On the dynamics of a test particle in the field of the de Broglie gravitational waves

The de Broglie gravitational waves are a solution of the linearized Einstein equations with properties that are absent in the standard gravity waves because they are also longitudinal waves and obey a dispersion relation that leads to an effective mass. Furthermore, they represent a classical realization of a form of dynamics, proposed for quantum particles by de Broglie in 1927. In this paper, we discuss the dynamics of a massive particle in presence of the de Broglie gravity wave. We will compute the analytical expression for the linear and angular momentum of the corpuscle. As an application, we will consider the case in which these oscillations of spacetime are associated to an electron travelling with a velocity equal to 1% of the light speed and we will estimate the order of magnitude of the quantities involved. We will show that a nearby positron oscillates and radiates an energy of 1eV in 10-5s, an effect that is, in principle, measurable.