The formulation of a dynamical theory of General Relativity, including matter, is viewed as a problem of coupling Einstein's theory of pure gravity, formulated as an action principle, to an independently chosen and well defined field theory of matter. It is well known that this is accomplished in a most natural way when the matter theory is formulated as a relativistic, Lagrangian field theory. Special matter models of this type have been available; here a thermodynamical model that allows for general flows is used. A problem that is of even older date, one that was pursued vigorously by leading scientists of the 19'th century, is that of subjecting hydrodynamics and thermodynamics to an Action Principle. A solution to this problem has been known for some time, but only 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, Special Relativity and General Relativity. The energy momentum tensor has a structure that is more general than that postulated by Tolman, and different from proposed generalizations; it appears to be well suited to represent rotational flows in General Relativity. It incorporates a conserved mass current, the relativistic analogue of the hydrodynamical equation of continuity.
Electrically charged regular black holes in higher dimensions: Maxwellian limit, branch point of the Lagrangian, and thermodynamics
New Uzbekistan University（新乌兹别克斯坦大学）；Ulugh Beg Astronomical Institute（乌鲁格别克天文研究所）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）；Tashkent State University of Economics（塔什干国立经济大学）
Thermodynamic Volumes of Extended Black Hole Thermodynamics with Auxiliary Gauge Fields
Beijing Normal University（北京师范大学）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
