dorsal/arxiv
View SchemaInterpolated Topology Change in a Spin Cobordism and the Chiral Weyl Curvature Diagnostic
| Authors | Keith Andrew, Eric V. Steinfelds, Kristopher A. Andrew |
|---|---|
| Categories | |
| ArXiv ID | 2601.05957vv1 |
| URL | https://arxiv.org/abs/2601.05957 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
Topology change in Lorentzian quantum gravity demands geometric regulators that control curvature, spin structure, and chirality during nontrivial interpolations. We develop a framework for regulated topology change based on smooth Lorentzian spin cobordisms with interpolating metrics, allowing a transient failure of global hyperbolicity while preserving smoothness, Lorentz signature, and spin compatibility. Within this framework we introduce the Chiral Weyl Curvature Diagnostic, a curvature-based functional that weights topology-changing geometries by conformal curvature, spin admissibility, and topological complexity. The diagnostic functional is built from Weyl curvature invariants and includes a parity-odd dual Weyl term that is sensitive to geometric chirality. Spin consistency is enforced via a Stiefel-Whitney constraint, ensuring that only physically admissible cobordisms contribute. As an example, we construct a smooth spin cobordism between a Morris-Thorne wormhole and asymptotically flat Minkowski spacetime. In the throat region the curvature response is shown to be Weyl-dominated, and the parity-odd Weyl contribution sharply distinguishes chiral knotted embeddings while vanishing for amphichiral configurations. We then show that braids provide a natural language of throat dynamics: evolving wormhole throats trace time-dependent braid movies, with elementary braid generators representing the fundamental topological operations of the cobordism. Replacing crossing number by a braid-based complexity refines the diagnostic functional to operate at the level of these elementary exchanges and extends it naturally to multithroat and networked configurations.
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"abstract": "Topology change in Lorentzian quantum gravity demands geometric regulators that control curvature, spin structure, and chirality during nontrivial interpolations. We develop a framework for regulated topology change based on smooth Lorentzian spin cobordisms with interpolating metrics, allowing a transient failure of global hyperbolicity while preserving smoothness, Lorentz signature, and spin compatibility. Within this framework we introduce the Chiral Weyl Curvature Diagnostic, a curvature-based functional that weights topology-changing geometries by conformal curvature, spin admissibility, and topological complexity. The diagnostic functional is built from Weyl curvature invariants and includes a parity-odd dual Weyl term that is sensitive to geometric chirality. Spin consistency is enforced via a Stiefel-Whitney constraint, ensuring that only physically admissible cobordisms contribute. As an example, we construct a smooth spin cobordism between a Morris-Thorne wormhole and asymptotically flat Minkowski spacetime. In the throat region the curvature response is shown to be Weyl-dominated, and the parity-odd Weyl contribution sharply distinguishes chiral knotted embeddings while vanishing for amphichiral configurations. We then show that braids provide a natural language of throat dynamics: evolving wormhole throats trace time-dependent braid movies, with elementary braid generators representing the fundamental topological operations of the cobordism. Replacing crossing number by a braid-based complexity refines the diagnostic functional to operate at the level of these elementary exchanges and extends it naturally to multithroat and networked configurations.",
"arxiv_id": "2601.05957",
"authors": [
"Keith Andrew",
"Eric V. Steinfelds",
"Kristopher A. Andrew"
],
"categories": [
"gr-qc"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Interpolated Topology Change in a Spin Cobordism and the Chiral Weyl Curvature Diagnostic",
"url": "https://arxiv.org/abs/2601.05957",
"version": "v1"
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