I know that if one astronaut falls into a black hole, then a distant observer will see him take an infinite amount of time to reach the event horizon (provided the observer can see light of arbitrarily large wavelengths).
But the falling astronaut will only take a finite amount of time to reach the horizon.
My question is: What will the falling astronaut see if he "looks backwards" while falling. Will he see the distant observer growing old and all the stars dying by the time he reaches the horizon ?