Rigidity for initial data sets and spacetimes
14.12.2023, 16:00
– Room 0.14, House 9
Forschungsseminar Differentialgeometrie
Jonathan Glöckle (Regensburg)
Initial data sets are pairs of a Riemannian metric and a symmetric 2-tensor on a manifold . 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 as well as an assumption on the topology of . 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.