Cosmo 101 The Schwarzschild metric

We had some homework to do on the Schwarzschild metric. Now as we were staying yesterday, when one calculates a radius near a heavy object you have to be careful how you calculate it. There is the normal radius which is measured directly from the center of the object out, and there is what we call the reduced circumference (which is actually a radius and not a circumference) and it is what we calculate from knowing the circumference. But these, as we said yesterday, are different. It turns out that when you get very close to the black hole these things get very different. In fact as you approach the black hole the difference between these two gets larger and larger till it goes to infinity. Until of course you get sucked into that black hole. Quite a strange concept. But why does this happen. Well I asked the professor and he said just because the spacetime ‘fabric’ around that object is so distorted. I know it is very hard to comprehend something like that but that’s the answer he gave us. Now I’m not saying that’s a bad answer but it’s not the most satisfying of answers. It’s like being hungry and someone giving you a wafer. I don’t really like wafers but I do like big Macs! I would like a big Mac answer to the question but I’m afraid that is not something that will come easily. But if any of you have some clues or thoughts please comment!