Electromagnetic waves, gravitational coupling and duality analysis

In this letter we introduce a particular solution for parallel electric and magnetic fields, in a gravitational background, which satisfy free-wave equations and the phenomenology suggested by astrophysical plasma physics. These free-wave equations are computed such that the electric field does not induce the magnetic field and vice-versa. In a gravitational field, we analyze the Maxwell equations and the corresponding electromagnetic waves. A continuity equation is presented. A commutative and noncommutative analysis of the electromagnetic duality is described.