I read a saying in wiki of asymptotically flat spacetime http://en.wikipedia.org/wiki/Asymptotically_flat_spacetime
"In general relativity, an asymptotically flat vacuum solution models the exterior gravitational field of an isolated massive object. Therefore, such a spacetime can be considered as an isolated system: a system in which exterior influences can be neglected."
So my questions are :
1.Given cosmological constant $\Lambda=0$, is the spacetime generated by isolated system always asymptotic flat? " I remember that there exist vaccum solutions that are not asymptotically flat(see below). So can an isolated system generate a vaccum solution outside the system that is not asymptotically flat? Is it possible that although two objects are far enough away from each other, the gravitational effect cannot be neglected?
For example, $$ds^2=-2xydt^2+2dtdz+dx^2+dy^2$$ the determinant is $-1$ for all $t,x,y,z$, the Riemann Tensor is constant but not zero in all spacetime. And the Ricci tensor is zero in all spacetime. So this is a vaccum solution even in global spacetime, while it is still not a asymptotically flat spacetime.