Spin Hydrodynamics and Symmetric Energy-Momentum Tensors -- A current induced by the spin vorticity --

Understand

We discuss a puzzle in relativistic spin hydrodynamics; in the previous formulation the spin source from the antisymmetric part of the canonical energy-momentum tensor (EMT) is crucial.

• The Belinfante improved EMT is pseudo-gauge transformed from the canonical EMT and is usually a physically sensible choice especially when gauge fields are coupled as in magnetohydrodynamics, but the Belinfante EMT has no antisymmetric part.
• We find that pseudo-transformed entropy currents are physically inequivalent in nonequilibrium situations.
• We also identify a current induced by the spin vorticity read from the Belinfante symmetric EMT.