Jonathan Glöckle (Regensburg)
Initial data sets are pairs of a Riemannian metric and a symmetric 2-tensor on a manifold \(M\). They arise in General Relativity as induced Riemannian metric and induced second fundamental form, respectively, on a spacelike hypersurface of a Lorentzian spacetime. In this talk, I will explain how Dirac-Witten operators can be used to derive a rigidity result for initial data sets à la Eichmayr-Galloway-Mendes (DOI:10.1007/s00220-021-04033-x) in the spin setting. There, the observed rigidity is a consequence of the interplay of the dominant energy condition (dec) for the initial data set, a condition on the null expansion scalars along the boundary of \(M\) as well as an assumption on the topology of \(M\). As an application, we will study the problem of finding dec spacetime extensions for initial data sets and derive a local uniqueness result in that context.
