Spin hydrodynamics and symmetric energy-momentum tensors - A current induced by the spin vorticity -

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. (C) 2021 The Authors. Published by Elsevier B.V.

Automated summary

In this article, a puzzle in relativistic spin hydrodynamics is discussed, highlighting the absence of an antisymmetric part in the Belinfante EMT and the physical inequivalence of pseudo-transformed entropy currents in nonequilibrium situations. Additionally, a current induced by the spin vorticity read from the Belinfante symmetric EMT is identified.