Understanding AdS Global Hyperbolicity: Insights from Hawking and Ellis

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Is there an easy way to see this? can it be see via the penrose diagram? does it have anything to do with how when a stone is thrown in AdS it will alwayscome backk in finite time..
 
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I'm not familiar with AdS spaces, but according to the Wikipedia page, it says that these spaces have closed time-like curves. Any manifold with closed time-like curves cannot be globally hyperbolic.
 
Have a look at Hawking and Ellis.
 
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