Field equations of electromagnetic and gravitational fields

TL;DR

This paper demonstrates that Maxwell's equations remain valid in the coexistence of electromagnetic and gravitational fields when using quaternion and octonion algebra, with only the displacement current direction affected.

Contribution

It introduces a quaternion and octonion algebra framework to show the invariance of Maxwell's equations alongside gravitational fields.

Findings

Maxwell equations are unchanged in coexistence with gravitational fields.

Newton's law of gravitation remains consistent with classical theory.

Displacement current direction is the only aspect affected in the combined fields.

Abstract

The paper studies the validity of Maxwell equation in the case for coexistence of electromagnetic field and gravitational field. With the algebra of quaternions, the Newton's law of gravitation is the same as that in classical theory of gravitational field. Meanwhile the Maxwell equation is identical with that in classical theory of electromagnetic field. And the related conclusions can be spread to the case for coexistence of electromagnetic field and gravitational field by the algebra of octonions. The study claims that Maxwell equation keeps unchanged in the case for coexistence of gravitational field and electromagnetic field, except for the direction of displacement current.