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I figure at least some of it comes from the idea that mathematically, a singularity is a point (e.g., in the graph of z=1/w, there is a singularity at the point w=0, and in the graph of z=(1-w)²/(1-w) there is a removable singularity at w=1 (that is, the function is undefined at w=1, but if you put a point at (1,0), the graph will be continuous and no longer have any holes in it). The fact that both have the same name and the similar behavior of a black hole singularity to a mathematical singularity¹ can lead people to make an incorrect assumption.

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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.

As someone with basically only popsci knowledge of black holes: people claiming it would be a literal point never made much sense - fundamentally, common sense (as much as it can apply here) dictates that you cannot compress particles to an absolute point.

Or read Susskind's "The Theoretical Minimum: General Relativity". For a non-spinning blackhole at least, not only is the singularity not a point, it is a surface in time, not space (as the book explains, the space and time coordinates switch places as you cross the event horizon).

> Anyone who has taken a graduate level class in General Relativity would have been able to tell you the same.

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.

I think it's not even a valid critique of that and it's sort of playing games with what the definition of a singularity is to reach the claim that it's making. I think the topology of the singularity is not even a well defined question and certainly not well understood enough to bear the strong claims in the paper.

Some PBS Space Time episodes featuring the Penrose Diagram (in order - the first two are from 9 years ago, the last from 6)

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

I enjoyed this Veritasium video on the subject, which includes Penrose Diagrams.

https://youtu.be/6akmv1bsz1M

Sorry man, that's not what this is about.

They do speak of the gravitational singularity (not the event horizon). It's within the horizon, there is a contradiction between the need for two infallers' position to reach the singularity (thus hitting a point) and the causal impossibility of them actually meeting (following General Relativity?). This suggests that the point should maybe be a surface.

I don't follow most of the arguments however.

No, they are theorizing about the Kerr metric. The Kerr metric describes rotating black holes and instead of a point like singularity predicts a ring of zero thickness with infinite density additional work posits the ring is unstable and collapses to a surface all inside the event horizon, they then proceed to make predictions about the nature and behavior of that surface.

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.

I believe that's called an echo chamber, and exemplified by a board meeting.

I dunno. Those rationalists seem to be in some kind of intellectual black hole which never had any danger of sucking me in. Like I have seen many strands of posthumanism and transhumanism, speculations about an intelligence explosion circa 1970, and figure it would have been just as much fun to sit around the campfire, pass a joint around, and talk about crazy stuff with these guys

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.

Kinda sounds like a "linguistic manifold."

You need at least 11 for the math to work out but it's okay most can be compacted.

Normally people think of gravity as pulling on objects. You can instead think of it as pulling on the space those objects are in.

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.

Why not just say it's something with such strong gravity you can't escape even if you go at the speed of light? Maybe that loses too much accuracy for you?

It's a region of space from where not even light can scape.

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.

The problem there is that not even the physicists completely agree on the details, because we know black holes definitely exist, but every explanation breaks one rule or another that should apply from different disciplines. It's part of why they get so much ongoing attention.

A one-way door in space.

Consider a balloon. I don’t imagine in visuals but if you do, either a solid color or a patterned balloon works. Let’s say it’s a cow print design.

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

"A really interesting and cool thing for astronomers to talk about...but you might want to pray that not one of 'em ever comes within a million trillion miles of the Earth."

Rolling the clock backwards toward the big bang, it is not matter which is directly compressed, it is the fabric and metric of space itself. Matter being compressed is merely a side effect of the fact that "all of the locations that the matter occupies" are also compressed (though again, remain aware that calling it "compression" only makes sense when you rewind time in our cosmological model backwards).

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.

The big bang didn't happen at a single point, it happened everywhere. You can look out from anywhere and see the cosmic background radiation having expanded from your location, wherever that location might be.

Physicists say a singularity is a classical prediction so most likely wrong.

It could also be an infinite dimensional ball which technically also has 0 surface area & volume even though it has a non-zero radius.

That is the whole question. My gut says no, infinites and infinitesimals are the edges of our understanding not real.

Depends on whether anything less than the Planck length has meaning.

Another thing that may blow the minds of some is that M87* is less dense than air at 0.44kg/m³ so if you could bring it to sea level (in a large enough theoretical test area) it would float like a helium balloon (sea level air is 1.2kg/m³).

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

Consider the magnetar.

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."

It blows my mind that, in the frame of an outside observer, time appears to stop at the event horizon. An observer falling through the horizon (who survived the radiation and tidal forces) would not perceive this.

> densest objects before black holes

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

>what's really going to blow your mind is while you probably assumed or knew spinning black holes move space around them spinning black holes also move TIME around them

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.

Good PBS spacetime episode that looks at this: https://www.youtube.com/watch?v=jeRgFqbBM5E ( Could The Universe Be Inside A Black Hole?) Also, this spacetime episode is interesting the context of the paper and your statement: https://www.youtube.com/watch?v=x4TdColoIu8 (We Thought Black Holes Created Event Horizons. It Might Be the Opposite)

No, sorry, the singular surface in a Schwarzschild spacetime is not the event horizon. Nothing particularly interesting (from the GR point of view) happens at the event horizon.

Downvoted back to the dark ages.