Final answer:
To an outside observer, a person's heart rate would appear to slow down and eventually appear to stop as they approach a black hole's event horizon due to extreme gravitational time dilation.
Step-by-step explanation:
If a person falls as far as the event horizon of a black hole, their heart rate would appear to an outside observer to have slowed down significantly and would continue slowing down as they approach the Schwarzschild radius. Eventually, as the person reaches the event horizon, their heart rate would appear to us to have stopped. This is due to the extreme gravitational time dilation experienced in the vicinity of a black hole, where time for the falling person would seem to run more slowly relative to an outside observer at a safe distance. However, for the falling person, their perception of time would remain normal, and they would not notice any change in their heart rate. As they cross the event horizon, the outside observer would never see them cross it; instead, they would seem to freeze in place due to the effects of time dilation and redshift.