Off-topic, but it makes me think of "reasoning black holes": you get enough like-minded people together that they start reinforcing each other's logic and beliefs until not only those people get completely detached from reality, but anyone who interacts with them gets sucked in as well unless their own logic ("velocity") is adequate to skirt the edge and escape, forever altered by the experience.
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.
Should be pointed out that this is a critique of common popsci journalism tropes and not a fancy new research result. Anyone who has taken a graduate level class in General Relativity would have been able to tell you the same.
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.
Unfortunately you are wrong. Everything the paper is saying is well understood and has been for decades. The definition of "singularity" that the paper is using is perfectly fine, and its topology is perfectly well-defined. A good textbook treatment is that of Wald (1984).
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.
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).
> the space and time coordinates switch places as you cross the event horizon
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.
Because it's very misleading. Time and space do not switch places past the event horizon. What happens is that the direction/path between an object and the singularity becomes a timelike dimension, and the direction that plays the role of time outside of the event horizon becomes a spacelike dimension. That is not the same as them swapping or that time becomes space and space becomes time not to mention that space has 3 dimensions and time has only 1 dimension so how could they even swap places.
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.
it might help to think of the singularity as not a point in space but rather a future that cannot be avoided. All possible paths through space and time, no matter what happens, will go towards the singularity.
It's not? Schwarzschild has a space-like singularity. That's the wiggly horizontal line at the top left of the diagram. If you are in the black hole you can't avoid hitting it. Seems to be exactly what the paper is remarking on.
Would this apply also to the singularity at the beginning of the universe? I guess I thought that the singularity was where all matter is compressed so much that it occupies a zero dimension point. I'm not sure if that applies equally to black holes and the singularity at the beginning of the universe. I'm kind of dumb on this stuff even though it fascinates me.
Consider a spherical 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?
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.
> Normally people think of gravity as pulling on objects. You can instead think of it as pulling on the space those objects are in.
(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!
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.
Black holes are essentially where our knowledge of spacetime breaks, and we can’t even see into it. It’s hard to really concretely know much about it directly.
"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."
Well... yeah? That's describing the event horizon. It's a term roughly as widely used as "singularity".
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.
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)
Yes, magnetars are considerably more rare than black holes and considerably more interesting to study in terms of raw horsepower. Imagine a type-2 civilization using them as engines or launchers for spacecraft to zip around the galaxy.
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*...
Interesting work. The idea that the singularity is a surface rather than a point was unexpected to me even though it seems to follow logically from the theory of relativity.
I wonder how this reconciles with quantum gravity. If the singularity is truly a two-dimensional surface, perhaps it's related to Hawking radiation and the thermodynamics of black holes?
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.
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.
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.
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.
[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
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
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?
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!
(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.
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.
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)
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
Of course if you did do that, the air itself would collapse into a black hole larger than M87*...