Density of the gravitational field energy.
Ruslan A. Sharipov.
We continue to get acquainted with a new non-Einsteinian theory of gravity, whos name is "3D-brane universe model". This name seems like a reference to string theory and membrane theory. This is how the artificial intelligence from the Google search engine reacts to this name. However, this is an erroneous association. The "3D-brane universe model" is a purely three-dimensional theory of the universe, in which the four-dimensional spacetime serves only as a mathematical abstraction, in which various moments in the evolution of the three-dimensional universe are mapped and stacked layer by layer.
In the purely three-dimensional universe the energy conservation law has a purely three-dimensional form.
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Here H is the total energy density of all fields, J is the vector of the total energy flux density of all fields. The contribution of the gravitational field to the energy density H is given by the formula
The contribution of the gravitational field to the components of the energy flux density vector J is given by the formula
The gravitational field in Einstein's general relativity is isolated from other fields and does not contribute to the energy conservation law. Soviet and Russian academician L. D. Faddeev characterized this situation in general relativity with the following words: "The energy of the gravitational field is not localized, i.e. there is no uniquely determined energy density" (see the journal Soviet Physics Uspekhi, 1982, vol 25, issue 3, pages 130-142). The formulas given above show that there is no such problem in the new theory. There is a uniquely determined energy density of the gravitational field. The density of the energy flow of the gravitational field is also uniquely determined.
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