Final answer:
To an observer watching from a safe distance away, the astronaut falling into a black hole will remain visible but visibly redshifted. The strong gravitational field around the black hole causes the astronaut's clocks to run more slowly, leading to the spacing between her signals growing longer and longer. This results in a significant redshift of the light she emits, making it appear redder and giving the impression that she is frozen at the event horizon.
Step-by-step explanation:
When an astronaut falls into a black hole, to an observer watching from a safe distance away, she will remain visible but redshifted. As the astronaut approaches the event horizon, the strong gravitational field around the black hole causes her clocks to run more slowly, making the spacing between her signals grow longer and longer. This results in a significant redshift of the light she emits, causing it to appear redder. Eventually, the spacing between her signals approaches infinity, making it appear to the observer that the astronaut is slowly coming to a stop and frozen at the event horizon.