Relativistic first-order spin hydrodynamics via the Chapman-Enskog expansion

TL;DR

This paper derives relativistic first-order spin hydrodynamics using Chapman-Enskog expansion, showing no first-order spin effects on fluid motion equations, thus highlighting the need for second-order theories to incorporate spin-orbit coupling.

Contribution

It provides a detailed derivation of first-order spin hydrodynamics from a nonlocal collision term, clarifying the role of spin in relativistic fluid dynamics.

Findings

First-order spin effects do not alter the fluid motion equations.

Energy-momentum tensor remains unaffected by spin at first order.

Highlights the necessity of second-order theories to include spin-orbit interactions.

Abstract

In this paper, we present a detailed derivation of relativistic first-order spin hydrodynamics using the Chapman-Enskog method to linearize the nonlocal collision term for massive fermions proposed in \cite{Weickgenannt:2021cuo}, which well describes spin-orbit coupling in the collision process and is relevant for the research on local spin polarization. Based on this collisional term, we provide a formal discussion about first-order spin hydrodynamics and determine the motion equations of fluid variables and nonequilibrium corrections to the energy-momentum and spin tensors. The results indicate that the motion equations show no differences compared to spinless first-order hydrodynamics and the energy-momentum tensor receives no corrections from spin as far as first-order theory is concerned, which calls for the construction of second-order theory of fluids naturally incorporating the effect of spin-orbit coupling.