- #1

- 1,444

- 0

I understand the definition of stationary as existence of a timelike Killing vector field and as a result the fields (metric plus anything else e.g. gauge fields etc) cannot have any time dependence.

Static is a stronger constraint that satisfies the above plus requires the Killing vector fields to be orthogonal to the spacelike hypersurfaces. This orthogonality tells us g_{tx}=0 and consequently, there can be no time-space components of the metric.

That's all fine.

My question is: can objects move in a) static spacetimes b) stationary spacetimes

According to post #2 in https://www.physicsforums.com/showthread.php?t=593850, in a static spacetime, if we make a measurement at t1 and again at t2, along the observer's world line, nothing will have changed i.e. the curvature of spacetime (metric), the fields e.g. gauge fields etc are all unchanged. Does this mean that any objects in the system just sit around and do nothing as time evolves? Surely not otherwise, why would we study static spacetimes - they would be insanely boring!

What about stationary spacetimes? Here we can have dt dx components of the metric eg in the Kerr black hole metric. This black hole is rotating and so surely there is time dependence on something? I would have guessed there should be time dependence in the metric due to such a rotation but that appears to be wrong since the metric components aren't functions of t!

This is annoying because based on this understanding, nothing would ever move and based on experimental observations of cars on the road outside my bedroom window, that is not true! Of course....we probably don't live in a static/stationary spacetime!