Klaus Kröncke: The Einstein equation on an anisotropic background

We will consider the product of the Milne model with a compact Ricci-flat manifold which is linearly stable and integrable and investigate its nonlinear stability as a vacuum solution of Einstein's field equations. In order to handle the non-autonomous nature of the perturbed system and the moduli space of Ricci-flat metrics, we introduce an involved generalization of the spatial harmonic gauge whose construction I will explain in detail. This is joint work in progress with David Fajman.