Is the Accretion Disk of a Black Hole just an illusion?

Question

As a matter of fact, I recently learnt that as an object is approaching a black hole, to an outside observer the object seems to be getting slower and slower and will cross the event horizon after an infinite amount of time ie will not cross the horizon. Now this matter which the observer was observing seems to be stopped at the boundary outside the event horizon, thus forming the accretion disk. But since the object is actually inside the black hole since it has crossed the event horizon from his viewpoint. Thus we conclude that the object is actually inside the black hole but to an outside observer it’s not inside.

Let me put up a thought experiment.

Imagine me and my good old friend are somewhere in space nearby a recently formed black hole. It has no apparent accretion disk but we know it’s somewhere in a specific direction. Now my friend volunteers to go into the black hole. According to calculations the time taken for him to cross the event horizon be some interval “t”. Now he goes. After “t” interval my friend is inside the black hole and sadly has been reduced to ..... . I know he must have crossed the event horizon but I can still see him outside of it. Now I also go towards the black hole. Just before I reach the horizon I can still see my friend outside but in reality he is already inside. And then I cross the horizon. Just imagine for a split second that I can see inside the black hole. What will I see ?

I will see my friend and myself. And if any more matter comes from outside I can see it. But from an outside observer, my friend and me are still before the event horizon thus forming an accretion disk. But since we are actually inside the black hole. Then the accretion disk must be an illusion. Cause how can me and my friend be both inside and outside the black hole.

Now please tell me if I m correct in my reasoning regarding it. I have been pulling my brains over and over again, running the experiment several times and conclusion is this only that the accretion disk is an illusion.

Hopefully, you all may give insights regarding this question.

Thank you.

Answer 1

Now this matter which the observer was observing seems to be stopped at the boundary outside the event horizon, thus forming the accretion disk.

That's not an accretion disk. Accretion disks are mostly made of matter at a substantial distance from the black hole, which isn't dramatically redshifted and isn't on the verge of crossing the event horizon.

I would say that you're right about what you mistakenly call an accretion disk. The frozen image of your friend at the horizon is an optical illusion. The image freezes because the light takes increasingly long to reach you, not because the object that emitted it really slowed down in any objective way.

I suppose your concern is that this conflicts with what's normally claimed about accretion disks. It does, but only because accretion disks are a different thing entirely.

Answer 2

Because of the intense gravitational pull near the event horizon, very little light reaches us from the parts of the accretion disk close to the horizon (and none, of course, from the infalling part of the accretion disk that has crossed the eveny horizon). In practice, the parts of the accretion disk that are bright enough to see have to be a certain distance from the event horizon, so we are seeing material outside, not inside.

I know he must have crossed the event horizon but I can still see him outside of it. Now I also go towards the black hole. Just before I reach the horizon I can still see my friend outside but in reality he is already inside.

Your friend was only able to emit finitely many photons before he crossed the event horizon, so you wouldn't really "see" him there forever: after that last photon from your friend pre-crossing reaches you, you don't perceive ghost images of him any more.

Not only that, the black hole's gravity means that your friend was already getting visually dimmer as he approached the black hole: as he got closer, more and more photons that would have come from him to you (remember, you were further away from the black hole) failed to escape the black hole's gravity and fell inwards towards the event horizon.

So it's more accurate to picture your friend, slightly ahead of you on the fall into the black hole, getting darker and darker until he finally disappears from view, rather than "freezing" permanently outside the black hole.

And then I cross the horizon. Just imagine for a split second that I can see inside the black hole. What will I see? I will see my friend and myself.

For the same reasons discussed above, you'll never visually see your friend again once he crosses the event horizon, unless you speed up your trip to the singularity and get closer to the singularity than your friend is (in which case you'll be able to see him again once you "lap" him on your way in).

Any photon emitted by your friend within the event horizon is constrained to decrease its radial distance from the singularity. "Inside a black hole, time and space switch places:"

• any object outside the black hole's event horizon is free to increase or decrease its distance from the singularity, but must constantly increase its time coordinate ("time's arrow")

• any object inside the black hole's event horizon is free to increase or decrease its time coordinate (i.e. time travel), but must constantly decrease its radial distance from the singularity, and this forced decrease for objects inside is not controllable, in exactly the same way that objects outside cannot control, stop, or reverse their motion in time.

Which means that if you are at or within the event horizon, and your friend is closer to the singularity than you are, then it's physically impossible for photons emitted by your friend to reach you, since they would have to increase their distance from the singularity to get to you, and that's no longer possible inside the event horizon.