Abstract

The formulation of equations of state for a continuous medium and gravitational field is considered in the framework of the general theory of relativity, using the fundamental variational equation. The arbitrariness of determination of equations of state is examined in detail, and problems of determining the energy-momentum tensor for the medium and gravitational field are clarified in the case of invariant dynamic and generally physical Euler's equations. Obtained formulas and deductions are specifically defined for the gravitational field in vacuum. The developed theories make possible a proper evaluation of the essence of the various assumptions prevailing in the theory of the energ-ymomentum pseudotensor and in the general problem of the possible form of equations of state for physical models.

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