As you're freely falling through the air you don't feel any force except the wind - but you're also getting *stretched* a tiny amount because gravity is a bit stronger near your feet. This is called a 'tidal force' because it creates tides: for example, water on the side of the Earth facing the Moon is pulled toward the Moon more than water on the opposite side.
As a star falls toward a black hole it can get stretched and even destroyed by this tidal force - we've seen it happen! It can create a huge flare of radiation.
But surprisingly, the bigger the black hole, the smaller the tidal force is near the event horizon. We could be falling through the event horizon of a truly enormous black hole right now, and we'd never notice - though I consider this very unlikely.
More importantly, a star like the Sun will only get disrupted *before* it crosses the event horizon if the black hole is < 100 million solar masses. Otherwise it will get sucked in and be lost to sight without any drama!
The big black hole in the center of our galaxy is only 4 million solar masses, so this 'silent death' doesn't happen here. But it happens elsewhere. The biggest black hole known is 66 *billion* solar masses!
Black holes emit flares of light that we don't understand. Some must be from stars falling in. But many flares show very little light in hydrogen's spectral lines! This talk is pretty fun, and it's all about these mysteries.
@johncarlosbaez "We could be falling through the event horizon of a truly enormous black hole right now."
I've been always puzzled by this. Surely you'd see the horizon as a black surface coming at you, since no light can escape the black hole. And once your legs get past the horizon, you'd lose the feeling in them forever. Although the math inside a black hole gets really crazy, so I don't know how much I can trust my intuitions.
@BartoszMilewski - trust the equivalence principle: any small enough patch of spacetime is indistinguishable from Minkowski spacetime for a free-falling particle.
If you fall through the event horizon of an enormous black hole with your arm outstretched before you, your hand doesn't disappear as it crosses the horizon. But if you use rockets to hover outside the horizon and stick your arm in, it gets ripped off and disappears from view.
@johncarlosbaez
If my hand doesn't disappear, it means I can see things in front of me, including the singularity? What does the singularity look like?
@BartoszMilewski - light never comes out through the horizon, yet your outstretched hand doesn't disappear as you fall in a big black hole. Explain!
You never see the singularity, even from inside a black hole, because it's always in your future.
@BartoszMilewski - both these questions can be answered using the Penrose diagram of a black hole. Light moves at 45 degree lines. Think about what happens when you and your outstretched arm fall, at less than light speed, through the horizon! You are always looking back in the past along 45 degree lines.
@johncarlosbaez But presumably @BartoszMilewski's statement that "you'd see the horizon as a black surface coming at you" is true at some level, because what you see in the distance is not only a function of local spacetime (unless you're inside an enclosure, which is the usual conceit of equivalence principle thought experiments).
@johncarlosbaez @internic
This is NASA simulation of a fall into a black hole. It shows a black wall.
@BartoszMilewski @johncarlosbaez Incidentally, that video is the work of @SchnittGetsReal
@BartoszMilewski - I hope you read this... another branch of this sprawling thread:
@johncarlosbaez @internic
So you see my confusion: If the approaching horizon looks like a black wall, you shouldn't be able to see your hand that has just crossed it.
@BartoszMilewski
As far as I understand GR, even long before you actually arrive at the proper horizon things will get very dark, as only the light moving in a narrower and narrower cone will be able to escape.
@johncarlosbaez @internic
@j_bertolotti @BartoszMilewski Right. The situation with your arm is different, and that's where the conformal diagram that @johncarlosbaez posted is helpful. If you imagine an extended object falling into the black hole you can see that light from the left side (closer to the center) will always reach the right side at a later time. If, however, the object stops falling inward while partially over the horizon, light from the portion inside the horizon will never reach the portion outside (correspondingly meaning no causal force law can possibly keep them from tearing apart).
I think that another way to think of it is that near the horizon light is moving outward from the center more and more slowly (in terms of Schwarzschild coordinate distance vs. coordinate time), at the horizon it's standing still, and inside the horizon it's actually falling inward. If you're stationary outside the event horizon, the light from inside never reaches you. If you're falling inward, you will catch up with with the light from stuff further toward the center, because while it is falling toward the singularity, it is doing so more slowly than you (or any massive body).
