Main Question or Discussion Point
Gravitational waves are quadrupoles, they bend and stretch spacetime. Does the expansion of spacetime due to gravitational waves exceed flat (Minkowski) spacetime or is flat spacetime it's limit?
I think there is some confusion behind this question, but I'm not sure what it is or how to resolve it.Does the perturbation "stretch" spacetime beyond asymptotic flatness? ...Causing an expansion?
That's correct, it is. Heuristically, the reason for this is that the wave is entirely "made" of Weyl curvature (which is the only kind of spacetime curvature you can have in the absence of stress-energy), and Weyl curvature is inherently volume-preserving.I believe the expansion scalar for this wave is zero
Moreover, in a non-vacuum asymptotically flat spacetime with GWs being produced by a source, we can measure the energy carried away from the source by GWs by looking at the difference between the ADM mass and the Bondi mass.a vacuum space-time with GW's can have a non-zero ADM mass due to the presence of the GW's
You appear to be trying to look at this as though the GWs "change" spacetime in some way; but that's not how spacetime works. Any given spacetime is a 4-dimensional geometry that already contains all the information about how everything in it, GWs or otherwise, "changes" with "time". Asymptotic flatness is a property that a 4-dimensional spacetime either has or doesn't have; it can't "change" based on the presence of GWs or anything else.Does the perturbation "stretch" spacetime beyond asymptotic flatness? ...Causing an expansion?