Initial Data Rigidity via Dirac-Witten Operators
Explore a rigorous mathematical talk on initial data rigidity using Dirac-Witten operators. Delve into the derivation of a rigidity theorem in the spin setting, inspired by the work of Eichmayr-Galloway-Mendes. Examine initial data sets (g,k) on manifolds with boundaries, satisfying the dominant energy condition and specific null expansion scalar conditions. Discover how Dirac-Witten operators are employed to prove that the manifold M must be diffeomorphic to a cylinder N x [0,1] and foliated by MOTS with non-trivial parallel spinors for induced metrics. Additionally, investigate a special case rigidity statement for Riemannian metrics with non-negative scalar curvature and mean convex boundary. This 54-minute presentation, delivered by Jonathan Glöckle at the Erwin Schrödinger International Institute for Mathematics and Physics, was part of the Thematic Programme on "Spectral Theory and Mathematical Relativity."