|MadSci Network: Astronomy|
Difficult question! It's true that, according to the theory of general relativity, within a black hole the laws of physics as we understand them do not apply.
As you know, a black hole's gravitational attraction is so strong that not even light---the fastest thing in the universe---can escape. The region within is therefore effectively cut off from our Universe, and so different laws can apply.
Therefore, Heisenberg's uncertainty principle may not apply, but as no information could pass between the two regions we would never know. It's worth noting that despite the best effort of physicists for the last 40 years, we have no real theory which combines relativity and quantum mechanics, so the situation is far from clear.
[Moderator: Actually within the event horizon, general relativity makes reasonable predictions, so there's no expectation that our understanding of the laws of physics breaks down everywhere inside the event horizon. However, general relativity also predicts that inside an event horizon there will be a singularity of infinite density. This prediction of infinite density seems unreasonable and is what people mean when they say that our understanding of the laws of physics breaks down. Thus, only near the very center of the black hole would we become uncertain about the uncertainty principle, but there is no way to test this expectation either.]
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