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Pauli exclusion principle states that 2 identical electrons cannot be in the same state, where state includes a spacial component.
I have heard that, in order to avoid being in the same state, in a white dwarf, the De Broglie wave length of the electrons becomes shorter and shorter, meaning that they have a higher and higher momentum/ energy. Eventually, when the gravitational pressure is too high, they form neutron stars, since neutrons have smaller De Broglie Wave lengths due to their higher mass.
My question is, by applying more and more pressure, can we confine more and more identical neutrons/ other fermions in an arbitrarily small space, eventually forming a black hole? Or, at some point, fermions must be converted into bosons?