@glenngara,
The Radius collapses. The gravitational attraction is proportional to the mass and inversly proportional to the square of the distance, in this case radius, As the star collapses, yes the mass stays the same, but the radius of where that mass is found becomes smaller.
Once that radius reaches a ctitical point a singularity is achieved.
In simplistic terms (Classical almost)
the escape velocity from a body is when the sum of kinetic energy (1/2*m*v^2) and the potential (m*G*r) is zero
this is when
ve=Sqrt (2*G*m/r)
ve is escape velocity
G is gravitational constant
m is mass of the star
r is the distance to that mass
now set that ve equal to the speend of light and as m is known, calculate r--This r is then the Swhartzwild (sp) radius, that distance where the escape velocity is equal to the speed of light, Any mass with a radius less than that is a black hole.
Rap