Clock rate in hyperbolic space-time manifold

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SUMMARY

The discussion centers on the behavior of clocks in hyperbolic, or negative, space-time manifolds. It emphasizes that the perception of clock rates is relative and depends on the reference frame and the specific paths taken through spacetime. The concept of "external perspective" is questioned, highlighting the need for clarity in defining comparisons between clocks. Ultimately, the rate at which a clock runs is contingent upon the conventions used to synchronize time across different clocks.

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From an external perspective does a clock run faster in a hyperbolic, or negative, space-time manifold?
 
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wreveley said:
From an external perspective does a clock run faster in a hyperbolic, or negative, space-time manifold?
You will get better and more helpful answers if you can state your question more completely.

It's not clear what "external perspective" could mean in this context. "External" to what?

As with all "does a clock run faster/slower?" questions, there is an implied "as compared with this other clock" and the answer will vary according to the path of that other clock through spacetime and what convention we use to define "at the same time" in statements of the form "At the same time that clock A read ##T_A## clock B reads ##T_B##"
 
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