The compressibility of matter is the crucial point in this investigation. This relates to gravitational collapse.

http://en.wikipedia.org/wiki/Gravitational_collapse[Gravitational collapse is the inward fall of an astronomical object due to the influence of its own gravity which tends to draw the object toward its center of mass. In any stable body, this gravitational force is counterbalanced by the internal pressure of the body acting in the opposite direction. If the gravitational force is stronger than the forces acting outward, the equilibrium becomes unstable and a collapse occurs until the internal pressure increases sufficiently that equilibrium is once again attained (the exception being a black hole).]

The crucial sentence is "If the gravitational force is stronger than the forces acting outward, the equilibrium becomes unstable and a collapse occurs until the internal pressure increases sufficiently that equilibrium is once again attained".

The key thing is to plot all potential stages of equilibrium for a variety of mass sizes.

Another crucial point is this.

"According to Einstein's theory, for even larger stars, above the Landau-Oppenheimer-Volkoff limit, also known as the Tolman–Oppenheimer–Volkoff limit (roughly double the mass of our Sun) no known form of cold matter can provide the force needed to oppose gravity in a new dynamical equilibrium. Hence, the collapse continues with nothing to stop it."

The Tolman–Oppenheimer–Volkoff limit is then the key to determining if black holes of 3 solar masses can actually form.