A study of the de Broglie gravitational waves

摘要

We study some interesting properties of the de Broglie gravitational waves. In particular, we investigate the properties of the polarization and the energy momentum tensor and the geodesic deviation associated with these waves. We observe that the polarization tensor has both transverse and longitudinal components and depends on the wave number. We find a new effect which does not occur in the standard gravitational waves. Our waves are responsible of a longitudinal shift of test particles placed along the direction of propagation. The amplitude of the shift decreases when the velocity of the source becomes closer to the speed of light; so slow massive particles must be used for an experimental test of the theory.