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 , energy density and pressure, which complete a solution to the conservation equations.
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