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 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 dens...

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Veröffentlicht in:Annals of physics 2010-08, Vol.325 (8), p.1566-1594
Hauptverfasser: Becattini, F., Tinti, L.
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Tinti, L.
description 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.
doi_str_mv 10.1016/j.aop.2010.03.007
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subjects ACCELERATION
ANGULAR MOMENTUM
BOLTZMANN STATISTICS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DENSITY
ENERGY RANGE
EQUILIBRIUM
Fluid dynamics
FLUID FLOW
FLUIDS
Gases
IDEAL FLOW
INCOMPRESSIBLE FLOW
MATHEMATICAL SPACE
PARTICLE PROPERTIES
PHASE SPACE
PHYSICAL PROPERTIES
Relativistic fluids with spin
RELATIVISTIC RANGE
Relativistic thermodynamics
Rotating relativistic gas
SPACE
SPIN
STEADY FLOW
TENSORS
Theory
THERMODYNAMICS
VELOCITY
title The ideal relativistic rotating gas as a perfect fluid with spin
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