Abstract
The use of a background space makes it possible to construct for gravitational fields tensor densities that satisfy local conservation laws. In the case when the background space is asymptotically identical to a Riemannian space and admits a group of motions, the locally conserved tensor density can be identified with the density of the total energymomentum tensor, and there is a hope that the use of this entity will assist in the formulation and solution of problems of energy and momentum transport by gravitational fields. However, the properties of the energy-momentum tensor density constructed in this way do not fully correspond to the naive expectations. In particular, the energy density of a static gravitational field is negative, in the present paper, the properties of the energy-momentum tensor of the gravitational field are demonstrated for the analytically solvable example of elastic spheres.
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