Can Gravitational Waves Exist in a Static Spacetime?

[TrickyDicky]

Are gravitational waves (where the field varies with time) possible in a static spacetime(no time derivatives)?
I would expect them to be predicted only in a expanding spacetime but I'm not totally sure.

 

[Dale]

Gravitational waves are usually analyzed in a perturbative approach. You can certainly have gravitational waves as a small perturbation on top of a static spacetime, but I think that technically the wave makes the spacetime non-static.