Where does the energy of gravity come from?

[Vanadium 50]

Have we abandoned the B-level?

 

[PeroK]

Have we abandoned the B-level?

@vanhees71 doesn't do B-level!

 

[PeterDonis]

does the interpretation of gravity as an interaction then depend on the global topology of spacetime?

In the sense that finding that the global topology of our actual spacetime was not $\mathbb{R}^4$ would rule out the spin-2 field on flat spacetime interpretation, yes.

In fact, finding a different global topology might not even be necessary. One can argue that for the spin-2 field on flat spacetime interpretation to work, the actual spacetime must be asymptotically flat, so that the field goes to zero at infinity. But the spacetime of our actual universe is not asymptotically flat. So one can argue that that in itself is sufficient to rule out the spin-2 field on flat spacetime interpretation.

 

[PeterDonis]

in the end you end up with the full Einstein equations, which show that you could have started from every background you wanted

Not if you started by assuming a particular background. Then it doesn't matter that the field equations you end up with would, taken in isolation, allow other backgrounds--because on this interpretation the field equations can't be taken in isolation. They have to be taken in conjunction with the background assumption you made to derive them; any solution to the field equations that is not consistent with that background assumption cannot be allowed if you adopt this interpretation.