If the remnant left behind by the supernova is massive enough, it will be a black hole. (If not it will be a Neutron star)
More generally, if anything is compressed within its Schwarzschild radius, then a black hole will form.
RS = 2Gm/ c2 = (m/ msun ) ! 3km
The boundary of a black hole is called the event horizon. When something passes through the event horizon, it can no longer communicate in any way with the world outside. Surprisingly, if you fell into a large black hole, you wouldn’t know when you had passed through the event horizon.
COSMOS to HUMANITY, Spring 2008
The radius of the sun is actually about 700,000 km.
Lecture 2 , slide 15