TITLE:
New Approach to the Creation of General Theory of Relativity
AUTHORS:
Valentin V. Mdzinarishvili
KEYWORDS:
Mathematical Pendulum, Separatrix, Hamiltonian Equation, Riemannian Surface, Pseudo-Riemannian Surface, Lorentz Transformation
JOURNAL NAME:
Open Access Library Journal,
Vol.10 No.2,
February
28,
2023
ABSTRACT: It has to be noted that Albert Einstein used the extremal property of geodesic line when developing the general theory of relativity (GTR). In the following years, after the development of the GTR, it became known that the expression for a geodesic line can be replaced by the Euler-Lagrange equation. In the present work, the extremal property of the separatrix of a mathematical pendulum is used to develop a new approach to the general theory of relativity. The pendulum separatrix satisfies the Euler-Lagrange equation. A transcendental equation has been obtained, the solution of which makes it possible to determine the angle of rotation of the separatrix φs as a function for the angle of rotation of the mathematical pendulum. It makes possible for a fixed point φs,i located on the separatrix, to find the corresponding value of the function th(φs,i) used in determining the speed vi of movement of this point according to the general theory of relativity. The proposed approach is invariant to the distance along which the point moves. The examples illustrating the proposed approach have been considered.