Application of the law of gravitation to explain the formation of black holes?

Specifically for a black hole the range of gravitational influence is calculated by the "Shwarzchild Radius" and surprisingly the radius is quite small for even the biggest blackhole, If a blackhole had the mass of the earth, then the Shwarzchild radius would only be a centimeter! Meaning you would have to come with in a centimeter of the blackhole to get sucked in.