@internic @j_bertolotti @johncarlosbaez
Let's simplify the problem. Two observers are free-falling one after another. We are the second observer filming the first one. Does the first one disappear behind the horizon?
Assume this is a humongous black hole, so tidal forces are negligible.
@BartoszMilewski @j_bertolotti @johncarlosbaez No, from the perspective of the second observer the first never disappears. You can see this by taking the above conformal diagram and drawing two timelike world lines that cross the event horizon and end at the singularity. If you then draw a set of outward-pointed light rays (moving up and to the right at 45°) from events on the first world line, you will see they continue to intersect the second. However, also note that the image that the second observer receives just before crossing the event horizon is of light the first observer emitted just before crossing the event horizon.
It's also worth noting that technically even for a stationary observer an in-falling object never disappears, it just appears to gets dimmer, slower, and more redshifted as it approaches the event horizon (until it becomes imperceptibly dim as an effectively frozen image at the event horizon).
@internic @BartoszMilewski @j_bertolotti - Nick is right. You can see it clearly from here if you remember that light moves along 45 degree lines.
@johncarlosbaez @internic @j_bertolotti
I'm trying to visualize this. Right before I hit the horizon, in my free fall, I will see in front of me everything that has ever fallen into the black hole. So that's not really a black wall. It's more like a windshield of a speeding car.
@BartoszMilewski @internic @j_bertolotti - but the infalling objects are quickly redshifted to oblivion so you don't actually see them. You see the sky above you shrinking to a smaller and smaller disk. There are movies of this on Youtube.
@johncarlosbaez @internic @j_bertolotti
So back to the original question: Can you tell whether you're approaching the event horizon, even if the black hole is enormous?
@BartoszMilewski @internic @j_bertolotti - the larger the black hole the harder it is to tell if you're falling through the horizon, especially if everything you know is falling in with you.
@johncarlosbaez @internic @j_bertolotti
So what do you see when you look towards the singularity? You're looking into the past of the black hole, seeing all the stuff that's fallen into it--progressively red shifted. Sort of like looking at the Big Bang. So all these animations are wrong.
@BartoszMilewski Your personal clock is only a tiny bit redshifted from the things closer to the boundary. In your personal coordinate system, and theirs, things are happily passing through the boundary.
Which is to say, I thought this is merely a coordinate singularity, no?
@4raylee @BartoszMilewski @internic @j_bertolotti - one crucial thing, when doing these mental visualizations, is to decide whether you're freely falling into the black hole or powering yourself with rockets to hover it at a fixed height. The results are different. I can't tell which one you folks are talking about here.
(Let's ignore that either way, you die a miserable death before you get too close to the horizon, unless you're freely falling into a very large black hole, in which case the pain only comes *after* you cross the horizon.)
I recommend these animations:
@johncarlosbaez @4raylee @internic @j_bertolotti
I'm interested in a free falling observer. I think I understand that it's possible to cross the horizon, but I think you can tell when you're crossing it by looking around you. You'll see the black circle turning into a black wall. You'll also get a glimpse of the back of your head surrounding you in a circle at 90 degrees.
@BartoszMilewski @johncarlosbaez @internic @j_bertolotti a little bit off topic: I've always found that textbooks on GR arrive to black holes after such a long way behind that they're like exhausted, and deal with the topic lightly. Perhaps this is not the case with an specific book, like the one by Chandrasekhar.
@davidsuculum - have you read Gravitation by Misner, Thorne and Wheeler, or General Relativity by Wald? I think both of these handle black holes in quite a lot of detail, though in such different ways that you need to read both to get the full picture.
These are my two favorite books on general relativity.
@johncarlosbaez I have a copy of MTW that I should probably revisit. Wald seems that it could be a bit over me.
@davidsuculum @johncarlosbaez It's well worth going to Wald after MTW (or some other first GR book). The effort will repay itself. Wald's semi-popular book 'General Relativity from A to B' is (I think) an excellent non-technical approach to give you some kind of orientation for the technical literature, and well worth looking at before gritting your teeth and braving MTW..
@RobJLow @johncarlosbaez have you ever read Chandrasekhar? Wald seems much more succinct: few calculations in detail for a dense material. Chandrasekhar looks like exactly the opposite: lots of calculations in detail. (Well, and Chandrasekhar deals only with the subtopic of black holes).
