This may be pretty basic but how can black holes have different masses, rotate, obtain material or have mass if black holes are finite points. I'm sure it has something to do with mathematics or theory but it is difficult for me to make any sense of this. Black holes make sense to me until I factor in that they are supposed to be a finite point. Even the fact that they attain mass and matter is confusing. They are a finite spot that can be accessed at all points, 3 dimensions, so where does the matter go?
We don't really know whether black hole singularities are pointlike. Would it bother you to have ten solar masses compressed to, say, [itex]10^{-105}[/itex] cubic meters (one cubic Planck length)?
It IS basic, a fundamental unknown. but not simple. And that is one major reason black holes are so fascinating to theorists. Immense gravity, best described by general relativity, and the physics of the small, best described by quantum theory, come together at the singularities. But so far neither theory can handle the exact description of whatever that "singularity" may be. Quantum gravity is an attempt at such descriptions, not yet fulfilled. More here, but I think many here would disagree with some of the description: http://en.wikipedia.org/wiki/Black_hole#Singularity Note that the words don't say "finite points"....it's a subtle distinction. And within in the description are contradictions .... versus So we have more to learn.
Another perspective in answering the OP question. I was just reading a section of Black Holes and Time Warps, by Kip Thorne and on page 463 he discusses an interesting feature of black holes discovered by Roger Penrose: That "end" is the singularity. How spacetime gets destroyed there is unknown.