Extension of Killing vector fields in pseudo-Riemannian manifolds

par Elena Giorgi (Columbia University)

mercredi 21 juin 2017, 14:00 → 15:00 Europe/Paris

I will talk about the problem of the extension of a Killing vector field in a pseudo-Riemannian manifold. In the case of an analytic manifold, the problem was solved by Nomizu in the 60's in all its generality, while in the smooth setting, Ionescu and Klainerman proved that the extension can be done in the case of null-convex domain in a Ricci flat manifold. I will present a generalization of their proof to the case of a pseudo-Riemannian manifold verifying the Einstein equation with electromagnetic tensor. I will present how this problem is related to the rigidity problem of black holes in general relativity.