An Introduction to the Matrix Classical Theory of Field. New Formalism, Equations and Solutions

A purely mathematical matrix approach to the equations of the Classical Theory of General Relativity is developed. The absolute matrix of field is understood as the absolute electromagnetic-gravitational field matrix. The symmetric part of this matrix is the gravitational field matrix. The antisymmetric part is the electromagnetic field matrix. The equations for both these matrices and the metric matrix equation are derived. It is shown that the metric and field matrix equations are connected with each other. The general solution for the static spherically symmetric gravitational field is found. Two particular cases of the general solution are compared. One solution is the Schwarzschild metric. Another solution has no singularity as the Schwarzschild metric. It is shown that a second-order differential equation for the planar orbit is the same for both metrics, but the dimensionless energy (and an angular velocity) of the moving particle is different. The formulae for the minimum and maximum orbital velocity and for the perihelion precession of planets through perihelion and aphelion distances are given. The symmetric (gravitational) field matrix field and the solutions for the zero and nonzero invariant density are considered for the Friedmann-Lobachevsky model.