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Let's assume there is an astronaut with a very long rope trailing behind him. As he approaches a very large black hole, he can look back and see the rope behind him trailing off into the distance.

What would he see after he crosses the event horizon and looks back along the rope while a portion of the rope is still outside the event horizon?

Deschele Schilder
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Andrew
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3 Answers3

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Dale's answer is correct, but I want to further emphasize that nothing special happens in the vicinity of an event horizon. It's just like any other region of spacetime.

Here's an analogy. Suppose you're in a building that's rigged to explode at a certain time. If you're in the building and too far from an exit at a late enough time, you won't be able to escape before the explosion even at your top speed. If it's a single-story, square building and you can exit at any point on the edge, then the region from which you won't be able to escape at a given time is square. It starts in the center of the building and expands outward at your maximum running speed. The boundary of that region is the "escape horizon".

If you don't escape and die in the explosion, then the escape horizon will necessarily sweep over you at some point before your death. When it passes you, nothing special happens. You don't notice it passing. You can't detect it in any way. It isn't really there. It's just an abstract concept that we defined based on our foreknowledge of the future.

The event horizon of a black hole is defined in the same way, with a singularity in place of the explosion and the speed of light in place of your running speed. If your worldline ends at the singularity, then the event horizon will sweep over you, at the speed of light, at some earlier time. But you won't notice. You can't detect it in any way. It isn't really there.

People get confused about this because there's phenomenology associated with black hole horizons: the closer you get to them, the faster you have to accelerate to avoid falling through, the slower your clock runs, the hotter you get from the Hawking radiation, and so on. They also behave like electrical conductors for some purposes, though it's not mentioned as often.

The thing is, if you mispredict where the singularity is going to be, and try to escape from what you think is the horizon but actually isn't, all of those same things happen. Any event horizon defined by any future spacetime points, whether singular or not, has these properties, even in special relativity. (See Rindler coordinates and Unruh effect for more about the special-relativistic case.)

So the answer to any question about what you'd see while falling through an event horizon is always the same as if the event horizon was somewhere else.

benrg
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    This answer deserves better than the first! – Deschele Schilder Aug 31 '20 at 06:44
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    ... horizons are unphysical but they also conduct electricity? What? If they conduct electricity then can't my ohm-meter tell me where they are? – user253751 Aug 31 '20 at 10:58
  • @user253751 They behave like conductors for some purposes, e.g. when calculating the field of a charge outside the horizon. I don't know what happens if you try to probe the horizon with an ohmmeter, but whatever happens is a consequence of the fact that the probe tips are accelerating very very rapidly. – benrg Aug 31 '20 at 15:49
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    @user253751 I toned down the claim about conductivity and added a Wikipedia link. – benrg Aug 31 '20 at 15:55
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    What is confusing to me is that if the falling observer does not notice anything "special" they should still think that they can climb out again, for example using that rope? (Assuming it's not falling with them but is attached somewhere "outside" the event horizon). Maybe they are not even falling but very carefully crossing that threshold, holding on to the rope... – Peter - Reinstate Monica Sep 01 '20 at 11:18
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    One thing though. What if one body part enters the zone of no return? It is a special kind of piece of spacetime. – Deschele Schilder Sep 01 '20 at 20:48
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    @descheleschilder Thought exercise: if the "body" were a kind of 3D hologram made of photons travelling tangential to the horizon, the part that crosses the horizon is torn off and falls in while the other part has sufficient velocity to escape. But since body parts aren't made of photons and can't travel at the speed of light, any "body part with mass" that enters the "zone of no return" must necessarily be attached to a body part with insufficient velocity to avoid the same fate. This also means no part gets torn off at the horizon, though tidal forces will eventually rip the body apart. – Chappo Hasn't Forgotten Sep 05 '20 at 23:30
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    @descheleschilder ... or to put it another way, a BH's event horizon is the "zone of no return" for photons, but for things with lesser velocity the "zone of no return" is much further out, its radius dependent on the maximum velocity of the body trying to escape. In [@]benrg's clever analogy, I guess your question really is "at the point that the blast front hits the escaping body, what happens to a part of the body escaping faster than the front is moving?" I think the escaping part escapes, and the blasted part doesn't. – Chappo Hasn't Forgotten Sep 05 '20 at 23:50
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    Good experiment! When made out of photons, to make a circular trajectory, there is a radius connected with this trajectory. Photons can't travel tangent to the event horizon ( I thought it's called the photon radius, but I'm not sure). Doesn't matter (to speak of which). I'm not sure right now if the massive matter can make a circular trajectory tangent to the event horizon, but if it did, you'll probably get sucked in, never to return again. But hanging stationary just above it, you can reach out with your hand and cross its line. it'll be stuck forever. My wife: tank photons? Sorry dear..... – Deschele Schilder Sep 06 '20 at 00:13
  • @ChappoHasn'tForgottenMonica Did you get my comment? I forgot to mention your name. – Deschele Schilder Sep 06 '20 at 00:55
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    @ChappoHasn'tForgottenMonica Look here:https://en.wikipedia.org/wiki/Photon_sphere Greetings to Monica. – Deschele Schilder Sep 06 '20 at 01:31
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He would still see the rope trailing behind him. There is nothing that prevents light from the rope to fall from the rope inward through the event horizon and to his eyes.

