I've never understood the reasoning behind the statement I've read in several places that if a black hole is sufficiently large, one falling through its event horizon wouldn't notice. Seems if I were falling in feet first, from the perspective of my head, my feet would never get there. I don't understand why my head doesn't qualify to be "an observer at a distance" from my feet as my feet approached the horizon. Can anyone explain this to me?

 

Thanks in advance.

What do you think would happen if you pass through an even horizen that has a very low gravitational gradiant? (a very large black hole) And why?

That's a very good question. The answer has to do with which coordinates you use. What you said supposes that the head is stationary with respect to the black hole. In that case, time would freeze at the horizon relative to the head. But if the whole body is in free fall, the time measured by the head is only slightly different from that measured by the feet. So the whole body goes in without any problem. See chapter 3 in Melia's "The Black Hole at the Center of Our Galaxy."