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