Quote (novocane @ Oct 21 2011 06:10pm)
that definition implies that escape velocity is part of the reason light can't escape
also, its more than just a one-line definition; they use it to calculate the radius of black holes
so why would they put something in the definition and then use it to make calculations even though that something is completely irrelavent
If spacetime didn't warp at all, then the escape velocity description would be completely valid. That's why it's used to calculate that radius. Something can be mathematically useful and conceptually irrelevant at the same time. It's just that escape velocity is a simpler calculation than performing the one to find the point where the spacetime curvature is such that everything points back towards the black hole.
A parallel would be like using Newtonian Mechanics to describe the motion of a block being pushed instead of using the more mathematically complex Legrangian mechanics to describe its movements. Both will give you the same answer, but one calculation is much simpler and more intuitive.