@davidsuculum @RobJLow - I could never fight my way through Chandresekhar's book - too many calculations. I would do it if my specialty were black holes, or maybe if I really *really* wanted to understand the bizarre structure of the maximal extension of the solution that describes a rotating black hole.
For now I just David Madore's web page:
@johncarlosbaez @davidsuculum @RobJLow When I was a kid I had some magazines or books with these diagrams and used to fantasize about travelling through them - without really understanding what they were.
@johncarlosbaez @RobJLow Madore's web looks like a great resource, thanks!
@BartoszMilewski @johncarlosbaez @internic @j_bertolotti the event horizon is a not a local concept, it only makes sense in the context of the full spacetime. It's the surface from which nothing can escape to infinity. This is not the same as nothing can make it to you.
Think of the following situation: You're falling to a small black hole outside its event horizon. So clearly, you can see your outstretched arm. Later, I.e in your future, a gigantic object falls in. This now extends the event horizon, and you're suddenly inside. This is because the horizon is a spacetime property, not a local one.
Only in a static spacetime do local and global horizons agree. But the local one is kind of fictitious
@sergedroz @BartoszMilewski @internic @j_bertolotti - right! Your example shows why crossing the horizon is like 'having the happiest day in your life' - it's not something you can know is happening until later: if you get hit by a car next week we may suddenly realize that yesterday was the happiest day in your life.
@johncarlosbaez @j_bertolotti I would expect the movie @BartoszMilewski posted elsewhere in this discussion to be pretty accurate, as it was made by @SchnittGetsReal and co. based on simulation.
https://mathstodon.xyz/@BartoszMilewski/113525935025414414
@BartoszMilewski @johncarlosbaez @internic : You never see your hand (or anything) the way it looks right now; you see it as it appeared in the past, when the light left it. As you fall in, hand first, your hand passes the event horizon (entering the black hole) while you're receiving the light from before it entered. Then when your head enters, you receive the light from when your hand entered. Later, you'll see the light that left your hand at the time when your head entered.
@TobyBartels @BartoszMilewski @internic - I told Bartosz to contemplate the Penrose diagram while keeping in mind that light moves along 45 degree lines, but I guess it takes practice to read Penrose diagrams. So yes: as you fall in the black hole, Toby's scenario takes place, and you never lose sight of your hand.
Alternatively you can use rocket thrusters to permanently keep your head and body out of the black hole while you lower your hand through the horizon. Then it will inevitably get ripped off, and you can pull back the bloody stump of your arm if you're strong enough.
@johncarlosbaez @TobyBartels @BartoszMilewski @internic
I did a long set of calculations exploring various scenarios for lowering things through a horizon. These calculations use a Rindler Horizon, but that works as a good approximation to the horizon of a black hole large enough that tidal effects are irrelevant.
It’s not exhaustive, but it’s nice to have some explicit calculations that are near enough to a few of the “Yes, but what if I did X?” questions that people sometimes propose as ways to “cheat” an event horizon.
https://www.gregegan.net/SCIENCE/Rindler/RindlerHorizon.html
@gregeganSF - by the way, your page makes me a bit sad that I went along with Chris Hillman when he demanded that I remove his page "Relativity on the World-Wide Web" from my website. He was being harassed by people whose work he had criticized, and he wanted to simply disappear. Now I'm trying to see if I kept a backup.
Yes.
@johncarlosbaez @gregeganSF : It's also on the Wayback Machine (just barely, with the first archive only 3 months before it was removed).
@TobyBartels @gregeganSF - thanks, Toby. I have no idea what became of Chris. The last emails I received from him, years ago, were quite sad.
@johncarlosbaez @TobyBartels @gregeganSF Oh no! I'd no idea that had happened, that's terrible.
@johncarlosbaez @TobyBartels @internic
Yes, it takes practice to read Penrose diagrams. The difficulty for me is to figure out what the world looks like from the point of view on a given observer. I think the "dust trail" in @gregeganSF visualization comes closest to the situation I'm interested in. I think, for a very large black hole, the dust lines would be practically vertical. Is that right?
