When an object crosses the future horizon, what do you see?

Question

First, there should be a redshift due to the velocity of the object before it crosses the horizon. And then, does the object's light just shut off?
Note: There are several cosmological horizon that we can talk about (the particle horizon, the event horizon, the Hubble radius, the future horizon). Since the Universe is expanding and the expansion is accelerating, there should be a future horizon as well. Is it right?

niels nielsen · Answer

I assume you mean the event horizon of a black hole.  I'll take the case where the black hole is not rotating, or charged.
In this case, an observer (at a safe distance) will watch the object falling towards the horizon grow redder and dimmer as it gets closer and closer to the horizon.
If the object is a clock, the observer will see the clock hands moving more and more slowly as it gets closer to the horizon.
Viewed from a safe distance, the observer will never see the object actually fall through the horizon; instead the reddened object with its clock hands almost completely frozen will fade into invisibility right at the event horizon.

When an object crosses the future horizon, what do you see?

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