If you are in an accelerating space elevator, and you throw a clock upwards and then it falls down, the clock looks to be accelerating, but it is in a constant inertial frame not accelerating and so your time should slow due to acceleration according to the equivalence principle of General Relativity (Gravity=time dilation & Gravity=inertia force) but you can't observe other clocks that are in space around you not accelerating to be effected by this form of time dilation.
So if it is equivalent then you should be able to see that if you let a clock be effected by gravity (fall) it should also tick faster than your time rate. So a clock thrown into a black hole, at least as far as General Relativity is concerned should be seen to tick at a normal to an observer far away from the black hole! At least until it stops falling. This is not AFAIK a recognized conclusion of General Relativity. John