@BartoszMilewski @johncarlosbaez @TobyBartels @internic
If you mean the world lines of infalling dust particles on that Penrose diagram, I’m not sure; I don’t know exactly what coordinate system is used there.
BTW, this other page I wrote on things falling into black holes might also be of interest:
@gregeganSF @johncarlosbaez @TobyBartels @internic
The scenario I'm interested it is of two astronauts Alice and Bob jumping off the ship. Bob can't see Alice crossing the horizon before he himself crosses it. So either he sees Alice splashed on the horizon, or the horizon recedes in front of him. I can't make sense of it.
@BartoszMilewski @johncarlosbaez @TobyBartels @internic
OK, Alice jumps first, followed by Bob.
Bob does not see light from Alice at the moment she crossed the horizon until he, too, is crossing the horizon. He certainly doesn’t see her pinned to the horizon and fading away from redshift, as he would have if he didn’t fall himself and just stayed at a fixed distance from the horizon.
But I don’t know why you think the horizon “recedes”. Alice recedes from Bob, because she fell first. He reaches the horizon himself in a finite time by his own personal clock, and at that point he sees Alice at the moment she crossed the horizon.
@gregeganSF @johncarlosbaez @TobyBartels @internic
Assume that they are both falling one after another along the same straight line towards the singularity (they maneuvered themselves into this trajectory when still at some distance from the black hole). Bob sees Alice always directly in front of him. So unless he bumps into her crossing the horizon, his perception of where the horizon is must be different from hers.
@BartoszMilewski @gregeganSF @johncarlosbaez @TobyBartels @internic@qoto.org Looking at https://www.gregegan.net/SCIENCE/Rindler/RindlerHorizon.html#FREEFALL and keeping in mind "Seeing" is along a 45degree angle down...
(Imagine Bob leaving the ship sometime after A{dam/lice} does: a second vertical line)
I think: Bob sees A cross the horizon at the same time Bob does, though at a different point on the horizon. A sees Bob cross the horizon after they do.
But, Penrose diagrams still confuse the heck out of me, so I could be misreading that.
@BartoszMilewski @gregeganSF @johncarlosbaez @internic : So If I understand your issue, it's this: The ship is hovering above the black hole, and Alice and Bob jump from the same place, so they should hit the event horizon at the same place (from their point of view), albeit at different times. When Bob crosses the event horizon, he sees Alice cross the event horizon, and while he knows that he's seeing something from an earlier time (like everything we see), he also sees this happening somewhere else, unless she appears to be right in his face (which shouldn't happen). So the place the event horizon was when Alice crossed it must be somewhere different from where he is now; the event horizon has receded (or, which seems more like it to me, approached). Is this the problem?
@BartoszMilewski @johncarlosbaez @TobyBartels @internic
OK, I see what’s troubling you.
The horizon isn’t really a “place”: it’s traced out by null rays in spacetime, rather than timelike rays. For a black hole, the horizon has a constant area, which makes it seem like a thing that’s standing still in some sense, but it’s generated, geometrically, by light rays, so it’s moving at the speed of light.
For two people who cross the horizon at different times, the latter one will see the former one when they are both crossing the horizon, but that doesn’t imply that they bump into each other.
Bob’s notion of his distance from *the horizon* (in the sense of the distance to a spacetime event that lies on the horizon “right now”, in his reference frame and with his notion of simultaneity) goes from being fixed to being monotically decreasing when he jumps out of the ship.
But his notion of his distance *from Alice* when she emitted the light with which he is currently seeing her starts *increasing*.
That’s not a contradiction, because these are two different things.
@gregeganSF @BartoszMilewski @johncarlosbaez @TobyBartels @internic
This whole thread is a beautiful representation of the best social media have to offer in terms of scientific discussion.
Thank you to all the people involved, I love it! 🤩
@j_bertolotti @gregeganSF @BartoszMilewski @johncarlosbaez @TobyBartels I agree @j_bertolotti, so now I'm going to try to take advantage of it for another splinter topic: Sometimes people talk informally of space flowing into a black hole, as a way of understanding some of the phenomena we've been discussing. They also sometimes talk of analogues to "dumb holes", which (in addition to being a potentially cutting insult) are scenarios where a fluid flows at an increasing rate until it exceeds the speed of sound, creating a sort of event horizon for sound waves.
