Most of the fundamental equations of nature happen to be *linear* partial differential equations... This includes Maxwell equations and the Dirac equation (don't know about QCD field eqs). On the other hand, the gravitational field equation of general relativity is a nonlinear PDE. As far as I know, the nonlinear behavior is significant only in extreme situations, like near a black hole. In most situation one can approximate with a linearized field equation. Is there any easily explained reason why gravitational field should differ from other fields in this respect? Does the difficulty of quantizing gravity have anything to do with this nonlinearity? Can gravitational field exhibit chaotic behavior like many other systems governed by nonlinear PDE:s (turbulence in Navier-Stokes flow, for example).