>>12068961Black holes are objects into which there is a point at which no light can escape. Naturally, this is what makes them black.
Now, how about all the other properties of them? In general relativity, black holes are described by the Schwarzschild solution. This describes the space-time of non-rotating, massive spherically symmetric objects under a certain 'static' condition. They are a vaccum solution, meaning there is no matter in the space-time-so, for say the sun, it applies only up to the surface, and then another solution works for the inside. One doesn't need to worry about the schwarzschild radius then. But, if we concentrate the mass of an object to an incredibly small size, it can be seen that it will invariably be the case that light (and hence mass) heads towards the center-it starts collapsing on itself. As a static solution and taking into these considerations, the mass must all be located at the center. Now, notice the actual size of the black hole doesn't change, since there is the same amount of mass, the Schwarzschild radius is the same and so the same considerations on what distances light can escape apply. It should then be noted a few other things-in the Schwarzschild solution, the center is a true singularity and isn't a really defined point. So, the entire space-time is empty yet the black hole has mass since it has apparently collapsed to a singularity.
The above ideas come from some mathematical derivations of using GR on black holes. The term singularity means just that-a place where a model breaks down in some manner. Also, there are singularity theorems that in general require these in GR. This can act as a tell perhaps that GR doesn't account when one gets on the really small scale and indeed this is where quantum mechanics tends to come in.
