In this talk, I will review some works in collaboration with Jonathan Luk on the behaviour of high frequency solutions to the Einstein equations. In the eighties, the physicist Burnett conjectured that the adherence of the solutions to the Einstein equations, converging strongly at the level of the metric, and with boudedness assumptions at the level of derivative of the metric, are the solutions to the Einstein-massless Vlasov equations. I will focus on the resolution of this conjecture with the additionnal assumption of a translation symmetry, and explain how to approximate a solution to the Einstein-Vlasov equations by vacuum solutions.