- #71
PeterDonis
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PeterDonis said:I think this is only possible if there are closed timelike curves in the spacetime, or if there is some kind of discontinuity in the light cone structure...I haven't dipped into Hawking & Ellis in quite a while, but I suspect there is something in there about this.
Well, thanks to Google and Wikipedia, I don't even have to crack open Hawking and Ellis.
Check out the Wiki page on causality conditions:
http://en.wikipedia.org/wiki/Causality_conditions
There's a fair bit of technical jargon here, but the upshot appears to me to be that my quote above is basically correct. The key causality condition is "stably causal", which is described on the Wiki page; this condition basically entails that there are no closed causal (timelike or null) curves in both the spacetime itself, and in any "nearby" spacetimes that can be produced from it by a small perturbations (this is where the "stably" part comes from). If a spacetime meets this condition, then there is a global time function on the spacetime, which prevents the sort of thing TrickyDicky was describing from happening. Note that there are *no* symmetry conditions imposed in any of the relevant theorems; the spacetime does not have to be homogeneous, isotropic, spherically symmetric, stationary, etc., etc. It just has to be stably causal.