On the phenomenological three-graviton vertex

In General Relativity, the graviton interacts in three-graviton vertex with a tensor that is not the energy-momentum tensor of the gravitational field. We consider the possibility that the graviton interacts with the definite gravitational energy-momentum tensor that we previously found in the G2 approximation. This tensor in a gauge, where nonphysical degrees of freedom do not contribute, is remarkable, because it gives positive gravitational energy density for the Newtonian center in the same manner as the electromagnetic energy-momentum tensor does for the Coulomb center. We show that the assumed three-graviton vertex does not lead to contradiction with the precession of Mercury’s perihelion. In the S-matrix approach used here, the external gravitational field has only a subsidiary role, similar to the external field in quantum electrodynamics. This approach with the assumed vertex leads to the gravitational field that cannot be obtained from a consistent gravity equation.