Solutions of scalar and electromagnetic wave equations in the metric of gravitational and electromagnetic waves

Abstract

The wave equation of a scalar field Q and vector potential A' are solved in the background metric of a gravitational wave. The corresponding solutions when the metric is generated by a plane electromagnetic wave is obtained from these solutions. The solution for the scalar wave is discussed in detail. It is found that because of the interaction, two new waves are generated in the lower order approximations. One of them has the same phase dependence as the original wave while the order shows a transient character. There is no interaction when the waves are along the same direction.