Observing the event horizon of a black hole

[Peter953]

For an observer far away, nothing ever seems to actually cross the event horizon of a black hole, but to "freeze" right at the event horizon. Does this mean that if we could observe a black hole, we would be able to still see everything that has ever entered the black hole? Would every object still look to us as if it was still there, right at the event horizon? Or is no light able to escape the event horizon, so that we can't see these objects?

 

[PeterDonis]

For an observer far away, nothing ever seems to actually cross the event horizon of a black hole, but to "freeze" right at the event horizon.

No, that's not quite right. What the observer sees is objects that are falling in getting closer and closer to the horizon, without ever reaching it. See below.

Does this mean that if we could observe a black hole, we would be able to still see everything that has ever entered the black hole?

What do you mean by "observe a black hole"?

If you mean "watch the light signals coming from near, but outside, the black hole's horizon", then, if we assume you can see light signals of arbitrarily long wavelength (which is not a good assumption in practice), then yes, you would see images of all the objects that fell into the hole, getting closer and closer to the horizon, without ever reaching it.

If you mean "observe events at or inside the horizon", then no, it's impossible to observe anything at or inside the horizon, from outside the horizon.

 

[Peter953]

Yes, I mean watching the light signals near, but outside the black hole's horizon. Would not this be a way to discover black holes? Enormous quantities of mass would seem to us to be surrounding their event horizons?

 

[PeterDonis]

Would not this be a way to discover black holes? Enormous quantities of mass would seem to us to be surrounding their event horizons?

In principle this could work, if we restrict ourselves purely to classical GR (but see below); but in practice, as I said, we can't detect light signals of arbitrarily long wavelength. In practice, according to classical GR, light signals from objects falling into black holes very soon get redshifted to the point where we can't detect them any more. So this strategy for detecting black holes won't work, even based on purely classical theory.

In reality, though, light emitted by objects falling into black holes is not continuous, as classical theory assumes; it is quantized--it gets emitted as individual photons, i.e., in discrete packets. So light will not be emitted continuously as an object falls through a black hole's event horizon; there will be some "last photon" that gets emitted before the object falls below the horizon, and that photon will be emitted at some finite altitude above the horizon. Once we receive that photon (assuming that we can--see below), we will never see any more light from that object; and it will not take an indefinitely long time to receive it. So in reality, we won't actually see lots of objects "piled up" close to a black hole's horizon; at any given time, we will only see the relatively small number of objects that fell in recently enough that we haven't yet seen their "last photon".

Actually, in practice, we won't be able to detect the last photon that infalling objects actually emit; it will be way too redshifted for our detectors to detect it. The last photon we actually detect from an infalling object will be emitted some time before the absolutely last photon, so in practice, the object will disappear from our view sooner than if we could actually detect the absolutely last photon it emitted.

 

[Peter953]

Thank you for your reply. So in a way, when observing something moving towards a black hole, there will come a point when we can't detect the object any longer. By that time it will, at least from its own perspective, have passed the event horizon anyway. If there is no way for an observer to detect the object any longer, when or before its last photon has been emitted, then it is perhaps wrong to claim that to an observer it never seems to cross the event horizon? When we can't detect it any longer, it has crossed?

 

[PeterDonis]

So in a way, when observing something moving towards a black hole, there will come a point when we can't detect the object any longer.

Yes.

By that time it will, at least from its own perspective, have passed the event horizon anyway.

There is no absolute way to compare time for the infalling object with time for us observing it at a distance. So there is no absolute way to compare the time at which the distant observer detects the last photon from the object, and the time at which the object crosses the horizon, and say which event happened first. This is a sort of GR version of relativity of simultaneity.

If there is no way for an observer to detect the object any longer, when or before its last photon has been emitted, then it is perhaps wrong to claim that to an observer it never seems to cross the event horizon?

The claim that is often made is not just that to a distant observer, the object never "seems" to cross the horizon. That claim could just as well be interpreted purely as a statement about what light the distant observer detects--and on that interpretation, it is true, since, as we've seen, the distant observer can never receive light signals from events at or below the horizon.

But the claim that is often made is that, because the distant observer never detects the object crossing the horizon, that the object never crosses the horizon in some absolute sense. That claim is false, and it would be false even if it were possible to detect light emitted by the object all the way down to the horizon, so that the scenario we talked about earlier in this thread, of seeing objects "piling up" near the horizon as they appear to fall more and more slowly, were actually possible. Even in that case, that appearance would be an optical illusion; the objects would still fall through the horizon; we, the distant observers, would just never see it happen.

When we can't detect it any longer, it has crossed?

That's one fairly useful practical criterion for saying when the object crosses the horizon, from the standpoint of the distant observer, yes. As I noted before, there is no absolute answer to the question of when the object crosses the horizon, from the standpoint of the distant observer.

 

[Peter953]

OK, so to a faraway observer the object seems to be moving extremely slowly, and the light is extremely red-shifted as it approaches the event horizon, and we never see it cross since anything beyond the event horizon is not observable, but finally we can't observe it any longer.

Even though all of this is mind-boggling, if that is the way it works, this particular phenomenon is not as strange as I imagined.

Thank you!