Covariant formulation of the weak conservation law in the general theory of relativity without the energy-momentum of the gravitational field

A systematic covariant formulation is given of the weak conservation law in the general theory of relativity for arbitrary coordinate transformations without introducing the unsatisfactory definition of the energy-momentum of the gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 13–16 July, 1979.