Work

Pseudo-timelike loops in signature changing semi-Riemannian manifolds with a transverse radical

Year: 2025

Type: article

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 H 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 p ∈ M there exists a pseudo-timelike loop self-intersecting at p . Equivalently, M 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 H , such loops may appear as the creation of a particle–antiparticle pair at two distinct points.

Source: Results in Physics

DOI: 10.1016/j.rinp.2025.108478

Authors: N.E. Rieger, W. Hasse

Institutions: University of Zurich, Technische Universität Berlin

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,920

Funders: National Centres of Competence in Research SwissMAP, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung