A gravitational analogue of Faraday rotation

In an effort to shed some light on the problem of nonlinear interaction of gravitational radiation we have studied the behaviour of cylindrical gravitational waves in vacuum. When only one mode of cylindrical gravitational waves is present, the well known solution is the Einstein-Rosen¹ waves which do not display any nonlinear behaviour. The general solution of two modes is unknown. To study it we express the cylindrical Einstein equations in a characteristic form and obtain an analytical approximation and a numerical solution for the general evolution of cylindrical waves. We report here that the propagation of these waves displays a reflection of ingoing to outgoing waves (and vice versa), combined with a rotation of the polarization vector between the + and × modes. The latter effect is a gravitational analogue of the electromagnetic Faraday rotation.