An approximate method is developed for calculating averages with the aid of a relativistic Oort distribution function for gravitating particles with cylindrical symmetry. Accuracy estimates are obtained for the method. The relativistic Oort formula is derived for the dependence of the mean velocity of the particles on the distance to the rotation axis, and this formula is in agreement with results of nonrelativistic statistics for low velocities ϑ≪c. The relativistic particle number density, the component of the mean velocity 4 - vector, and the momentum - energy tensor are calculated. The relativistic particle number density coincides with the familiar barometric formula for low velocities ϑ≪c and for low potentials Ф≪c^2. Reliance on Eckart phenomenological yields equations of state which coincide in the relativistic limit with the equations of state of an ideal gas.
Department of Theoretical Physics
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