  We prove Burnett's conjecture in general relativity when the metrics satisfy
a generalized wave coordinate condition, i.e., suppose $\{g_n\}_{n=1}^\infty$
is a sequence of Lorentzian metrics (in arbitrary dimensions $d \geq 3$)
satisfying a generalized wave coordinate condition and such that $g_n\to g$ in
a suitably weak and "high-frequency" manner, then the limit metric $g$
satisfies the Einstein--massless Vlasov system. Moreover, we show that the
Vlasov field for the limiting metric can be taken to be a suitable microlocal
defect measure corresponding to the convergence. The proof uses a compensation
phenomenon based on the linear and nonlinear structure of the Einstein
equations.
