Wave Equations in Electromagnetic and Gravitational Fields

摘要

The paper studies the wave equations for the electromagnetic field when there is the gravitational field at the same time. In the description with the algebra of octonions, the deductions 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. The inference can be used to rephrase the law of reflection, Snell's law, and Fresnel formula etc. The study claims that the deductions of wave equation for electromagnetic fields keep unchanged in the case for existence of gravitational fields. The electric components of electromagnetic waves can not be determined simultaneously with magnetic components in electromagnetic fields.