetimes

In this paper, we find that under a diffeomorphic of nonlinear geodesic equations are concerned with light-like extremal surfaces in curved spaeetimes. It is interesting to transformation of variables, the light-like extremal surfaces can be described by a system Particularly, we investigate the light-like extremal surfaces in Schwarzschild spacetime in detail and some new special solutions are derived systematically with aim to compare with the known results and to illustrate the method.

Geodesic equation in non-commutative gauge theory of gravity

In this study,we construct a non-commtative gauge theory of the modified structure of the gravitational field using the Seiberg-Witten map and the general tetrad fields of Schwarzschild space-time to show that the noncommutative geometry removes the singularity at the origin of the black hole,thus obtaining a non-singular Schwarzschild black hole.The geodetic structure of this black hole presents new types of motion next to the event horizon within stable orbits that are not allowed by the ordinary Schwarzschild spacetime.The noncommutative periastron advance of the Mercury orbit is obtained,and with the available experimental data,we find a parameter of non-commutativity on the order of 10^(-25)s·kg^(-1).This result shows that the new fundamental length,√h■,is on the order of 10^(-31)m.