The ideal relativistic rotating gas as a perfect fluid with spin

We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor sigma(mu),. After having obtained the expression of the local spin-dependent phase-space density fix(x, p)omicron tau. in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Omega(omega),constructed with the Frenet-Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term (1/2)Omega(omega sigma omega). We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e. t(mu)=omicron omega mu nu not equal 0, in contrast to the common assumption t(mu) = 0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects. (C) 2010 Elsevier Inc. All rights reserved.