I'll use the term 'understand' here. By that, I mean that I understand in laymen's terms. From my questions, it should be obvious that I don't understand mathematically.
I understand how black holes form, and I understand how matter is accreted. I even understand how they will eventually evaporate. But, there's a lot that I don't grasp.
At the centre of a black hole is a singularity, and by definition that cannot grow any bigger (or smaller). It is infinitely dense and therefore can't gain any density. It doesn't have a definable position in space-time, so how can something 'hit' it? How does a singularity get bigger in some way -- how does it gain mass?
Then there's the idea that information cannot escape a black hole, but, surely, if adding matter increases its mass and that has an effect on the space-time surrounding the black hole, then some information is indeed escaping -- information about how much it has eaten.
And, how can something outside of space-time affect space-time?
Or, do I need to wait for quantum-gravity to be solved to get any answers?