= Canonical vorticity of a relativistic fluid
{title2=$\omega=d(\epsilon u^\flat)$}
The canonical vorticity two-form is $\omega_{ab}=\nabla_a(\epsilon u_b)-\nabla_b(\epsilon u_a)$, with <specific enthalpy per particle> $\epsilon$. Potential flow $\epsilon u_a=\nabla_a\chi$ has $\omega=0$ for a <torsion-free connection>. Contracting this identity with $u^a$ yields $\epsilon u^a\nabla_au_b=\nabla_b\epsilon-u_bu^a\nabla_a\epsilon$, the isentropic <relativistic Euler equation> in signature $(+---)$. This canonical condition does not mean the unweighted four-velocity one-form is closed.
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