Godbillon-Vey invariants of Non-Lorentzian spacetimes and Aristotelian hydrodynamics

DOI10.1088/1751-8121/ACFC07zbMATH Open1530.53040arXiv2304.12722MaRDI QIDQ6063360

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Publication date: 7 November 2023

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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 $mathsfG$-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.

Full work available at URL: https://arxiv.org/abs/2304.12722

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