Maxwell Equation in Electromagnetic and Gravitational Fields

The paper studies the validity of Maxwell equation in the case for coexistence of electromagnetic field and gravitational field. In the description with the algebra of quaternions, Newton's law of gravitation is the same as that in classical gravitational theory. While Maxwell equation is identical with that in conventional electromagnetic theory with vector terminology. 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.