Abstract
The general theory of relativity gives an absolutely covariant formulation of Helmholtz's laws of vorticity which is valid in arbitrary reference systems. For small relative velocities ui, (with ui,u′≪ε2) these generally covariant laws deliver Helmholtz's first law for a vorticity ωi in a rigidly rotating references system\(\frac{d}{{dt}}(\omega _i - \Omega _\iota ) = (\omega ^l - \Omega ^l )u_{l,i} \) with the angular velocity Ω of the rotation.
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Schröder, W., Treder, H.J. On general relativistic vortex-dynamics. Found Phys 26, 417–422 (1996). https://doi.org/10.1007/BF02069481
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DOI: https://doi.org/10.1007/BF02069481