Nonlinear resonant wave interaction in vacuum

The basic equations governing propagation of electromagnetic and gravitational waves in vacuum are nonlinear. As a consequence photon-photon interaction as well as photon-graviton interaction can take place without a medium. However, resonant interaction between less than four waves cannot occur in vacuum, unless the interaction takes place in a bounded region, such as a cavity or a waveguide. Recent results concerning resonant wave interaction in bounded vacuum regions are reviewed and extended.