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1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.

They don't just have the same name, they are the same thing.

A Schwarzschild black hole has both: a removable singularity at the event horizon that is just an artefact of a particular choice of coordinates and a true non-removable mathematical singularity at r=0 where curvature really does go to infinity. It also wouldn't be much of an issue in classical physics, because this singularity is always hidden from outside observers, so the mathematical weirdness there can't screw with your normal predictions in space outside the black hole. The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions. This has opened a whole can of worms with a bunch of solution attempts, which are all sadly untestable for the foreseeable future.

https://en.wikipedia.org/wiki/Oppenheimer–Snyder_model

How is this any different than classical? Isn't it still just an ~impossibility hidden behind an event horizon in either model?

My point is, it’s not super meaningful to argue whether a black hole has an inside.

Well, the Ricci curvature scalar blows up to infinity, which is obviously unphysical.

I was shown it at school, using microscope glass slides that we waved over a Bunsen burner running cold, to coat with soot. We then carefully etched parallel lines with a compass by hand. Our (~17 y/o) efforts were a bit random but we did get some smudgy banding results on the screen.

History of the Universe : What Is Hidden In The Core Of A Neutron Star? - https://youtu.be/YoYjkNQ27T8

That video goes into it... without getting mathy at any point.

One of the bits that you're having trouble with is the compression of matter to a point. There's a theoretical type of black hole known as a kugelblitz - https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics)

    A kugelblitz is a theoretical astrophysical object predicted by general relativity. It is a concentration of heat, light, or radiation so intense that its energy forms an event horizon and becomes self-trapped. In other words, if enough radiation is aimed into a region of space, the concentration of energy can warp spacetime so much that it creates a black hole. This would be a black hole the original mass–energy of which was in the form of radiant energy rather than matter

I haven't watched the video, but if we're compressing electrons, neutrons, or other fermions, I imagine if we want to keep compressing that down to an arbitrarily small radius, won't we pretty quickly find it favorable to shift those fermions to something else, probably photons, to respect Pauli exclusion?

Really, I don't know enough physics to figure out the reason why it shouldn't always end up in this incorporeal energy-curving-space situation either way, if we're compressing arbitrarily far.

Pauli exclusion isn't an impenetrable force field - as you say, it's just often more favourable to do something else than to work around it. Consider an iron atom with however many electrons though - all those orbitals except the inner one are electrons working around Pauli.

I'm not a physicist either.

Of course I'm missing something here. I've taken QM and not GR so I would have this interpretation.

And if they didn't form a superconductor. I'm not sure why they would but if they did they would violate it. That's actually what makes superconductors superconducting - the really weird state where electron pairs act like bosons.

The easy thing to miss, and blew my mind when I read it. is that general relativity is the concept of space-time, emphasis on the time, and this is also compressed by the mass, so if this singularity can actually occur it would also take an infinite amount of time to fall into it. So nothing can actually enter it. From the point of view of an astronaut(deliberately ignoring all the other relativistic implications) flying directly toward the event horizon. As you approach you will quickly see the rest of the universe age and die. and if hawking radiation is real the black hole will evaporate in front of you before you can reach it.

But in the object's own time coordinates the math says it does hit the singularity. If you fell in you wouldn't die of old age before you hit it.

See https://physics.stackexchange.com/questions/82678/does-someo...

You could travel arbitrarily far into the future by getting close to a black hole's event horizon for a while without crossing it and then leaving, assuming you had the energy for it and you didn't get obliterated by all the mass and energy falling into the black hole in that timeframe.

All objects within a given radius of the black hole (possibly modulo spin) would experience the same time dilation. Remote objects in the universe would not experience the dilation.

From the perspective of the astronaut falling toward the singularity, the rest of the Universe would age at an ever-increasing rate.

From the perspective of a remote observer, the astronaut falling toward the singularity would be experiencing time at an ever-decreasing rate.

