Effects of the circularly polarized beam of linearized gravitational waves

Abstract

Solutions of the linearized Einstein equations are found that describe a transversely confined beam of circularly polarized gravitational waves on a Minkowski backdrop. By evaluating the cycle-averaged stress-energy-momentum pseudotensor of Landau & Lifshitz it is found that the angular momentum density is concentrated in the 'skin' at the edge of the beam where the intensity falls, and that the ratio of angular momentum to energy per unit length of the beam is $2/\omega$, where $\omega$ is the wave frequency, as expected for a beam of spin-$2$ gravitons. For sharply-defined, uniform, axisymmetric beams, the induced background metric is shown to produce the gravomagnetic field and frame-dragging effects of a gravitational solenoid, whilst the angular momentum current additionally twists the contained space helically.