Sari Ghanem: Stability of Minkowski space-time governed by the Einstein-Yang-Mills system

mercredi 20 déc. 2023, 14:00 → 15:00 Europe/Paris

I shall start by presenting the Einstein-Yang-Mills equations and by writing them in the Lorenz gauge and in wave coordinates as a coupled system of non-linear hyperbolic partial differential equations, and I will then show how one constructs the initial data for a Cauchy hyperbolic formulation of the problem. Thereafter, I will present the philosophy behind the proof of the non-linear stability of the Minkowski space-time, solution to the Einstein-Yang-Mills system, in the Lorenz gauge and in wave coordinates, in all space dimensions greater or equal to three, based on a continuity argument for a higher order weighted energy norm. In the critical case of three space-dimensions, we use a null frame decomposition, that was first used by Lindblad and Rodnianski for the Einstein vacuum equations. We then deal with new difficulties that do not exist for Einstein vacuum nor for Einstein-Maxwell fields. In particular, we treat new terms that have a different structure in the non-linearities, and we derive a more refined formula to estimate the commutator term. This provides a new independent proof of the result by Mondal and Yau, that I posted on arXiv two months ago in a series of three papers that build up on each other, which cover all space dimensions greater or equal to three:

Paper 1: Stability for space dimensions greater or equal to five (166 pages): https://arxiv.org/pdf/2310.07954.pdf ,

Paper 2: Exterior stability for four space dimensions (55 pages): https://arxiv.org/pdf/2310.08611.pdf ,

Paper 3: Exterior stability for three space dimensions (309 pages): https://arxiv.org/pdf/2310.08196.pdf .