How does gravitational time dilation affect a clock falling toward a black hole as seen by a distant observer?

• A. The clock speeds up for distant observers as it approaches the horizon.
• B. The clock stops completely for both observers as it nears the horizon.
• C. As the clock approaches the horizon, its ticks appear to slow and freeze to a distant observer, while its own proper time continues normally.
• D. Time dilation makes the clock appear to speed up to the local observer.

Answer: (C)

Gravitational time dilation is the idea that clocks deeper in a gravity well run slower compared to clocks far away. For a clock falling toward a black hole, its own experience is normal: in its own frame, it ticks away as time passes. But the light it emits must climb out of increasingly strong gravity. As the clock nears the event horizon, the signals it sends become more and more redshifted and delayed in the distant observer’s frame. To someone far away, each tick takes longer to arrive, and the interval between ticks stretches toward infinity. So the distant observer sees the clock slow down and effectively freeze at the horizon, even though the clock itself continues ticking normally and crosses the horizon in finite proper time.