The gravitational faraday rotation for cylindrical gravitational solitons

By using cylindrical soliton solutions, the nonlinear behavior of gravitational waves in vacuum is studied in terms of a rotation of the polarization vector between two independent modes. This effect was emphasized by Piran, Safier, and Stark as a gravitational analogue of the Faraday rotation. The polarization of the soliton wave is calculated, and it is found that the+mode which was dominant near the axis of symmetry is fully converted to the×mode at some interaction region and then the disturbance propagating along a light cone like a gravitational wave pulse contains both polarizations.