What is the physical criterion that determines if a core collapse leaves behind a neutron star or a black hole?

Answer

The mass of the remaining core material that did not escape after the rebound.

The ultimate fate of the collapsed core—whether it becomes a neutron star or a black hole—is directly dependent on how much mass remains condensed in the center after the outward rebound shock has launched the outer layers away. If the remnant core mass is below a certain threshold, often cited around 1.5 to 2 solar masses post-collapse (depending on the precise equation of state), the resistance offered by neutron degeneracy pressure is sufficient to stabilize the object, resulting in a neutron star. If the core mass exceeds this limit, gravity overwhelms even neutron degeneracy pressure, leading to complete collapse into a black hole.

What is the physical criterion that determines if a core collapse leaves behind a neutron star or a black hole?
Corestarsupernovablack holecollapse