A
black hole could be
defined as matter the mass of which lies within the Schwarzschild radius of that mass.
This is interesting because the volume increases as the cube of the radius (double the radius is eight times the volume). This means that as the mass is proportional to the radius (from the equation) the required density for the matter is lowered as the amount of matter rises.
I seem to remember a discussion a few years ago that once you got up to the scale of the known universe then the theoretical Schwarzschild radius was actually larger than the universe. Does this mean that we live inside an enourmous black hole?
The answer I suspect is that we don't have nearly enough knowledge about the universe and attempting to apply a rule for one situation to a more general situation is fraught with danger. Like applying Newtonian physics to relativistic situations.
It does however lead to all sorts of interesting speculation about black holes within black holes and such.
Not being a physicist this is the limit of my knowledge but I'm sure there is someone out there who can expand on (and maybe replace) this node.