The de Broglie-Einstein-Rosen gravitational wave

Abstract de Broglie gravitational waves are solutions of the linearized Einstein's field equations in vacuum, with intriguing properties. They are axially symmetric and have an effective mass, which is responsible for longitudinal effects that are absent in standard gravity waves. Moreover, they represent a classical realization of a form of dynamics proposed for quantum particles by de Broglie one hundred years ago. In this paper we will show that this perturbation field can be obtained, apart from a proportionality constant, in the weak field limit of a particular Einstein-Rosen field, which we call the de Broglie-Einstein-Rosen wave. Some properties of this exact solution are also discussed.