Non-stationary spacetime What is an example for a spacetime that is non-stationary that is considered as a description of something in nature?
So far all the spacetimes I encounted have always been stationary (Schwartzschild, FRW, Kerr, etc.).
 A: The simplest physical example is just given by FRW (differently from what you wrote!) models describing the large scale of the universe:
$$ds^2 = -d\tau^2 + a(\tau)^2 d\Sigma^2\:.$$
If $a$ is not constant (as it happens in our universe) $\frac{\partial}{\partial \tau}$ is not a Killing vector. In general, these metrics do not admit local or global timelike Killing vectors (even different from $\frac{\partial}{\partial \tau}$).
Another case is the spacetime of a  collapsing star in the absence of spherical symmetry (otherwise Birkhoff's theorem would imply that the metric is stationary in a region).     
A: While the spacetime surrounding a one-dimensional mass with finite length is stationary (not static), the spacetime surrounding it when it is rotating will be non-stationary. Gravitational waves will travel away from the mass. For a point mass the surrounding spacetime is static. For rotating, spherically symmetrically distributed matter, the surrounding spacetime is non-stationary also. Due to frame dragging gravitational waves will appear.