Dale
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It depends on your point of view. For the astronaut, nothing, in particular, happens.
For us, as distant observers, the astronaut will get frozen in time. Someone once wrote (in this question I read on this site) that upon entering the BH's event horizon, the astronaut's hand will be pulled off his body, due to the fact that time stands still on the horizon. This is obvious nonsense. For the astronaut, nothing seems to be going on. He's just falling freely through the horizon. Looking back he just sees the rope falling with him. And because the BH's mass is that big he won't get spaghettified (this may seem strange because of the enormous mass of a galaxy-like BH, but the radius of the event horizon is huge too).
If he/she is hovering above the event horizon ( which takes an enormous amount of energy) put's his/her into the hole, he/she won't see, feel, or is able to pull his/her hand back. When they start moving away from their stationary hovering position, they...I'll let you think about this.

His/her information content is completely lost and we won't be able to tell from the Hawking radiation what he/she looked like. Contrary to the ADS/CFT correspondence approach which is based on string theory and states that information isn't lost. I don't accept string theory to correspond to reality, so neither do I accept that information isn't lost.
We will never know what will happen if she falls on and on. Maybe she'll end up in another Universe, maybe she'll get spaghettified, but for sure she's lost forever.

In short: Because someone (in a special suit) is in free fall and as long the someone is not torn apart by tidal forces, that someone will observe nothing strange. He/she would see everything as here on earth. It's only for us as distant observers that time- and one space-coordinate take each other's place. In free fall, the time, t-, and spatial (radius, in the case of polar or spherical coordinates), r-coordinates don't interchange.

