Closed timelike curves

Asked May 14 '21 at 13:01

Active May 14 '21 at 13:03

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In a paper, I have read that the manifold

$$S^1 \times \mathbb{R}^n$$

with the metric $g=-d \theta^2 +g_0$, where $-d \theta$ is the standard metric on $S^1$ and $g_0$ is the euclidean metric on $\mathbb{R}^n$ always possesses closed causal curves.

Is the reasoning behind this that each closed curve along the unit circle is a closed timelike curve?

edited May 14 '21 at 13:03

asked May 14 '21 at 13:01

User1

1,803

Do you mean $S^1$ or $S^2$? – RobertTheTutor May 14 '21 at 13:02
"Yes", that is correct for this metric. – Andrew D. Hwang May 14 '21 at 17:17
For the metric $g= d \theta+g_0$ it wouldn't be correct, right? – User1 May 14 '21 at 17:28
The metric $d\theta^2 + g_0$ doesn't have the right signature for relativity...? – Andrew D. Hwang May 15 '21 at 13:19
Forget about my comment, I don't know what I was thinking – User1 May 15 '21 at 15:56

Closed timelike curves

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