Transverse Signature-Type Change in Singular Semi-Riemannian Manifolds

Abstract

In the early eighties, Hartle and Hawking put forth that signature-type change may be conceptually interesting, paving the way to the so-called no-boundary proposal for the initial conditions for the universe. Such singularity-free universes have no beginning, but they do have an origin of time. This leads to considerations of signature-type changing spacetimes, wherein the “initially” Riemannian manifold, characterized by a positive definite metric, undergoes a signature-type change, ultimately transitioning into a Lorentzian univers Show more