|MadSci Network: Physics|
That is a very good question. The Pauli exclusion principle is not a force; it is a consequence of quantum theory. Nevertheless, it also manifests itself as a "degeneracy pressure" that prevents the formation of black holes from neutron stars, unless the gravitational force exceeds this pressure. For a discussion see e.g. thinkquest or physics forum.
Mathematically spoken, it is due to the spin-statistics theorem of quantum field theory: the spin of a particle governs its symmetry, that means the symmetry of the wave function describing the particle. The spin might be an integer or half-integer number. Particles with half-integer spin - such es electrons, protons, neutrons - have a antisymmetric wavefunction, whereas particle with integer spin - photons, gravitons, pions - have a symmetric wavefunction. This is also true for composite systems. A system consisting of 2 identical fermions, is antisymmetric with respect to exchange of the particle states. Therefore, they cannot occupy the same state, since the wavefunction then vanishes; e.g.
f(a,b) = f_1(a) f_2(b) - f_2(a) f_1(b)exchanging 1 with 2 leads to - f(a,b), and f(a,a), which means that particles 1 and 2 are in the same state, is zero,
When the extreme gravitational effects that can produce a black hole are at work, we enter the regime of quantum gravity. And the principles of both quantum (field) theory and gravity become questionable. No consistent theory of quantum gravity is known up to now. Therefore, the pressure from the Pauli exclusion principle can be overcome, since the theory loses its strict validity.
I hope this helps,
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