Linearization Instability of Gravitational Waves Interacting with Matter in General Relativity

The gravitational wave solutions obtained from a perturbation about conformally flat backgrounds in Einstein gravity are investigated. A perturbation theory analysis of the Lesame, Ellis and Dunsby results, based on a covariant approach, shows that for gravitational waves interacting with irrotational dust, the equations are linearization unstable. The gravitational wave equations based on the Weyl curvature tensor must be solved by non-perturbative methods. The significance of this result for gravitational wave calculations and experiments is discussed.