Some Wave Equations for Electromagnetism and Gravitation

TL;DR

This paper derives wave equations for electromagnetic fields in the presence of gravity using octonion algebra, confirming their form remains consistent with classical theory and exploring wave properties and limitations.

Contribution

It introduces an octonion-based approach to derive electromagnetic wave equations in gravitational fields, extending classical electromagnetic theory.

Findings

Electromagnetic waves are transverse in vacuum.

Wave equations remain unchanged with gravity.

Electric and magnetic components cannot be simultaneously determined.

Abstract

The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that in conventional electromagnetic theory with vector terminology. By means of the octonion exponential function, we can draw out that the electromagnetic waves are transverse waves in a vacuum, and rephrase the law of reflection, Snell's law, Fresnel formula, and total internal reflection etc. The study claims that the theoretical results of wave equations for electromagnetic strength keep unchanged in the case for coexistence of gravitational and electromagnetic fields. Meanwhile the electric and magnetic components of electromagnetic waves can not be determined simultaneously in electromagnetic fields.