my thinking is that, due to the Pauli exclusion principle, singularities must be formed of bosons (if anything), and not fermions since fermions may not occupy the same quantum state as one another. Is this correct?
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1Closely related: Does black hole formation contradict the Pauli exclusion principle?, and also How does a quark star collapse into a black hole? – Chiral Anomaly Sep 18 '21 at 01:20
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2The simplest observation is that general relativity and and its singularities are a classical theory. The PeP is a quantum mechanical principle, i.e. a type of axiom for quantum mechanical theories. GR has not been definitively quantized. Cosmological models use effective quantization in the region of singularities, which makes them a locus and not a point. See https://en.wikipedia.org/wiki/Big_Bang#/media/File:CMB_Timeline300_no_WMAP.jpg – anna v Sep 18 '21 at 03:51