The center of a Black Holes's Gravity is 0. So no gravity = No time aceleration witch means nothing can happen.
Zero gravity does not mean time stops. Relative acceleration and relative velocity are what makes time vary relatively I think. Gravity is the same as acceleration so as you cross the event horizon, your perception of time will slow to a stop. This does not mean YOU will slow to a stop, nor does it mean your mind would stop. I think it would mean that when you reached the center of the black hole from your perspective eternity would have passed.
As you approach the event horizon, your perception of time will not slow down or stop. Your perception of time will remain normal just like before.
Maybe I was wrong about eternity passing. I'm not sure.
I was thinking its kind of like how a photon is ageless. It is practically immortal because it travels at light speed so time doesn't pass for it. So if a space ship traveled at c between two galaxies and had an atomic clock on board, it would not advance at all during the travel so from the person's perspective on board he would reach the other galaxy instantaneously while in the rest of the universe thousands of years may have gone by.
But I guess only a short amount of time would pass in the rest of the universe as you enter a black hole, since you are traveling at a definate speed and will reach the center in a certain amount of time?