Interaction and transformation of electromagnetic and gravitational waves in Einstein-Maxwell field

Abstract

The interaction and the transformation of the electromagnetic and gravitational waves and the variation of those amplitudes are analyzed theoretically, where the Einstein-Maxwell field is assumed. Two waves are defined such that the electromagnetic vector potentials and the gravitational tensor potentials and their first derivatives are continuous while their second derivatives are discontinuous at a wave front. It is proved that the concomitant electromagnetic and gravitational waves can interact with each other if an external electromagnetic field exists. The global behaviors of interaction and transformation of the two concomitant waves are also investigated, where a Lorentz metric space-time is assumed. The variation formulas for amplitude are derived. The amplitudes may grow or decay according to a factor depending on the mean and Gaussian curvatures of an initial wave front and to a factor depending on the external electromagnetic field. When there is no external electromagnetic field, there is no interaction between the two waves and they propagate independently, while when an external field exists, the electromagnetic wave may transform into the gravitational wave and vice versa. In a case of a weak constant external electromagnetic field, where a flat space may be assumed, the amplitude of a wave varies sinusoidally with respect to the distance measured along its ray. The length of interchangeability is defined by the length in which a wave is completely transformed into its dual wave, and it is inversely proportional to the strength of an external electromagnetic field.