# Proper time and asymptotic flatness

I'm trying to understand the concept of asymptotic flatness in general relativity, and came up with the following question:

If the proper time $\tau$ is infinite for a timelike geodesic, does it mean that the spacetime is asymptotically flat? Or am I confusing concepts here?

Would be grateful for any clarifications.

• Are you asking "if at least one geodesic has infinite length, then the space is asymptotically flat" or "if all geodesics have infinite length, then the space is asymptotically flat"? (The answer is no in both cases.) – Ryan Unger Feb 24 '16 at 1:49