@article{70005c1f5aba4b4684a9a4a0f2f53f53,
title = "Godbillon-Vey invariants of Non-Lorentzian spacetimes and Aristotelian hydrodynamics",
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.",
keywords = "G-structures, foliations, fluid dynamics, non-relativistic structures, Godbillon-Vey class",
author = "Marotta, {Vincenzo Emilio} and Szabo, {Richard J.}",
note = "Funding Information: V E M thanks Leo Bidussi for very helpful discussions. R J S thanks the Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA (Project ID 39083149), the Centro de Matem{\'a}tica, Computa{\c c}{\~a}o e Cogni{\c c}{\~a}o of the Universidade de Federal do ABC (S{\~a}o Paulo, Brazil), and the Institute for Physics of Humboldt University Berlin for hospitality and support during various stages of this work. The work of V.E.M. was supported in part by a Maxwell Institute Research Fellowship and by the GACR Grant EXPRO 19-28268X. The work of R J S was supported in part by the STFC Consolidated Grant ST/P000363/1 and by the FAPESP Grant 2021/09313-8. Publisher Copyright: {\textcopyright} 2023 The Author(s). Published by IOP Publishing Ltd.",
year = "2023",
month = nov,
day = "10",
doi = "10.1088/1751-8121/acfc07",
language = "English",
volume = "56",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing ",
number = "45",
}