I think you you want to formalize this notion of "space flowing into a black hole", what they really mean is just that a gravitating body tips light cones towards it, so if you fill some spacelike hypersurface with a grid of tests masses and let them fall freely (without interacting with each other or other matter) the geodesics will tend to flow toward the center of gravity (so space itself is not really flowing, of course).
But I admit that this way of talking about it really makes me uneasy, because speaking of space flowing or analogies to sound waves seems to smack of aether theory and, therefore, seems like it will be a trap that results in misconceptions. So I'm curious to what degree folks in this thread believe that ideas along this line are a productive way of thinking to guide intuition.
@internic - I don't like to talk about "space flowing", because as you say that suggests space is made of particles, or aether, or something, whose motion you can detect. I think general relativity is clearest if you learn about the geometry of spacetime and think in terms of geometry. This sort of geometry is called Lorentzian geometry or semi-Riemannian geometry, and any decent book on general relativity spends a lot of time explaining it. I don't think shortcuts or analogies really help very much: they may seem to help, but eventually they break down and leave you on the roadside in the dark with no cell phone service.
@gregeganSF @johncarlosbaez @TobyBartels @internic
I think we have to assume that "passing the horizon" is a subjective thing. Suppose they both can tell when they are passing their horizon. Alice blinks when she does. When Bob sees her blinking, he is passing his horizon. He infers that Alice's horizon is different from his.
I see one problem with this, though. Theoretically, it should be possible to put a fence very close to the horizon--a swarm of near-light-speed particles orbiting it. From Bob's perspective, he'd be hitting it while watching Alice hitting it at the same time.
@BartoszMilewski @gregeganSF @johncarlosbaez @internic : If the particles are moving at exactly lightspeed, at exactly the event horizon, then Bob will see Alice hitting them exactly when Bob sees himself hitting them, but that's normal; every time Bob looks at Alice, he sees her hit a photon exactly (and I mean *exactly*) when he sees that photon hit his retina.
If the particles are moving slightly below lightspeed, accelerating slightly to maintain their distance slightly outside the event horizon, then Bob will see Alice hitting slightly different particles than he hits. Even though Alice jumped out well ahead of him, he sees her hit almost the same particles as he does, because those particles are moving so fast; the particles that she hit almost reach him before he hits slightly different ones.
For this reason, I think that it's fair to say that the event horizon is approaching Bob. But that's from Bob's perspective; you could also say that he's falling towards it.
@gregeganSF @johncarlosbaez @TobyBartels @internic
Granted, such a fence might be impossible because of the "plunging region" around a black hole. If so, this is a very nontrivial explanation.
@BartoszMilewski @johncarlosbaez @TobyBartels I wonder if it might be helpful to think about the Rindler horizon that a uniformly accelerated observer experiences (which was mentioned elsewhere in this thread by @gregeganSF).
The thing that's interesting there is that a uniformly accelerated observer has this horizon (because the uniform acceleration means that light from events sufficiently far behind it will never catch up to it, so they are causally disconnected), but as soon as that observer stops accelerating (say, turns off their rocket engine) then the horizon ceases to exist for them. This should be somewhat analogous to the difference between the observer holding a constant position relative to the center of the black hole and one in free fall toward the center. (I'll leave it to others whose GR is stronger than mine to say exactly how close that analogy is.)
@internic wrote: "I'll leave it to others whose GR is stronger than mine to say exactly how close that analogy is."
You mentioned one big difference. The Rindler horizon exists only if you keep accelerating at a constant rate. This is a fancy way of saying that if you keep on accelerating at a constant rate that there are things you'll never see, but if you quit you'll eventually see them. The event horizon, on the other hand, doesn't go away no matter what you do. This is just a fancy way of saying that once you cross it there are things that will never see you.
I don't think discussing Rindler horizons, or any other stuff, will help Bartosz understand event horizons. It may be fun. But as a teacher I try to stick very tightly to the students' specific questions, and answer those as simply as I can, and not talk about anything else. Especially if they are struggling.
@internic @BartoszMilewski - right, as you approach the horizon it looks dark except perhaps for Einstein rings.
From a distance: