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I've heard it mentioned many times that "nothing special" happens for an infalling observer who crosses the event horizon of a black hole, but I've never been completely satisfied with that statement. I've been trying to actually visualize what an infalling observer would see (from various angles), and I'd like to know if I understand things correctly.

Suppose we travel near a sufficiently large black hole (say, the one in the center of the Milky Way) so that we could neglect tidal effects near the horizon, and suppose that it's an ideal Schwarzschild black hole. Suppose that I'm falling perfectly radially inward, and you remain at a safe distance (stationary with respect to the black hole).

1) If I'm looking inward as I fall, the event horizon will always appear to be "in front" of me, even after I've crossed the event horizon relative to you, and will continue to be "in front" of me right until I'm crushed by the singularity. This makes perfect sense (and correct me if it's wrong), but it's the following case with which I'm having the most difficulty:

2) If I'm looking back at you (an outside observer), what effects, if any, would I observe? My reasoning was: as I approach the event horizon, a "cosmological horizon" begins to close in around me, beyond which I can no longer observe the universe. At the point when I cross the event horizon relative to you, my cosmological horizon will have "engulfed" you, since I'm effectively traveling faster than light relative to you. Therefore, for me, the universe would redshift out of observability when I cross the event horizon.

Is the above correct? I guess it can't be, if all sources say that "nothing special happens"... but I don't completely understand why. Or is the following more accurate:

2a) If I'm looking back at you, I will continue to observe you even after crossing the event horizon (until my demise at the singularity), since the light emitted by you went into the event horizon along with me, even though I can no longer communicate with you (but I have no way of knowing it). And if this is true, would you appear at all red- or blue-shifted to me? Also, if this is true, do I still have a rapidly-collapsing cosmological horizon around me (even though I can't observe it)?

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you are still able to see rays from outside the event horizon after you fall, they just become severely blue-shifted –  lurscher Jul 23 '12 at 17:57
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I don't understand your 1) question - since the event horizon is invisible (there is nothing special going on at the event horizon) then in what sense is it visible "in front of me" as you pass it. –  FrankH Jul 23 '12 at 18:06
    
@FrankH, it would be "visible" in the sense that I would see a black circular region in front of me, no matter how close to the singularity I get. Is that not correct? –  Dmitry Brant Jul 23 '12 at 18:25
    
I think I agree with your statement in 2. As you are looking back at the outside observer, you would see the observer rushing away from you at an increased velocity. Eventually, the observer will be beyond your observable universe (like you said, you are moving away faster than the observers light can reach you.) –  Michael Jul 23 '12 at 18:33
    
Your eye would be pulled apart from the rest of your body before you reached the event horizon. ? –  Bingo Jan 16 '13 at 10:08

1 Answer 1

The answer is actually a little werider than you imply. The proper way to look at this problem is to look at the paths of light rays intersecting your position as you get closer and closer to the black hole (since these are reversible, they can represent you sending a signal out, or you observing distant stars).

When you are far away, the black hole will get gradually larger as you approach. The closer and closer you get, a bigger and bigger fraction of the sky will appear dark, until it fills the whole horizon. You are still not inside the event horizon, however. As you move closer, the event horzon will fill a larger and larger portion of the sky behind you, until the whole universe will appear as a little dot on the horizon directly away from the hole, and then will disappear as you cross the horizon.

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