Clock rate in hyperbolic space-time manifold

[wreveley]

From an external perspective does a clock run faster in a hyperbolic, or negative, space-time manifold?

 

[Nugatory]

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 $T_B$"