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Not quite: inside a closed surface you can't escape, but things can repeat.

You can avoid a coordinate, for example by choosing not to go there, or revisit another one repeatedly.

A black hole on the other hand doesn't have that: you cannot revisit old locations - attempting to do so moves you closer to the singularity.

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Unless it's a spinning black hole, which contains closed timelike curves that can be reached from and can escape back to the outside universe?
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