What happens if you fly through the Earth?

The Funniest part of theoretical physics is that you can ask a stupid question and get your answer (sometimes too stupid). For example, what if you drilled a hole through the center of the Earth and leap through it? "Who could do such a stupid thing to do?" - You ask. Apparently no one. Such an act will kill you very sophisticated and split the millions of times. Let's assume that some brave soul ventured into it for the sake of science? What can happen, theoretically?