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).
@internic @BartoszMilewski - right, as you approach the horizon it looks dark except perhaps for Einstein rings.
From a distance:
@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 @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 @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 @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.
@j_bertolotti @gregeganSF @BartoszMilewski @TobyBartels