From Riemannian to Lorentzian: Embeddings of Signature-Changing Manifolds

Vortrag von Dr. Nathalie Rieger

Datum: 03.11.25  Zeit: 13.30 - 14.30  Raum: Y27H25

We examine a class of semi-Riemannian manifolds that undergo smooth metric signature change—from Riemannian to Lorentzian—across a hypersurface with a transverse radical. This class includes physically motivated cosmological models such as the Hartle-Hawking “no-boundary” proposal, in which the universe transitions smoothly from a Euclidean to a Lorentzian phase. We show that these manifolds admit isometric embeddings into higher-dimensional pseudo-Euclidean spaces and, in particular, prove the existence of global isometric embeddings of the canonical model into both Minkowski and Misner spaces. This framework provides a mathematical setting for studying smooth signature change and its role in higher-dimensional and cosmological models.