Photon perturbations induced by a Gravitational Wave

We have studied both the linear approximation and the exact form of a plane gravitational wave, which interacts with an electromagnetic wave. Using the linearized Einstein equations we calculated the changes induced on the four-potential field A^μ of the electromagnetic wave by describing the null geodesics followed by photons and we have identified the associated physical effects, namely phase shift, change of polarization vector, angular deflection and delay. Moreover, we have calculated the null geodesics of a space-time describing a sandwich pp-wave which is an exact solution of vacuum Einstein equations, and representing an exact plane gravitational wave. In this way we were able to identify the same physical effects calculated in the linearized theory. Finally, we have calculated the response of a Michelson laser interferometer (e.g. the LIGO and VIGO detector) to a linearized and exact gravitational wave