Jonathan Glöckle: Construction of spacetimes and initial data sets with lightlike parallel spinors

The goal of this talk is to present a general construction of initial data sets with lightlike parallel spinors, where the canonical foliation has compact leaves. Similarly to the previous construction due to Ammann-Kröncke-Müller, it starts with a family of Ricci-flat metrics $g_s$, $s \in I$, with parallel spinor on a closed manifold $Q$, parametrized by an interval $I$. It outputs an initial data set on $I \times Q$ with metric $u^{-2} ds^{^2} + g_s$ and a suitable second fundamental form $k$ and equipped with a lightlike parallel spinor. Compared the earlier result, we are now able to freely prescribe the Ricci curvature of the associated spacetime, which is reflected in the choice of the function $u$. If time permits, we will also briefly discuss how rigid the situation gets once the dominant energy condition is assumed to hold.