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arXiv · 2304.12722

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

Vincenzo Emilio Marotta·Richard J. Szabo
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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 $\mathsf{G}$-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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Vincenzo Emilio Marotta, Richard J. Szabo. 2023-04-25. Godbillon-Vey Invariants of Non-Lorentzian Spacetimes and Aristotelian Hydrodynamics. https://arxiv.org/abs/2304.12722

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