Crossing event horizon and Hawking radiation
Some thought experiments and questions. I would much appreciate any comments on whether my analyses below are correct.
1. I am falling feet first into a black hole. An external observer will never see me fall past the event horizon. However, in my frame of reference I will fall past it in finite time. Puzzlingly I can never see my feet fall past the event horizon either because if I could, I could relay this from my head mounted web-cam (which is not yet past the event horizon) to an external observer.
As best as I understand this peculiarity it is because the paths that light can take get bent and so light from my feet (and indeed any signal including nerve impulses) can never arrive at my head from my feet. This also includes the bits of my brain that are a little further away from the event horizon than other bits. So although I may pass through the event horizon in finite time I can never experience this or make any observations or even think about my passage through the event horizon. I presume this continues once I am through the event horizon. Thus I can never observe or think about anything about a black hole interior to the event horizon including any singularity that lurks in there.
Interestingly this occurs in large black holes where the gravity gradient at the event horizon need not be high. So I wont be ripped apart by tidal forces but I will still be separated from my feet and one part of my brain from another.
Another way of thinking about this is that as I get closer to the event horizon all light I see becomes restricted to a narrower and narrower cone above my head. Until at the moment of passage all incoming radiation is confined to a single dot directly above my head.
2. Because it takes me finite time to fall across the event horizon and to an external observer I never cross the event horizon from my perspective the entire history of the universe is played out as I look back up at the surrounding universe. Thus not only will I see all incoming light restricted to a small dot above my head it will become brighter and hotter as I fall in (think microwave background blue-shifted to gamma rays). This also includes infalling gravity radiation and matter. Seems like I will be subjected to seething cauldron of radiation, matter and gravity waves. (I am unsure whether this is ameliorated by the velocity I have accumulated as I fall in).
Not much left of my body by now.
3. Assume that black holes do indeed emit Hawking radiation as predicted. Also that given enough time any black-hole will eventually evaporate from Hawking radiation. Now it seems that as I fall into the hole I will start seeing the incoming half of the Hawking radiation as infalling onto my head. And in the finite time it takes me to fall across the event horizon I will see enough of that radiation to annihilate the black hole (including enough energy to annihilate the mass of my body).
The descriptions and analyses above seem to disagree with the popular (consensus?) description of what happens when you cross an event horizon. See for example the Wikipedia entry http://en.wikipedia.org/wiki/Black_hole. This view seems to be that you can blithely sail past an event horizon and as you sail on down to your doom in the singularity you can look around and observe and think about what is happening around you. However at the end of the Wikipedia article in talking about Hawking radiation it is assumed that the black hole will evaporate in finite time (both for an external and infalling observer?). The crux of my question is that these two views are contradictory.
The following is another puzzle that is more speculative (that is I am more confused about it).
4. The outgoing particle of the two virtual particles in Hawking radiation must be emitted from just outside the event horizon (or otherwise it could never be seen by an external observer as Hawking radiation - this could be very tricky indeed but I will forge on with the naive interpretation of what is going on - please someone help me here). Now consider an object that has the same mass as the black hole but which is just slightly bigger than the back hole (say its surface is half way between the event horizon and where the particle was emitted). Such an object is not a black hole. But the environment where the particle was emitted is locally identical to the situation where the original Hawking radiation was emitted. This implies that Hawking radiation is emitted not just from where there is a black hole but anywhere that space-time is curved. I wonder if this analysis is correct and if it is whether such radiation (say from Earth or some other handy space-time curving object) could be detected.
Re: Crossing event horizon and Hawking radiation
Welcome to the forum!
I will just answer the following question and leave the rest to others.
Your mistake is the bit I have emboldened. By the time the light from your feet crossing the horizon has reached your eyes, your eyes are already crossing the event horizon themselves, so now it's too late to send a signal out!
Re: Crossing event horizon and Hawking radiation
The bigger problem with this is that you cannot know that you are actually crossing the event horizon or even where it is. There is no local information in your surroundings that tells you that the fictitious point you have just passed is the point of no return.
An observer at infinity can infer where that point is and your fate (even if he never sees it actually happen), but you don't.
The analogy is fish going downstream in an ever increasing current. Past a certain point the velocity of the stream makes it impossible for them to ever turn around and go back to where they started, but from their reference point they still are swimming as usual, blithefully unaware of their fate. Nothing special happens for the local observer either a second before or a second after they've passed the horizon (on their clock at least).
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