Exploring Higher-Order Gravitational Waves

TL;DR

This paper derives and analyzes higher-order gravitational wave solutions, revealing their non-transverse-traceless nature and their role as corrections to second-order waves, with implications for quantum gravity and graviton definition.

Contribution

It explicitly obtains higher-order gravitational wave solutions and highlights their distinct properties from first- and second-order waves, offering new insights into gravitational wave structure.

Findings

Higher-order waves are not corrections to first-order waves.

All higher than second-order solutions correct the second-order wave.

Higher-order solutions are not transverse or traceless.

Abstract

In addition to the usual linear gravitational waves in transverse-traceless coordinates, higher-order gravitational field equations, as well as their corresponding solutions, are explicitly obtained. It is found that higher-order waves do not represent corrections to the first-order wave. In contrast, all higher than second-order solutions do represent corrections to the second-order wave, a property that makes the first-order gravitational wave to stand apart from higher-order waves. Furthermore, although the first-order solution is transverse and traceless, all higher-order solutions are not. As a consequence, the whole solution is neither transverse nor traceless, a result that could eventually have important consequences for quantum gravity, and in particular for the definition of graviton itself. Some additional properties and features of these higher-order gravitational waves are explored and discussed.