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The formulation of a dynamical theory of General Relativity, includingmatter, is viewed as a problem of coupling Einstein's theory of pure gravity,formulated as an action principle, to an independently chosen and well definedfield theory of matter. It is well known that this is accomplished in a mostnatural way when the matter theory is formulated as a relativistic, Lagrangianfield theory. Special matter models of this type have been available; here athermodynamical model that allows for general flows is used. A problem that isof even older date, one that was pursued vigorously by leading scientists ofthe 19'th century, is that of subjecting hydrodynamics and thermodynamics to anAction Principle. A solution to this problem has been known for some time, butonly under the strong restriction to potential flows.  A variational principle for general flows has now become available.  The present paper lifts this theory to the relativistic context, SpecialRelativity and General Relativity. The energy momentum tensor has a structurethat is more general than that postulated by Tolman, and different fromproposed generalizations; it appears to be well suited to represent rotationalflows in General Relativity. It incorporates a conserved mass current, therelativistic analogue of the hydrodynamical equation of continuity.

Relativistic Thermodynamics, a Lagrangian Field Theory for general flows including rotation