Nonlinear Gravitational Waves: Their Form and Effects

A gravitational wave must be nonlinear to be able to transport its own source, that is, energy and momentum. A physical gravitational wave, therefore, cannot be represented by a solution to a linear wave equation. Relying on this property, the second-order solution describing such physical waves is obtained. The effects they produce on free particles are found to consist of nonlinear oscillations along the direction of propagation.