# What does a closed time-like curve look like?

I want to see a plot of closed time-like curve in $(t,x)$.

$t$ - vertical axis
$x$ horizontal axis
(the usual setting just neglect $y$ and $z$ components of $(t,x,y,z)$).

What does it look like?

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Comment to the question(v1): How about simply taking Minkowski space, and declaring that the time coordinate $t\sim t + T$ is periodic, where $T>0$ is a constant? Would that be what you have in mind? – Qmechanic Feb 7 '12 at 1:33
No. I just want simplest space-time diagram where closed time-like curve is plotted. – Pratik Deoghare Feb 7 '12 at 1:52
If you want to do it in 1+1 dimensions, then I'm not sure it's possible, other than by making an identification as @Qmechanic suggested. Any metric in 1+1 dimensions is going to be conformally flat, so removing the restriction of a flat Minkowski metric doesn't help. Going to higher dimensional cases (like Goedel), and projecting the CTCs onto two dimensions doesn't give an interesting picture presumably? – twistor59 Feb 7 '12 at 8:35
@twistor59 What is the minimum number of dimensions required? – Pratik Deoghare Feb 7 '12 at 9:31
Apparently it's possible in (2+1) dimensions, but I'm not familiar with any of these solutions. For (1+1) I think you have to do some gluing like in Deutsch Politzer – twistor59 Feb 7 '12 at 10:18