The notion of relativity is that time-perception is relative, and dependent on acceleration, whether from motion (as on a spaceship) or from gravitational acceleration (as near a black hole). Objects in orbit around Earth, further from Earth's centre, and hence subject to reduced gravitational acceleration, age more quickly than objects on Earth's surface. This is actually measurable using atomic clocks, though the effect is quite small. It is sufficient that GPS satellites require time correction.

Where my imagination fails(above my pay grade) is in the face of infinity, what are the implications of infinite time compression?(everything happens at once?)

So time is localised? I’m not sure what localised time means but I’m hoping the question makes sense.

What do you mean by “particle” here? This kind of handwaving is fundamentally classical, and breaks down in the presence of quantum physics.

Common sense would tell you they can't exist at all because you can't compress atoms - you have lived your entire life with atoms being entirely incompressible for the practical purpose of anything you do.

Leaning on common sense to discuss fundamental physics has been wrong since round about the start of the practice of physics.

https://quicycle.com/understanding-electrons/

And the video essay on the subject https://www.youtube.com/watch?v=hYyrgDEJLOA (Huygens Optics: Williamson & Van der Mark electron model | Are electrons made of light?)

Although some physicists disagree, QM slants very anti-realist. There are no objects anywhere, no particles, no waves, only probabilistic interactions, some of which can be snapshotted into localised partially definite results.

So there are only interactions between probability distributions in space and time, and "particle-like events."

No pointy objects, and no need for them.

The agnostic view is it's just a mathematical model that makes accurate probabilistic predictions when measurements are made, which says nothing about what's really going on.

Of course treating particles as points is also mathematical.

It is in this sense that, AIUI, electrons are modeled as point particles.

Of course, that doesn’t mean that if we zoom in enough, probing at higher and higher energy scales, that it can’t turn out to have some non-zero fundamental size outside of just uncertainty in its center of mass position. I think string theory would say that at the string scale it would be a string.

But, AIUI, no experiment has shown it to have the kind of extent that would make it be called not a point particle (an extent in a sense beyond just uncertainty in COM position)

You say that and yet this thread is full of people arguing about it, and there's an entire Wikipedia article on this: https://en.wikipedia.org/wiki/Gravitational_singularity.

In fact, that article says:

> No complete and precise definition of singularities exist in the theory of general relativity,

So which is it? It can't both be trivial to any grad student but also an open question. And things like naked singularities aren't proven to not exist either.

Also, general relativity is a classical, geometric-only theory. It seems obvious that better understanding what a black hole's singularity is would require quantum mechanics because the singularity is effectively what's "left over" of the physical material once you go beyond a neutron star.

If Susskind's book does in fact say that, it's extremely disappointing to me, because, as a number of other GR textbooks will tell you (e.g., Misner, Thorne & Wheeler and Wald, the two great classic GR textbooks), the "switch places" is an artifact of a particular choice of coordinates (Schwarzschild coordinates), and does not represent anything physical. So it's not something that should be relied on. (Not to mention the confusion it causes when pop science sources repeat the statement and then draw all manner of wrong conclusions from it.)

The part about being "a surface in time" might be all right, assuming that by that he means "a surface representing a moment in time, not a place in space"--in more technical language, a spacelike surface. That is correct, and it's an invariant that does not depend on any choice of coordinates. But that invariant fact can be described without having to talk about the "switch places" thing at all.

If you really want to get a picture of what is happening, you can look at Eddington-Finkelstein coordinates. In particular at a light cone field diagram around a collapsing shell of matter that turns into a black hole. Then this whole stuff suddenly makes sense without even going into the math. You don't just see how an event horizon can form out of nothing, you also see how gravity starts to bend your causal forward light cone (i.e. all points in spacetime with events that you could interact with in the future) inward in such a way that you will necessarily always fall closer to the center of the mass once you pass a certain line (aka the event horizon). No need to deal with those weird infinities or points in time suddenly lying on a different axis.

The great Roger Penrose (the same guy who also came up with some of the most confusing diagrams) published a beautiful, simple overview of exactly this stuff in Scientific American: https://www.wkbpic.com/wkbx/SA/1972/1972-05-01.pdf (starting on page 38)

Still one of the best things you can read if you don't just want the math.

A Fleeting Detection of Gravitational Waves

https://physics.aps.org/story/v16/st19

Gravitational wave blues

https://aeon.co/essays/how-joe-weber-s-gravity-ripples-turne...

It's a spacelike line on the Kruskal diagram, yes.

> The issue is that these diagrams are for eternal, static black holes

The full Kruskal diagram is, yes. But the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse of a massive body. That includes the singularity being a spacelike line, and there being spacelike curves inside the horizon that are infinitely long.

I agree that Eddington-Finkelstein coordinates can help with intuitions about this spacetime geometry as well.

It also is in Schwarzschild coords, so you've gained nothing with respect to the original issue from switching coordinates. Kruskal-Szeres really is only useful for demonstrating that the event horizon is not such a weird place, but it does nothing for the singularity at the center.

>the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse

The issue is even the limited diagram doesn't really show you that and the full one goes crazy with white holes. So not a good place if you don't want to confuse laypeople.

True--indeed, the statement that it's a spacelike line is an invariant, independent of any choice of coordinates. But it's a lot harder to see that in Schwarzschild coordinates.

> Kruskal-Szeres really is only useful for demonstrating that the event horizon is not such a weird place, but it does nothing for the singularity at the center.

I disagree, and I think many GR physicists would as well. Indeed, both classic GR textbooks, Misner, Thorne & Wheeler (1973) and Wald (1984) discuss Kruskal coordinates and their associated spacetime diagram (MTW in Box 31.2 and sections 31.5 and 31.5, Wald in section 6.4), and those discussions contain a good deal more than just showing that the horizon is "not such a weird place".

Roughly the general public (including me) knows that gravity is meant to have some effect on the apparent passage of time, so it seems significant but under explained what it means to be in a region of space where all possible directions lead to the singularity.

It's not just that it's always in your future in the sense that you can't avoid it. It's that the reason you can't avoid it is that it's a moment of time, not a place in space. You can't avoid it for the same reason you can't avoid tomorrow. And which direction in space you move has no effect on whether or not you reach the singularity for the same reason it has no effect on whether or not you reach tomorrow.

But it is just a mathematical artefact of weirdly chosen coordinates. In reality, the singularity is still just a point in space (or a line in spacetime), except that inside the event horizon all paths you are allowed to travel lead to it. There's no need for this whole "space turns into time" notion apart from the fact that you are guaranteed to hit it in *your* future as a local observer. And in Eddington-Finkelstein coordinates you can easily see that globally, things simply hit the spatial coordinates of the singularity at certain slices of coordinate time. Other coordinate systems make this whole process seem much more weird than it is.

No, that's not correct. The fact that the singularity is always in your future inside the horizon is an invariant, independent of any choice of coordinates.

> the singularity is still just a point in space

No, it's not. A point in space would be a timelike line in spacetime. But the singularity is a spacelike line in spacetime. That's a moment of time, not a place in space.

> There's no need for this whole "space turns into time" notion

That's true; that notion is an artifact of Schwarzschild coordinates. But that does not imply the other claims you are making.

> the spatial coordinates of the singularity

I'm not sure what you mean by this. It's true that, since the singularity is a spacelike line, you can treat a coordinate that varies along it as a "spatial" coordinate marking different spatial points on the singularity. But the singularity itself is a moment of time (as above, a spacelike line), so it is not a "place", and it does not have a particular set of "spatial coordinates". A spatial coordinate marking different points along the singularity is marking different points in space at a moment of time.

(If anyone has the book, it is chapter 6 section "Interchange of Space and Time Dimensions at the Horizon" and the following section points out the singularity is a time (and you can't escape it (in a Schwartzschild model at least) just like you can't escape time). I'm sorry if my wording is still incorrect.).

That's good. However:

> Interchange of Space and Time Dimensions at the Horizon

This still seems misleading to me, because "Dimensions" makes it seem like it's not just an artifact of coordinates--but it is.

