1
$\begingroup$

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.

Improve this question
$\endgroup$
1
  • $\begingroup$ 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.) $\endgroup$
    – Ryan Unger
    Feb 24, 2016 at 1:49

1 Answer 1

Reset to default
0
$\begingroup$

Imagine that you follow a timelike geodesic in de-Sitter space. De-Sitter space is not asymptotically flat (since the Ricci scalar is non-zero everywhere) but you can pass an arbitrarily large amount of proper time on your geodesic.

Another example could be a non-flat universe (with curvature) that has a cosmological constant. Again, you can spend an arbitrary amount of time on a timelike geodesic there (for example if you have constant position in comoving coordinates).

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.