- #36

DrGreg

Science Advisor

Gold Member

- 2,466

- 1,991

This is correct for acianfa72 said:$$ ds^2 = \alpha(x)dx^2 - \beta(x)dt^2$$

*static*spacetime, but for a

*stationary*spacetime it will be

$$ ds^2 = \alpha(x) \, dx^2 - \beta(x) \, dt^2 +\delta(x) \, dx \, dt $$

which is a non-orthogonal coordinate system. This is related to the issue Dale mentioned earlier:

Dale said:Tetrads do not establish a synchronization convention, so they can be used to describe a congruence of rotating observers without getting into the well known synchronization problems.

*Aside: In my mind I associate "stationary but not static" with spatial rotation. But you can't have spatial rotation in a two-dimensional spacetime, which begs the question, is it possible for a two-dimensional spacetime to be stationary but not static?*

Last edited: