Gravitational waves as waveguides

We show that gravitational waves can act as waveguides for electromagnetic radiation, that is, if the latter is initially aligned with the gravitational waves, then the alignment will survive during the propagation. The analysis is performed using the Hamiltonian formalism and the Jacobi equation for null geodesics, and conditions for certain cases of polarization of the waves are obtained. The effect of waveguiding by the gravitational waves can influence the interpretation of associated gravitational and electromagnetic wave events, since the latter cannot necessarily obey the inverse square decay law for intensity.