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

Vincenzo Emilio Marotta*, Richard J. Szabo

*Corresponding author for this work

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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 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.
Original languageEnglish
Article number455201
JournalJournal of Physics A: Mathematical and Theoretical
Volume56
Issue number45
Early online date13 Oct 2023
DOIs
Publication statusPublished - 10 Nov 2023

Keywords

  • G-structures
  • foliations
  • fluid dynamics
  • non-relativistic structures
  • Godbillon-Vey class

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