Originally Posted by DFroN
You can't fly straight through it, once you get too close the ships safety thingy drops you out of supercruise (method of traveling very fast through solar systems in Elite) and you take a bit of damage. You can however fly really close to it and you get lots of cool light bending going on, it looks like you're traveling at thousands of times the speed of light and then it all stretches back into place as you come back out the other side (event horizon?).
So I take it you can't get close enough to the center to see the back of your head, or ship in this case, I guess.
I think I'd have a bit too much fun messing with black holes in that game. I purchased it in on of the recent Steam sales, and I have yet to try it. I do look forward to sitting down and spending some time with it though.