Reader Peter asked: What happens when a black hole reaches its criticial mass in relation to its envionment? ie. matter that it is 'feeding on'. Can it become too big/heavy/dense for its environment?
Don Page says: There is no upper limit to the mass of a black hole, so it can keep growing indefinitely. Of course, if it has swallowed all the mass in its neighborhood that it can, then there will be no more mass to feed it, so it could effectively stop growing.
If one then waits a very, very long time, the surroundings may thin out so much that the tiny remaining infall would be even less than the tiny Hawking radiation coming out from the black hole. Then the black hole will gradually shrink, faster as it gets smaller, and eventually end its life in a violent explosion. However, for a ten-solar mass black hole, that would take longer than 10^69 years, nearly a million million million million million million million million million million times longer than the current age of the universe, and for every ten times larger the mass is, it would take one thousand times longer.
A black hole is separated from the external universe by an 'event horizon', a mathematically defined boundary between what is inside and what is outside the black hole. That event horizon has a finite size: it would have a radius of approximately 3 km for a black hole with the mass of the Sun, for example.
An observer outside the event horizon cannot receive information from within the event horizon. However, anything that was outside the event horizon can, if following a suitable path, cross the event horizon and 'fall into the black hole'. The black hole, therefore, acts like a hole into which anything can fall, or be thrown, without limit. As more things fall into the black hole its mass will increase and the radius of its event horizon will increase in proportion.
An observer outside the event horizon can, in principle, measure the gravitational effects of the black hole and, thereby, determine its total mass. The outside observer cannot, however, determine how that mass is distributed inside the black hole. If the mass were distributed uniformly within the event horizon, or if it were concentrated at an infinitely dense point at the centre, the external effects would be the same.
If one describes a black hole mathematically, the simplest model is one in which the black hole's mass is concentrated at a point at its centre ... a concentration of finite mass in an arbitrarilly small volume ... hence, something with infinite density. Such a structure really makes no sense to our minds, but it is allowed by the mathematics. That infinitely dense thing is called a 'singularity'.
So, a singularity is an infinitely dense point at the centre of a black hole or, equivalently, at the centre of the spherical surface called the event horizon. We cannot see the singularity with our eyes, but we can feel the gravitational effects of its mass.
An object that falls into a black hole will fall to the centre and reach the singularity. It will be crushed to infinite density and simply have its mass added to the infinitely dense mass already there.
Classically, then, there is no way to escape from a black hole, but no limit to what can go in. The singularity is the end of time and space for anything that has fallen into the black hole.
Black holes are interesting concepts and structures, and your questions is one which has probed some of the peculiar properties of black holes. The work of physicists such as Stephen Hawking has revealed even more peculiar properties, including the fact that there are ways in which matter and energy can leak out of a black hole, or even be extracted.