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Assume an observer sent a beam of photons close to an event horizon, say at some distance x (a distance far enough to avoid the photons falling in.) This light would still be observable, albeit red shifted and with it's path curved appropriately. Now assume the black hole absorbs enough mass to expand it's event horizon beyond the distance x. This stream of photons would stop. Does the observer not have information about a process that occurred exactly at the event horizon, that is it's expansion? Isn't this a region that one should not be able to get any information about due to the fact that nothing could contact the event horizon and return to the observer?

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I am a little unclear about this question's formulation. Is the Observer actually at x and sending photons from there? I would expect there to be some object at x (somehow maintained there) which was sending photons. Are the photons heading in all directions from x? Then is the Observer at infinity, somewhere nearby to x, at the Event Horizon or moving into the Black hole? –  Roy Simpson Feb 22 '11 at 11:50
    
The observer would be somewhere nearby by x, not infalling- to observe a beam through a point that is at distance x- with a photodetecter detecting the light after it has passed through that point. The beam would originate near x from a source not infalling as well. The image I'm trying to convey is one of "shining a light" close to a black hole, almost across the event horizon, but not close enough to be absorbed. –  jaskey13 Feb 22 '11 at 21:01
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As I now understand the formulation of this question we have the following situation:(1) an observer is situated near the Event Horizon of a Black Hole;(2) a light source is situated a similar radial distance from the BH and is shining light which is reaching the Observer;(3) the radial distance of both from the BH is approximately x; (4) the Event Horizon expands (reducing the distance between it and the Observer/light source).

Several observations about what is likely to happen here:

(1) The Event Horizon is at R=2M for a Schwarzchild solution, but there are unusual photonic effects nearby outside too. At R=3M the photons will go into orbit around the BH. So perhaps if nearby the Observer is picking up a photon from its orbit. Even if a little further out the light bending will be quite extreme, and so the Observer is likely to "see" the light coming from another region of the sky.

(2) The photons of light from the source may already be in a kind of elliptical orbit which drags them into R=2M.

(3) With an expanded Event Horizon we are assuming greater gravitational force on both Observer and Source. At some point one or both may be overwhelmed by the increasing gravitation near the Event Horizon. Thus they would be unable to maintain any fixed distance, and be drawn in simply because they dont have an infinite power source in their engines. If such movement occured the light from source to Observer could be distorted further as they try to maintain position, but move in different orbits.

(4) As the Event Horizon approached both would cross the R=3M region, at this point the light source might no longer reach the Observer, depending on exact distances.

It should be noted that the "potential curve" for gravitation near a Black Hole is unlike a standard Newtonian one near a massive object. The exact trajectories of objects is also heavily dependent on a quantity related to the angular momentum of the photon.

To complicate matters further the use of the term "Event Horizon" in this expanding example may not be appropriate: other terms like "apparent horizon" may be more appropriate. In a sense the Event Horizon is theoretical construction best applicable to a Black Hole at the end of (its) time.

In short I am expecting the stream of photons to stop reaching the Observer somewhat before the Horizon meets the Source, unless the Source and Observer are on some very specially constructed orbits, in which neither are at position x. The rays connecting the two might reform later as both head into the Black Hole, resulting in a light that is intermittent. Finally I believe that anything demonstrated here, is a demonstration of the properties of an apparent horizon.

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When you look at a black hole, you never see the actual event horizon, because the proper distance to it is infinite and it would take a light signal an infinitely long time to come from it. What you actually see is the matter falling in as the event horizon is about to form. That's why an older name for black hole is "frozen star".

So, if you can't even observe the event horizon form, you definitely can't observe it expand. In your experiment, the closer the photons get to the event horizon the greater the proper length of their path, so the longer you have to wait to see them.

Also, you really should think of the event horizon as a 3-dimensional surface in spacetime, not just a 2-dimensional surface in space. The closer the worldline of the light gets to it, the longer you have to wait, so you can't get any information from the 3-surface itself.

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So with no experiment able to actually discern if a black hole exists- why do we keep talking about them like they are real? Isn't this a clear violation of the scientific method? Should we not instead be looking at "frozen stars"- an object where no event horizon or singularity has formed yet? –  jaskey13 Feb 20 '11 at 16:32
    
And (ran out of time time to edit my comment) if the answer to this is that an infalling observer see's the black hole form in finite proper time- what good is this as every other observer in the universe has no access to that information? –  jaskey13 Feb 20 '11 at 16:42
    
Exactly. There's this catch-22 situation because the only way to observe things at or inside the event horizon is to fall inside, but that takes an infinite amount of time from the perspective of any external observer, so you can't tell any of your friends. But that doesn't mean that all GR predictions about black holes are unfalsifiable. –  Keenan Pepper Feb 20 '11 at 20:34
    
For example, when Advanced LIGO is running, we'll be able to observe gravitational waves from inspiraling black holes, and although these are technically just from the extremely curved spacetime around the event horizon rather than the horizon itself, the pattern of the waves will look different from other things like inspiraling neutron stars, and we can compare it to detailed quantitative predictions made by numerical GR simulations. If it looks like a black hole and does everything we expect a black hole to do, why not call it a black hole? –  Keenan Pepper Feb 20 '11 at 20:37
    
And we would be able to distinguish this data from that of say a neutron star on the very cusp of being black hole, where the time it takes to reach the surface, as seen by an outside observer, is longer than the age of the universe? Wouldn't every process, even the absorption and reemission of light and all other physical processes, take too much time to practically measure? (Thank you ahead of time for your patience- I just feel like there is some sort of discontinuity here that I'm having trouble understanding) –  jaskey13 Feb 20 '11 at 21:42
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Let the light source be pointed directly upward. Assume that the observer (who receives the light) can remain hovering above the black hole as it expands. The observer would notice that the redshift of the light ever increases, until such moment that the last photon is received (subsequent photons fall into the black hole). The last photon could be received at any point in the observer's future: the closer to the horizon (but still above it) that the photon is emitted, the further in the observer's future it is received.

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