Unicity of general relativity in the field theoretic approach

It is well known that general relativity can also be obtained by an iterative procedure starting in an ideal pseudo-Euclidean space-time in which the field is described by a tensor potential. To each step of the iterative procedure, one has to introduce the energy-momentum tensor of that order as the source of the field equations. When measured by real rods and clocks, the observable space-time turns out to be Riemannian and general relativity is obtained as the theory to which the method converges. Such a convergence theorem was shown assuming proper energy-momentum tensors to each order. The aim of the present work is to show that, to each order, one can take the most general energy-momentum tensor required by the iterative procedure and that the convergence to the general theory of relativity still holds