patty144

The correct answer can be described conceptually, without the math. Take a look at chapter 3 in Melia's "The Black Hole at the Center of Our Galaxy."

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."

Some of the more recent popular science books written on this subject are those by Melia. For what you're after, you can try "The Edge of Infinity - Supermassive Black Holes in the Universe" and "The Black Hole at the Center of Our Galaxy." A lot has changed since books by Hawking, Thorne, etc. were written.