The ideal relativistic rotating gas as a perfect fluid with spin

摘要

We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor σ_(μν). After having obtained the expression of the local spin-dependent phase-space density f(x, p)_(στ) in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Ω_(μν) constructed with the Frenet-Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term -(1/2)Ω_(μν)σ~(μν). We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e. t~μ=σ_(μν)u~ν≠0, in contrast to the common assumption t~μ=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.