Deschele Schilder
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  • Possibly the knowledge that your trajectory will end in a singularity in short, finite own time, might be a little bit disturbing, even if going below the event horizon itself is not traumatic. – peterh Aug 30 '20 at 17:24
  • @peterh-ReinstateMonica Yeah, that's kinda surely will be a disturbing thought. Probably your last one, but who knows what behind the horizon...? – Deschele Schilder Aug 30 '20 at 17:27
  • Re, "...who knows..." There are very few places in the Universe where a human can survive. I mean, seriously! If I pick random coordinates, and I beam you there with my Transporter, that would be murder. It's inconceivable that the random place I selected would be a place where you could survive. I have no reason to think that the interior of a black hole would be an exception to that general rule. – Solomon Slow Aug 30 '20 at 21:49
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    @SolomonSlow As you have a transporter, I have a suit in which I can survive anywhere! Seriously! – Deschele Schilder Aug 30 '20 at 21:58
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    "His/her information content is completely lost and we won't be able to tell from the Hawking radiation what he/she looked like." That is false. The evolution of quantum states is time-reversible. – Acccumulation Aug 31 '20 at 03:59
  • @Acccumulation But isn't that what the information paradox is about? The "war" between Hawking's no and Susskind"s yes (i.e., information is lost) was won by Susskind, which is why I wrote that information is lost (an apparent contradiction, i.e., a paradox). I'm not so sure if Susskind right, but I assumed this in my answer. – Deschele Schilder Aug 31 '20 at 04:10
  • Hawking's position was that information is lost. Susskind's position is that it isn't. https://en.wikipedia.org/wiki/The_Black_Hole_War – Acccumulation Aug 31 '20 at 04:13
  • @Acccumulation I'm pretty sure that Hawking was the one who couldn't accept the loss of information. – Deschele Schilder Aug 31 '20 at 04:15
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    I just posted a link saying that Hawking thought that information is destroyed. I don't know why you're posting what you're "pretty sure" of without any citations. – Acccumulation Aug 31 '20 at 04:26
  • @Acccumulation After reading a Wikipedia article you are right indeed. I mixed them up. But the reason you gave for the conservation of information, is not the reason you gave in your comment. Since the answer is given in the context of string theory, which I think doesn't correspond to reality, I think the answer isn't correct. though. – Deschele Schilder Aug 31 '20 at 04:29
  • If "nothing particular happens" from a local viewpoint, what if I hover just outside the event horizon and stick my hand in? – vsz Aug 31 '20 at 18:54
  • @vsz The force you feel while hovering just above (or beneath) the event horizon of an extremely massive BH will be not so big (the bigger the mass of the BH, the smaller the G-force you experience). So imagine the case of an extremely massive BH. When you put your hand in, you would feel not much increase in the G-force. But because something that has crossed the horizon will never be able to get out again, you will be stuck forever. Until your rocket runs out of fuel before you die. In that case, you get sucked in together with your rocket and start accelerating into the unknown. – Deschele Schilder Aug 31 '20 at 19:15
  • @descheleschilder : so would it feel like a mysterious force has just grabbed my hand? (and it must feel numb too, as no signals are coming back to my brain). But then, if local gravity is almost completely uniform, why is there a very exact limit, if I put my hand exactly one planck length deeper it gets stuck, and if one planck length less then it doesn't? – vsz Aug 31 '20 at 19:19
  • @vsz Yes! For your hand, the time and the radial space component of spacetime (in radial coordinates) get interchanged. How does this feel? You wouldn't indeed feel anything at all. Your arm just stops at the horizon, and you can't see or feel it anymore. Very strange! In classical GR there is an exact limit. I don't know what is the case for quantum gravity (which I believe does not exist). I do think though that the smallest length is the Planck length but that's due (in my theory, at least) to a non-pointlike structure of elementary particles (and I don't mean strings). – Deschele Schilder Aug 31 '20 at 19:34
  • @SolomonSlow Why did you remove your comment? – Deschele Schilder Sep 01 '20 at 04:59
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    @descheleschilder, I don't remember. But with regards to "hovering...." While it's true that the gravity gradient at the horizon of a super-massive black is not great, the amount of force that your engine must produce in order to hover there approaches the infinite as your ship approaches the horizon. If you were hovering close enough to put your arm across, then you would be experiencing G forces from your ship's engine on an astronomical scale. Even if you were hovering much farther away, the sheer weight of your arm dangling over the side would have torn it right off of your body. – Solomon Slow Sep 01 '20 at 12:17
  • @vsz you're forgetting that the event horizon is defined by the speed of light, and since you can't possibly be traveling at that velocity, you can't possibly hover just outside the horizon. Solomon's astute last comment is an elaboration of this basic fact. – Chappo Hasn't Forgotten Sep 06 '20 at 00:01
  • @ChappoHasn'tForgottenMonica There is another radius connected to a circular trajectory of photons. It's bigger than the radius of the event horizon. Googleit! – Deschele Schilder Sep 06 '20 at 00:23
  • @SolomonSlow I didn't read your comment until now. You're indeed right that the force of gravity approaches infinity! I'll edit the answer later. I'm gonna sleep now ((it's 6:19 here in Holland...). – Deschele Schilder Sep 06 '20 at 04:20
  • @ChappoHasn'tForgottenMonica : by hovering I meant orbiting, but i guess geostationary (or blackholestationary?) orbit will not even be close the the event horizon... – vsz Sep 06 '20 at 04:35