Due to their nonlinear nature, the Einstein equations are not closed under weak convergence: failure of compactness, due to oscillations and concentrations,
produces an excess energy momentum tensor. In 1989, Burnett conjectured that, for vacuum sequences with high-frequency oscillations, the matter produced in this limit is captured by the Einstein-massless Vlasov model.
In this talk, we give a proof of Burnett's conjecture under some gauge and symmetry assumptions, improving previous work by Huneau—Luk from 2019. Our methods are more general, and apply to oscillating sequences of solutions to the wave maps equation in (1+2)-dimensions. This is joint work with André Guerra (Institute for Advanced Study).
Rita Texeira de Costa (Princeton): Homogenization of the Einstein equations under symmetry
