  In this paper we consider photon-photon scattering due to self-induced
gravitational perturbations on a Minkowski background. We focus on four-wave
interaction between plane waves with weakly space and time dependent
amplitudes, since interaction involving a fewer number of waves is excluded by
energy-momentum conservation. The Einstein-Maxwell system is solved
perturbatively to third order in the field amplitudes and the coupling
coefficients are found for arbitrary polarizations in the center of mass
system. Comparisons with calculations based on quantum field theoretical
methods are made, and the small discrepances are explained.
