High frequency limit for Einstein equations

In this talk, I will present the construction of a family of solutions to
vacuum Einstein equations which consist of an arbitrary number of high
frequency waves travelling in different directions. In the high frequency
limit, our family of solutions converges to a solution of Einstein equations
coupled to null dusts. This construction is an illustration of the so called
backreaction, studied by physicists (Isaacson, Burnet, Green, Wald...) : the
small scale inhomogeneities have an effect on the large scale dynamics in
the form of an energy impulsion tensor in the right-hand side of Einstein
equations. This is a joint work with Jonathan Luk (Stanford).