I have trouble really conceptualizing black hole physics, I just think of it as a mass so great that nothing, including light, can escape its gravity. Works for me.

The singularity in a rotating black hole is entirely different but the interior of classical Kerr (rotating) black holes is one of the most controversial if inconsequential topics in theoretical physics because there are reasons to believe (without real proof mind you) the Kerr solution is unstable inside the inner event horizon so that whatever happens in there is not what that theory says.

And of course black holes are quantum objects which might actually have an “interior” entirely different from the classical picture.

Everywhere else in the universe with mass and energy you can do what you want (sort of). An event horizon throws a hard shroud over that and drastically reduces opportunities: your free will to use mass and energy is significantly curtailed (you must head towards the singularity).

If you don’t have enough upward velocity to escape earths gravity, hitting the ground is also inevitable.

I'm sorry but this is blowing my mind. What???

Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time, specifically the amount of time left before you reach the singularity. It's not so mind blowing when you interpret it that way now is it? You can imagine many things in ordinary life that you use to measure time without claiming that time has literally swapped places with it. On a road trip, the number of kilometres to your exit tells you how long you have left, that's using space as a proxy for time... big deal. The notable difference between a road trip and a black hole is that on a road trip you could stop for a break, you could maybe take a detour, you could decide to go back home... and these would all break your use of space as a proxy for measuring time. Well with a blackhole you can't do any of those things, there is no going back, there is no detour, the relationship between the spatial direction towards the singularity and time is fixed and causal and there's nothing you can do about it.

The phrasing used is used almost certainly to evoke some kind of voodoo mind-blowing mystery that completely disappears when you get down to the more strict formalism.

That's not correct. There is a relationship between the radial coordinate r you are at and the time it will take you, by your clock, to reach the singularity (at least assuming you are freely falling), but that relationship can't be described the way you are describing it.

To put the issue with what you say as starkly as possible: at any event inside the black hole's horizon, there are spacelike curves in every direction from you that will hit the singularity! So "the direction in space between you and the singularity" is not even well-defined.

To be clear, you are right that Susskind's statement is very misleading (I posted my own criticism of it upthread).

Note that, once you're inside the horizon, you can't "turn around" and go back outside again. You're inside the hole for good.

And once you're inside the hole, yes, no matter which direction in space you move, you're moving "towards" the singularity. But a better way to look at it is that the singularity is a moment of time, not a place in space. You're moving "towards" the singularity in the same sense as you're moving "towards" next Tuesday. You can't stop moving towards next Tuesday by changing which direction in space you move. The same is true for the singularity once you're inside the hole's horizon.

Unless you went in butt-first, but the path of the photons would have changed and would now be going toward the black hole, and everything would look probably all smushed together.

You can avoid a coordinate, for example by choosing not to go there, or revisit another one repeatedly.

A black hole on the other hand doesn't have that: you cannot revisit old locations - attempting to do so moves you closer to the singularity.

The reason this phenomenon has a spooky-sounding name is that it also affects whether two objects can be causally connected. If you can only ever move closer to the center of the black hole, then there are (conceivably) other objects inside the event horizon that you can never have a causal relationship with.

But it doesn't mean that space and time literally switch places.

[1]: https://www.youtube.com/watch?v=O_2vnb_eVGE

Also read Nick Gorkavyi: The Oscillating Universe: Einsteinian Cosmology of Black Holes and Gravitational Waves

Some of the things the paper points out are not emphasized in other sources, which is probably why the authors chose to write it. But there is nothing in the paper that is in the least questionable or ill-defined; it's all standard General Relativity as applied to the Schwarzschild and Kerr black hole solutions.

https://jila.colorado.edu/~ajsh/insidebh/penrose_schw.gif

What Happens at the Event Horizon? - https://youtu.be/mht-1c4wc0Q

Escape The Kugelblitz Challenge - https://youtu.be/v3hd3AI2CAA

Mapping the Multiverse - https://youtu.be/4v9A9hQUcBQ

https://youtu.be/6akmv1bsz1M

Might they be trying to say this?

