system
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human
How does a black hole adhere to Pauli's Exclusion Principle and Heisenberg's Uncertainty Principle?

I was just watching Brian Cox's "A Night with the Stars" on BBC 2. He talked about how white dwarfs are limited to not exceed a certain mass as it would get too dense to support the two laws. Pauli's Exclusion doesn't allow it to get too compact as then the electrons would be forces to the lower energy levels together. Also, they can't be forced into too small a space (Heisenberg). If this is so, how do black holes get to the mass and density that they are at without breaking these laws?

Also, I was a bit distracted at the time, but I thought he said that Pauli's Exclusion Principle states that no two electrons in the universe can have the same energy at the same time. As a consequence, if I was to effect a bunch of electrons (e.g. burn a piece of wood), all the electrons in the universe would have to adjust to this. That just sounds so outlandish, I thought I must have misunderstood.

As a side note, if anyone wants to get a simple summary of quantum physics, it was a very good lecture for anyone with very little knowledge of physics.
gpt
The Pauli exclusion principle does provide an outward pressure that can balance the gravitational force, but it's not an infinite pressure, and gravity can overcome it. Any white dwarf is also made up of protons, which is necessary in order to balance out the electric charge of the electrons. Once a white dwarf is massive enough, the gravitational force is enough to push the electrons and protons together to form neutrons. The Pauli exclusion principle also applies to neutrons, though because they're more massive they can be pushed tighter together than electrons, resulting in a neutron star. If the neutron star is massive enough, gravity will also overcome the Pauli exclusion pressure for neutrons, forming either a quark star (which is still hypothetical) or causing a collapse to a black hole. All these rules of quantum physics go out the window once you've collapsed an object inside its Schwarzschild radius, or its event horizon, because it's impossible for a physical particle inside an event horizon to go anywhere but straight to the center.