I realize that energy is a touchy subject in GR in dynamical situations, and people argued for a long time whether or not gravitational waves carried energy. But it sounds like there has been agreement for quite awhile now that they do carry energy. Since in weak gravity situations, we can write equations that make gravity look similar to the fields of electromagnetism, and on top of this 1) gravity waves carry energy 2) gravity should "self couple" according to semi-classical treatments of gravity I don't understand why the Schwarzschild solution has a zero stress energy tensor. Shouldn't we include some energy for the 'gravitational field' itself? Sort of like the charged black hole solution. Where energy is included in the electric field. I wonder how this would affect planetary motion if we were indeed supposed to include such a term. Since the "gravitational field energy" would be such a small contribution to the sun's mass in this idea, it might not be measurable. Although it would make the mass of the sun appear to get slightly larger as you moved away from it (which bizarrely is what the pioneer anomaly saw, but is probably just a coincidence).