On the flow of perfect energy tensors

Abstract

The necessary and sufficient conditions are obtained for a unit time-like vector field $u$ to be the unit velocity of a divergence-free perfect fluid energy tensor. This plainly kinematic description of a conservative perfect fluid requires considering eighteen classes defined by differential concomitants of $u$. For each of these classes, we get the additional constraints that label the flow of a conservative energy tensor, and we obtain the pairs of functions $\{\rho ,p\}$, energy density and pressure, which complete a solution to the conservation equations.

28 pages, 1 figure and 3 tables. Added references 31 and 32

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• Thermodynamics of the universes admitting isotropic radiation