My question is to what extent the specifically non-linear properties of GR have been analyzed by theoretical physicists. Can they give rise to chaos and complexity, as many non-linear systems do? I also wonder: I've so far mostly read about linearized descriptions of gravitational waves. However in fact, gravitational waves do not obey linear superposition. Has this been considered so far in any approach to quantum gravity (I especially refer to identifying gravitational waves with gravitons)? Because I think, that point is a fundamental difference to the fields contained so far in the standard model - correct me if I'm wrong with anything here. But maybe this second question would rather belong into the "Beyond the standard model" category. I'm interested in your answers!