Relativistic spin hydrodynamics with momentum and spin-dependent relaxation time

TL;DR

This paper develops a relativistic spin hydrodynamics framework incorporating momentum and spin-dependent relaxation times, extending previous models to account for more general conditions and analyzing the impact on fluid evolution.

Contribution

It introduces a novel relativistic dissipative spin hydrodynamics model with momentum and spin-dependent relaxation times, broadening the applicability of spin hydrodynamics theories.

Findings

The relaxation time can depend on particle momentum and spin.

The evolution of the fluid remains unaffected by spin in the small polarization limit.

Constructed frame-invariant transport coefficients for bulk, shear, diffusion, and spin transport.

Abstract

Using the extended relaxation time approximation (ERTA) along with the theory of semi-classical spin, we develop a framework of relativistic dissipative spin hydrodynamics such that the relaxation time can depend on the momenta and spin of the constituent spin-1/2 particles. We also consider a general definition of the fluid four-velocity allowing the theory to be valid in a general frame and matching conditions. Consequently, we construct the frame-invariant bulk, shear, particle diffusion, and spin transport coefficients, showing that the evolution of fluid remains unaffected by spin in the limit of small polarization as was the case where the relaxation time was independent of spin or momentum.