1. The boundary of the black hole which traps light, etc, is called the event horizon, and sits at the Schwarzschild radius. This is a geometric surface.

2. There is no singularity at this surface.

3. In models of black holes, there is a gravitational singularity at a point in the centre: https://en.wikipedia.org/wiki/Gravitational_singularity which is a topic with nuances.

I don't follow most of the arguments however.

By the way the Kerr metric predicts a ring because the centrifugal acceleration due to the rotation partially counteracts the gravity. As far as I understand, not a physicist.

Similar questions arise: how would you know if you were inside one? The laws of logic ("physics") seemingly don't apply, but there's no way to test them in that environment.

https://en.wikipedia.org/wiki/Russian_cosmism

as it would be to do with anyone contemporary. In their orbit I get periodically annoyed but changed forever, no.

[1] This is just gravity, nothing specific to black holes, so the analogy isn't doing a lot of work here.

A black hole happens when there is enough gravity that space gets pulled inwards somewhere, at at least the speed of light.

Gravity falls off with distance, and the distance where space is being pulled inwards at exactly the speed of light is called the "event horizon".

It has this name because speed of light is the speed of causality: events that happen further in, are "over the horizon" for you, they cannot causally influence you.

(Very uneducated person here) I’ve always wondered if large objects caused gravity, or if maybe large objects form in the places where there is a lot of gravity. This is probably elementary, but I’ve never looked in to it. Maybe today is the day!

Mass represents a zone where probabilities want to be. The more that aggregate, the more they make other things want to glom on. With a high enough density, nothing that's nearby can glom to literally anywhere else, and there's your black hole. The Great Inevitable. In this space, there are no other possibilities. Very Demiurge-y.

(Is a collisionless gas really even an "object"?)

You can get a region like that by squashing a lot of mass in a small space, like happens when a star collapses under its own gravity. So here the intuition of "high density" makes sense.

But at the center of galaxies you have the so called "supermassive black holes" which are more or less comparable in size to the solar system and yes, they have a lot of mass but they are not very dense, a pop-sci trope is comparing it's density to cotton candy or even the air we're breathing right now.

So it's a matter of how you distribute mass/energy in a given diameter, not exactly of density.

Deflate it, then stretch the balloon over a vacuum cleaner tube and put on a rubber band to keep it in place.

If you pour sand on it, you can only get a small bump of sand and then it’ll run off the sides. Reasonable, logical, normal behavior. Clearly it’s a surface — it’s holding sand, it’s pouring sand in different directions over the edge, the sand is not all compacted into a single grain.

Turn on the vacuum cleaner. Assume a balloon stretchier than the strongest vacuum cleaner in the universe. What happens? Several things, each of which are perfectly reasonable:

1) The end of the tube is still a circle, and the balloon is still attached and covering the tube, so it’s still a two-dimensional circle.

2) A single grain of sand can’t block the vacuum tube, so it clearly hasn’t collapsed to a point.

3) The covered end of the vacuum cleaner tube is still the same circle, with the same diameter, as it was before you turned on the vacuum.

4) You can pour buckets more of sand onto that stretched circle of balloon than the handful you could before.

5) If you pour enough sand onto the circle, it’ll behave just like it did before: the sand will form a small mound and then newly-poured sand will run off whichever side the sand was poured on.

6) The rubber band is going to catch some of the overflowing grains of sand and hold onto them (‘accretion’), near but just outside the circle.

Next: Consider a more powerful vacuum cleaner. How much more? Lots. The most. An atomic Dyson powered by nuclear fusion. (This is a bit unrealistic, but that’s astrophysics for you.)

How much sand can you pour onto that two-dimensional, circular, balloon surface?

Lots. The most. Some of it will spill around the edges and get caught in the accretion band, but somehow that circle, that’s still the same size and clearly still blocking the vacuum tube, can hold an entire universe of sand.

