Interaction of gravitational waves with magnetic and electric fields

The existence of large-scale magnetic fields in the universe has led to the observation that if gravitational waves propagating in a cosmological environment encounter even a small magnetic field then electromagnetic radiation is produced. To study this phenomenon in more detail we take it out of the cosmological context and at the same time simplify the gravitational radiation to impulsive waves. Specifically, to illustrate our findings, we describe the following three physical situations: (1) a cylindrical impulsive gravitational wave propagating into a universe with a magnetic field, (2) an axially symmetric impulsive gravitational wave propagating into a universe with an electric field and (3) a ``spherical'' impulsive gravitational wave propagating into a universe with a small magnetic field. In cases (1) and (3) electromagnetic radiation is produced behind the gravitational wave. In case (2) no electromagnetic radiation appears after the wave unless a current is established behind the wave breaking the Maxwell vacuum. In all three cases the presence of the magnetic or electric fields results in a modification of the amplitude of the incoming gravitational wave which is explicitly calculated using the Einstein--Maxwell vacuum field equations.