Pseudo-timelike loops in signature changing semi-Riemannian manifolds with a transverse radical
arXiv:2409.02403 · doi:10.1016/j.rinp.2025.108478
Abstract
In 1983, Hartle and Hawking proposed the no-boundary proposal, suggesting that the universe has no beginning in the sense of a spacetime singularity or boundary. Nevertheless, there is an origin of time. Mathematically, this involves signature-type changing manifolds in which a Riemannian region smoothly transitions to a Lorentzian region across the hypersurface where time begins. We develop a coherent framework for signature changing manifolds with a degenerate yet smooth metric. Established Lorentzian tools and results are then adapted to this setting, and new definitions are introduced that carry unforeseen causal implications. A noteworthy consequence is the presence of locally time-reversing loops through every point on the hypersurface. Imposing global hyperbolicity on the Lorentzian region, we prove that for every point there exists a pseudo-timelike loop self-intersecting at . Equivalently, always admits a closed pseudo-timelike path around which the time direction reverses, preventing any consistent distinction between future- and past-directed vectors. To an observer near , such loops may appear as the creation of a particle-antiparticle pair at two distinct points.
Published in "Results in Physics"; this version corresponds to the final manuscript submitted to "Results in Physics". The authors thank the reviewers for their insightful comments and critique, which have helped to refine and improve this article. 36 pages, 8 figures