I have a problem with static/non-static spacetime. The problem is that the notion of spacetime includes time itself, so how can it change with time? Imagine an asteroid approaching the Earth-Moon system. The Earth-Moon system is a non-static spacetime, so presumably is giving off gravitational waves. But in principle it should be possible to use GR to calculate the asteroid's trajectory (treating it a test object), in other words, to obtain the equations of the geometry of spacetime of such system. Gravitational waves would be described within that geometry. I suppose that the spacetime geometry around such system is too complicated, so we choose to treat it as a static spacetime and then consider the movement of the two massive bodies as some kind of perturbation. So my question is: is the concept of non-static spacetime a mere approximation to the real thing?