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

TL;DR

This paper investigates the role of symmetric and canonical energy-momentum tensors in relativistic spin hydrodynamics, revealing a spin-induced current linked to spin vorticity and highlighting the physical differences caused by pseudo-gauge transformations.

Contribution

It demonstrates that pseudo-gauge transformations affect entropy currents and identifies a new spin vorticity induced current from the symmetric energy-momentum tensor.

Findings

Pseudo-gauge transformations lead to physically inequivalent entropy currents.

A new current induced by spin vorticity is identified from the symmetric EMT.

Differences between canonical and Belinfante EMTs are significant in nonequilibrium conditions.

Abstract

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.