For black holes as for any other body, gravitational attraction is given by F=GMm/r^2 where are is the distance separating the centre of mass of each body.Rum wrote:Given that there is a critical point in terms of mass at which a star, neutron star perhaps (?) collapses and becomes a black hole - i.e. nothing can escape its gravity, are we saying that when that happens they are a standard size and that as more and more matter falls in it grows? I assume what grows in that case is the distance from the 'centre' to the event horizon, i.e. as the mass increases so does the gravity.
The event horizon of a blackhole is a function of its mass. The bigger the mass, the larger the event horizon, given by the Schwarzchild radius:
r(s)=2GM/c^2
So as you suggested, the more massive a blackhole becomes, the larger it's event horizon becomes. It's a useful excerise to plug in the numbers using the mass of our sun to find it's event horizon... it's surprisingly small. Only about 3km. The gravitational force is so incredibly strong near the event horizon that a human would physically be ripped to pieces because the gravitation force at their feet would be so much stronger than that at their head (if they fell in feet first) that it would break the e-m bonds holding us together molecule by molecule, atom by atom.
The condition to form a black hole is that the implosive gravitational force is sufficient to overcome all the forces which oppose it, so it literally implodes under its own weight. This is fairly complicated to work out, and you can go into some detail by looking up stellar evolution which goes into the various details (mass, rotation, temperature) to get an idea of what conditions lead to what objects (neutron star, white dwarf, brown dwarf etc etc).