That’s how black holes work :)

ps. For those who dislike the crudity of my teaching analogy and want to pop the spherical cow balloon: Topologically, the surface covering the vacuum tube is always a circle, even if you have an infinitely-powerful vacuum cleaner. At no point — pun intended — can a vacuum cleaner apply a transformation applied that reduces the dimensionality of the surface, thus it must remain, topologically, a circle.

pps. So clearly I must choose the circle in front of me! Hahaha! Aaaahahahah!

ppps. dies

Though the issue of small black holes is worth bringing up. If you scrunch up one cubic kilometer of stone into a black hole, that's heavy to be stable for trillions of years, but light enough to pass between the Earth and the moon without causing serious problems. And we really have no idea what the smallest existing black hole is.

So it is not as though you and the Andromeda Galaxy are made out of matter that got flung out of a point explosion long ago so that now you have traveled a very long distance away from one another, it is more like "both you and the Andromeda galaxy sat still for 13.8 billion years but space expanded between you in that time, so originally you were right on top of each other along with everything else".

We can rewind the model until the entire observable universe was as small as a Planck volume, but we have abundant evidence that the universe is indefinitely larger than that so even "that time when our 98gly diameter patch of space was almost indistinguishable from a mathematical point" means little when even that "point" was still just one pinprick out of the smooth manifold of a larger universe which could have been stupidly large or infinite even that early on.

A bit of an odd thing to say, since "everywhere" implies there are multiple places to be, and at the instant of the big bang, there was only place to be. So it was both everywhere and at a single point: it was at all of the single place there was to be.

But your point (sorry) about expansion being from everywhere isn't specific to the big bang; space was expanding well after the big bang and it doesn't seem like the expansion ever had a "center" (at least, not since not-center places existed). It's expanding from everywhere. (But evenly everywhere? I have no idea. Hey, maybe black holes are like buttons in cloth, and it expanded everywhere except for where the buttons were holding things still at a rate relative to distance from the button. A brilliant hypothesis that explains exactly zero unexplained phenomena, at least none that I know of.)

One theory that might help you visualize an alternative is that the big bang was basically two 3D universes (floating in higher-dimensional space) slapping against each other really hard. That creates an explosion everywhere even if everywhere is quite big or even infinite.

while you probably assumed or knew spinning black holes move space around them

spinning black holes also move TIME around them

* https://www.science.org/doi/10.1126/sciadv.ady9068

so in theory a spinning black hole that's been around for billions of years has a time drag around it in a path that is billions of years old

(no we can't navigate it because yes that would be time travel to the past and violates causality)

black holes are just so weird with every new detail even more weird

oddly more interesting to me to try to grasp neutron stars (densest objects before black holes and are still visible, our entire solar system in a neutron star would be only 10km 6.2miles across)

Of course if you did do that, the air itself would collapse into a black hole larger than M87*...

https://en.wikipedia.org/wiki/Magnetar

"A magnetar's 10^10 tesla field, by contrast, has an energy density of 4.0×1025 J/m3, with an E/c2 mass density more than 10,000 times that of lead."

still trying to wrap my mind around kilonovas (colliding neutron stars)

ie. they can pop out earth-sized chunks of gold, in theory, and since they aren't black holes that would be VISIBLE, albeit also "in theory" lol

* https://www.nasa.gov/image-article/unfolding-story-of-kilono...

maybe Roman can spot one someday, that would be something

The can produce Earth masses of gold, but of course not in the form of "chunks". The gold starts as atoms in a highly ionized gas and only much later cools enough to form solids (dust).

(Which is another reason some people think we might be living inside a black hole. An entire universe of energy released in zero time is literally a Big Bang. It would form into stars and galaxies.)

Not quite, I think a (theoretical) quark star would be higher density?

Well, isn't called space-time for nothing. You can't have one without the other. Like in electromagnetism. I thought it was kinda obvious since Einstein and Minkowsky.

https://en.wikipedia.org/wiki/Fuzzball_(string_theory)

Talking about the inside of a black hole is indeed rather pop-misunderstood though, yes. But it's not like physicists are especially confident about the details either. Theoretical astrophysics changes a lot as time goes on and our instruments improve, and it's a rather hard field to do experiments on to get better data quicker.