Abstract:
The Hartle-Hawking "no-boundary" proposal redefines spacetime by offering a new way of thinking about the origin of the universe. Mathematically, this involves signature-type changing manifolds where a Riemannian region is smoothly joined to a Lorentzian region at the transition surface where time begins.
Motivated by the "no-boundary" proposal, I present a segment of a new framework for signature-changing manifolds, characterized by a degenerate yet smooth metric. Then I adapt some Lorentzian tools and results to the signature-type changing scenario, introducing new definitions that carry unforeseen causal implications. One such noteworthy consequence is the presence of time-reversing loops through each point on the locus of signature change.