Research
Kinematics and Dynamics of a Particle in Gravitation Field
It is accepted that three-dimensional physical space is a hypersurface with a Riemannian metric in four-dimensional space. The metric tensor of this three-dimensional space is defined by Einstein's equations. Another coordinate of fourdimensional space is time. In this space, the equations of the world line of a particle with a mass m are defined under certain initial conditions: the starting point of the space and the vector of the particle's initial velocity. This approach removes all the problems and contradictions noted in the monograph [1], and the resulting equations adequately describe, for example, the curvilinear motion of planets without energy change.
To Foundations of General Theory Relativity
It is shown that the foundations of the generally accepted theory contain a number of contradictory and unfounded statements. The geometric properties of the three-dimensional Riemannian space are successively described. It is shown that this space is locally Euclidean. The metric tensor can be algebraically diagonalized. In this case, all diagonal elements are equal to each other and differ from unity by a function of coordinates, which is called the gravitational potential. It is shown that this function is a solution of the differential equation of potential theory. If this solution is such that the potential can be represented by equipotential surfaces, then the trajectory of free motion of a material particle lies on this surface. The trajectory on the surface is a geodesic line determined by the initial conditions. The numerical value of the potential on the surface is included in the definition of the maximum possible speed on this surface, that is, a constant equal to the speed of light in vacuum is multiplied by a value less than one, determined by the value of the potential.
