What must happen to the core mass for gravity to overwhelm neutron degeneracy pressure and form a Black Hole?

Answer

The remaining core mass is greater than about 3 solar masses

If the resulting core mass after a massive star's supernova exceeds about 3 solar masses, even neutron degeneracy pressure is insufficient to support it, leading to complete gravitational collapse and the creation of a Black Hole.

What must happen to the core mass for gravity to overwhelm neutron degeneracy pressure and form a Black Hole?

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