Perturbative Construction of General Relativity

[ApplePion]

I remember reading a long time ago that there was a straightforward (but operationally difficult) way of constructing General Relativity from the Linear Field Equations. Essentially you start with the Linear Field Equations solution and then generate a stress energy pseudo-tensor for this Linear Field Approximation of the gravitational field, and use that stress-energy pseudo-tensor to generate a second level gravitational field. Then you use the stress energy pseudo-tensor the second level gravitational field to get to the third level etc. Eventually it converges to General Relativity.

This seems at first to be easy, but it is not clear that it is. The stress energy pseudo-tensors of the gravitational field are constructed solely such that the divergence of the sum of {the gravitational field stress-energy pseudo-tensor plus the stress-energy of matter} is zero. I am not sure the standard gravitational field pseudo-tensors ones will work on this procedure in the gauge that is used.

It was Weinberg that did this. If anyone can provide me with the Weinberg reference I would be very grateful.

 

[Matterwave]

That sounds kind of weird to me because the SET on the RHS of Einstein's field equations should only be the SET for matter...if you included the SET due to curvature, wouldn't that be "curvature coupling" and therefore forbidden by the Einstein Equivalence Principle?