Timelike freefallers in black hole metrics do not see the infinite future because the light entering the BH with them (and behind them) is also in free-fall. A

Timelike freefallers in black hole metrics do not see the infinite future because the light entering the BH with them (and behind them) is also in free-fall. Accelerated timelike observers inside a black hole can't accelerate for long. Inside the horizon, you won't see light that has already been further in than you are. Likewise, you can't send light to anything with is further out than you. Except that in inside regions of some BHs -- spinning ones, notably -- you can send signals on interesting orbits and might contrive a way to communicate with another inside-the-black-hole observer. This was basically what Roy Kerr's recent no-signularity paper deals with (substituting density for "you" and the other observers and pressure for communication). Pressure, spin, and contact forces could (if Kerr is correct) come into some equilibrium that supports a nonsingular configuration of matter against further inward migration, accelerating it outwards "forever", much as contact forces within the Earth accelerates you "forever". In that case if you could stand on that matter (the enormous surface gravity would squash you very very very very flat), you would see a significant blueshift of infalling light.