On energy-momentum tensors of the gravitational field

We discuss the phenomenological approach to gravitation in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors of the gravitational field are considered and compared in the lowest approximation. With the energy-momentum tensor of point-like particles, they satisfy the conservation laws when the equations of particle motion are the same as in general relativity. It is shown that in a newtonian approximation the considered tensors differ from the others in the way their energy density is distributed between the energy density of inter action (nonzero only at locations of particles) and the energy density of the gravitational field. Starting from the Lorentz invariance, the lagrangians for a spin-1 and mass-0 field are considered. They differ only by divergences. Using the Belinfante-rosenfeld procedure, the energy-momentum tensors are built. Using each of these tensors in a 3-graviton vertex, we obtain the Newtonian center in the G(2) approximation. Only one of these "field theoretical" tensors (namely, the half sum of the thirring tensor and the tensor obtained from the Lagrangian given by Misner, Thorne and Wheeler) leads to the correct value of the perihelion shift. This tensor does not coincide with Weinberg's tensor (directly obtainable from the Einstein equation) from the Schwarzschild field in harmonic coordinates. As a result, the motion of a relativistic particle in this field must differ from that predicted by the general relativity theory. This approach puts the gravitational energy-momentum tensor on the same level as any other energy-momentum tensor.