You can always choose a Lagrangian with the right stuff in it and . . . Or you can assume that Gauss's divergence theorem can't be generalized to four dimensions. This, however, isn't a very good idea. That would take care of the problem. Sad to say, this is an extremely bad idea.
Gravity is known, as a matter of fact, to be non-linear.
Surely you're kidding. All of the techniques and procedures are standard stuff. Trendy sophisticates would probably say that this is all pretty crude. But it seems to work. In the future that may change, but for now all equations in these documents are displayed as numerous inline gif Images.