Einsteins field equations are nonlinear but I guess that nobody has already found solutions to the full nonlinear equations (because of course it is very hard to do so). Nevertheless, such solutions could (I think) hold a number of surprises. Instead of linear gravitational waves, one could think of soliton like waves with strange properties. Solutions near spinning black holes could also be siginificantly modified by taking into account nonlinear terms. Finally, even cosmological models could have to be modified because of these nonlinearities. Maybe that there is no need then to invoke dark energy and other strange stuff. What do you think ?