Relativistic spin hydrodynamics from novel relaxation time approximation

With the help of a semi-classical kinetic theory, a new collision kernel is proposed, which simultaneously conserves the energy-momentum tensor and the spin tensor of a relativistic fluid of spin-1/2 particles irrespective of the frame and matching conditions, even when relaxation time is momentum dependent. The relativistic Boltzmann's equation is solved using this new collision kernel to obtain the expressions of the transport coefficients with general definitions for the frame and matching conditions. The results indicate the expected existence of Barnett-like effect and the non-existence of Einstein--de-Haas-like effects.