It is known in the physics literature that “high-frequency weak limits” of solutions to the Einstein vacuum equations are not necessarily vacuum solutions, but may have a non-trivial stress-energy-momentum tensor, which can be viewed physically as “effective matter fields” arising from back-reaction of high-frequency gravitational waves. Burnett gave a conjecture which aimed at completely characterization such high-frequency limits. I will discuss recent progress on the conjecture. This is based on joint work with Cécile Huneau.