Mathematical matrix theory of the field in n-dimensional metric space: rigorous derivation of the equations of the field with application in electromagnetic-gravitational fields

TL;DR

This paper introduces a novel mathematical matrix theory of fields in n-dimensional metric space, rigorously deriving equations of motion and unifying electromagnetic and gravitational fields within a matrix framework.

Contribution

It develops a new pure mathematical matrix theory of fields in n-dimensional space, providing a rigorous derivation of field equations and a unified electromagnetic-gravitational matrix model.

Findings

The field matrix in 4D space combines electromagnetic and gravitational components.

Symmetric and antisymmetric matrices correspond to gravitational and electromagnetic fields.

Elements of the matrices are Christoffel symbols or their derivatives.

Abstract

During the last century the tensor theory of the gravitational field was developed. We propose and develop the novel, pure mathematical, matrix theory of the field in n-dimensional metric space. The definition of the mathematical field matrix and the equations of motion of the mathematical point are given. The interpretation of the nature of the mathematical field and the mathematical points can be different and depends on our knowledge of the nature. It is shown that the equations of motion are different for symmetric and antisymmetric field matrices. In the matrix field theory the equations of the field are rigorously derived. This theory reveals that in the 4-dimensional metric space the field matrix is the electromagnetic-gravitational field matrix, where the antisymmetric part is the matrix of electromagnetic field and the symmetric part is the gravitational field matrix. The partial cases of this matrix are electric-gravitational, magnetic-gravitational and gravitational field matrices. It is shown that the elements of all obtained matrices are the Christoffel symbols of the first and the second order or their derivatives.