The frequency of light propagating in gravitational wave spacetimes

We study the propagation of light signals in two exact solutions of vacuum Einstein's equations, in the geometric optics approximation. The gravitational wave affects the frequency of light propagating in it (a known effect) even if the metric componentsgtt andgti (i=1, 2, 3) are zero. Moreover we find that red-/blue-shift depends on the relative spatial position of the light source and the observer, even if the wavefront is perfectly uniform, leading to a characteristic redshift pattern.