Nonlinear Gravitational Waves: Their Form and Effects

TL;DR

This paper demonstrates that physical gravitational waves are inherently nonlinear, requiring second-order solutions to accurately describe their energy transport and effects on particles, which include nonlinear oscillations.

Contribution

It derives the second-order solution for nonlinear gravitational waves, emphasizing their unique property of transporting energy and momentum.

Findings

Physical gravitational waves are nonlinear and cannot be described by linear equations.

Second-order solutions reveal nonlinear oscillations along the propagation direction.

Nonlinear waves can transport their own energy and momentum.

Abstract

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.