Event

Talk
Cauchy problems for Lorentzian manifolds with parallel spinor
Dr. Andree Lischewski (HU Berlin)
25 Apr 2016, 16:00 – 17:00
IRIS-Haus 2.07, HU Berlin

This talk intends to exhibit a new construction principle for Lorentzian manifolds with parallel spinor fields. Such geometries are important examples of Lorentzian manifolds with special holonomy and appear naturally in various contexts in mathematical physics. The idea for our construction is to start with a Riemannian manifold which is subject to suitable constraints and then to extend these data to a Lorentzian manifold in one higher dimension admitting a parallel spinor. These meth- ods are motivated by considering the well-studied Cauchy problem for the (vacuum) Einstein equations in General Relativity. Thus, in a first part of the talk I will provide a short self-contained introduction to the initial value problem for Ricci-flat Lorentzian manifolds and introduce the relevant methods from hyperbolic PDE theory. Subsequently, the second part of the talk applies these ideas to the construction of Lorentzian manifolds with parallel null spinor. The proof rests on the derivation and analysis of a suitable system of hyperbolic evolution equations. This is a joint project with Helga Baum (Berlin) and Thomas Leistner (Adelaide).