Godbillon-Vey Invariants of Non-Lorentzian Spacetimes and Aristotelian Hydrodynamics

2023/04/25 by Vincenzo Emilio Marotta, Richard J. Szabo, Marotta, Vincenzo Emilio +1 · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #hep-th #math-ph #math.DG #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.2304.12722

openalex publication_date 2023/04/25 · openalex created_date 2023/04/27 · openalex updated_date 2026/07/28

Abstract

We study the geometry of foliated non-Lorentzian spacetimes in terms of the Godbillon-Vey class of the foliation. We relate the intrinsic torsion of a foliated Aristotelian manifold to its Godbillon-Vey class, and interpret it as a measure of the local spin of the spatial leaves in the time direction. With this characterisation, the Godbillon-Vey class is an obstruction to integrability of the G-structure defining the Aristotelian spacetime. We use these notions to formulate a new geometric approach to hydrodynamics of fluid flows by endowing them with Aristotelian structures. We establish conditions under which the Godbillon-Vey class represents an obstruction to steady flow of the fluid and prove new conservation laws.

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Discussions

• This paper discusses "Aristotelian structures" on manifolds in a very mathematical way starting in Definition 2.17. It's fun imagining Aristotle trying to read this paper. (2/2) [bsky, 6 points, 0 comments]

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