Nonlinear Gravitational Waves: Their Form and Effects

Similarly to a Yang–Mills propagating field, which must be nonlinear if it is to transport its own charge, only a nonlinear gravitational wave is able to transport energy and momentum. The second order solution describing such physical waves is obtained. The effects they produce on free particles consist of nonlinear oscillations along the direction of propagation. This is the signature a detector will exhibit, and is the effect to be looked for when trying to detect gravitational waves. Since no second order spherically–symmetric wave can exist, the restrictions imposed by Birkhoff’s theorem on longitudinal gravitational waves do not apply to this case.