Is an event horizon absolute to all observers? Recently I had discussion whether the event horizon of a black hole is absolute or relative to different (outside) observers. Does someone just 1m above the horizon (disregarding effects of tidal forces, stability of orbits etc.) perceive it at the same depth as someone at infinity?
I'm not able to prove it theoretically. My only justification is that the relation "information from point $A$ can reach point $B$" is transitive, so all photons that can reach 1m above the horizon can also reach distant observers.
 A: The definition of the event horizon is `the boundary of the past of future null infinity', so it is the surface beyond which nothing can escape to infinity. It isn't defined with reference to any observer.
A consequence of the definition is that an observer can never really determine where the event horizon is, since its location depends on all future events. In principle, you could be falling through the horizon of a black hole right now and not know it, if some aliens conspire to collapse a big shell of matter on top of you at some time in the future.
A: I have to disappoint you. The Schwarzschild Radius is defined as Holographer points out, but with one constraint not mentioned here. And that is the Schwarzschild radius only applies to an observer with infinite distance to the observed object and at rest. The formula does not apply to any other distances or observers in movement. Thus any realistic observer will not observe the event horizon according to the Schwarzschild radius but instead an observer specific phenomena.
The gravity of the black hole bents not only space but space-time. This applies not only for empty space but for all observers likewise. Depending on their observation position they perceive mutually exclusive realities. This is not only true for black holes but applies in general to any observer in this universe as is explained and agreed upon already since long time by General Relativity.
Have a look at this research piece at the University of Colorado into the subject which provides even a video simulation of falling into a black hole. Its really cool!
A: According to the relativistic doppler effect light shifts into blue or red depending on the relative velocity of object and observer. Thus, looking at a redshifted light ray which source is close to the event horizon of a SMBH it must be possible to shift its light back into blue just by accelerating the speed of the observer by the relative amount. Transformed this onto the event horizon itself, where the redshift becomes infinite and thus the light won't escape anymore at that point, just by increasing the speed of the observer must have the ability to "unshift" the light again. Just by looking at this, the question „if“ light escapes a SMBH seems to be observer relative as well.
This further would mean that the radius in which hawking radiation is produced would be a observer-relative effect as well. (refrain from lynching me, I'm just theorizing)
Furthermore by approaching the strong gravitational field the observer would be subject to spacetime curvature as well as the object. Thus it only seems logic if relativistic effects again are perceivable. So, by moving closer to the event horizon, the observer itself being subject to spacetime curvature as well would then see the spacetime curvature at the (from outside seen) event horizon (or object) less curved, as he perceives it relative to his own experienced curvature. (Right ?) Thus it only seems logically that the event horizon will seem like shrinking once approaching it. An event horizon can't be proven absolute or observer independent if these assumptions cannot be disproved.
I appreciate if someone can prove me wrong without making more obvious mistakes than myself. I’m not a physicist, I’m just pondering why I can't find any big criticism to the absolute event horizon theory. The only alternative I have found is the apparent horizon, but its definition only seems to get applied on pertubed black holes and/or spacetime and does not inherit a difference between an apparent horizon and an absolute horizon in a black hole.
Further it is said, that the speed of gravitational waves cannot exceed c. Thus, the event horizon must not be only a barrier to light, but also for gravitation. Thus, how could a mass behind the event horizon be detected outside at all? Could it be that the classic idea of something "behind" the event horizon is misleading in that sense, as that spacetime due to its curvature does not permit any euclidic descriptions behind the event horizon, so that all the mass and energy exactly accumulates at the event horizon, because there "is" no behind ?
A: Good question. I think the event horizon has to be absolute, because as you suggested, light either gets out or it doesn't. I venture to suggest that isn't in accord with what most here would say is current teaching, but here's a couple of interesting facts:
1) Light is not redshifted when it ascends, and nor is it blueshifted when it descends. You can work this out by sending a 511keV photon into a black hole. The black hole mass increases by 511keV/c², not a zillion tonnes. Conservation of energy applies. There is no magical mysterious action-at-distance mechanism wherein a photon in space somehow acquires or loses energy. What happens is that I do work on you when I lift you up. So you have more mass-energy when you're higher, so you might think the ascending photon has lost energy. It isn't unlike SR redshift where you accelerate away from the light source and the photon appears to have lost energy. However the photon didn't change, instead you did. It's the other way round when you're lower, see the mass deficit.   
2) Light increases its speed when it ascends vertically. Like Einstein said, a gravitational field is a place where the speed of light is spatially variable. We say the "coordinate" speed of light varies with gravitational potential, and we note that optical clocks go slower when they're lower. See Wikipedia and note that at the event horizon of a black hole the coordinate speed of light is zero. It's zero for the guy 1m above the horizon, because he doesn't see the light getting out. It's zero for the guy 1000m above the horizon, because he doesn't see the light getting out. It's zero for the guy 1000000m above the horizon, because he doesn't see the light getting out. And so on. Because light doesn't slow down as it ascends, instead it speeds up. See this old Baez article and the new version along with these words by editor Don Koks: "light speeds up as it ascends from floor to ceiling". 
Given that there's no errors in the above, I can't see how the event horizon can be relative. If we had a gedanken string of lights dangling into the black hole, IMHO all observers would agree on how many lights are visible, because the light at some location either gets out or it doesn't.        
A: The event horizon is not absolute. It all depends on the observer. THAT is relativity. Space/time is relative to the observer. An event horizon is the consequence of space and time curving to a degree that light cannot escape relative to an observer at a certain point in space/time. An observer close enough to the black hole to be affected by its gravitational “force” would observe time differently, therefore the event horizon would be closer to the singularity. The closer to the singularity an observer, the more the event horizon would change from their POV. If able to observe the black hole from the singularity everything would become infinite. The observer would basically witness the end of the universe.
