43 ms·

Do black holes have singularities?

139 points by wrycoder 3y ago

fallingfrog 3y ago
What confuses me about black holes is that they appear to break time symmetry. Most equations in physics can be run forwards or backwards and the equations work the same. But if you imagine taking an object just after crossing the event horizon of a black hole, and then you were to flip the sign of its velocity vector so it was going backwards the way it came, you might expect the math to predict it to fly back out of the black hole. But, this can’t be right if nothing can escape the gravity of a black hole. Running the simulation backwards must not retrace the path it took when it went in. Doesn’t that break time symmetry?
- r0uv3n 3y ago
  No, classical general relativity is entirely time symmetric: time symmetry means here that if you have a solution for the equations that describe nature, then you still have a solution after you make the coordinate transformation t -> -t. This follows directly from the fact that the Einstein field equations involve only tensors and are thus diffeomorphism invariant. For the case of a black hole, the solution you get by reversing time describes a white hole., which is again an entirely valid solution to the Einstein field equations.
  - fallingfrog 3y ago
    Ah I see! Time reversed, every path eventually exits the black hole. So it’s a different thing. Thank you
- Ygg2 3y ago
  Time symmetry can be broken. Just not Charge Parity Time symmetry. Also if you invert time, black hole behaves differently.
- evanb 3y ago
  Time reversal symmetry is probably the most subtle of the discrete symmetries. Suppose you have a video that follows the moon and the Earth from some distance but that no other celestial bodies are visible, for simplicity. If you reversed the orbit of the moon but didn't change the rotational sense of the Earth (sun rises in the east) then you could distinguish a video of that system from the original true-to-life video played backwards. Only if you ALSO reverse the rotational sense of the Earth (sun rises in the west) do you have a system that you can't distinguish from a backward true-to-life video. The same thing is happening in your scenario; if you want to apply time reversal, you'd better time reverse EVERYTHING relevant. Here, what you're missing is that you also need to time-reverse the black hole, which produces something called a white hole [0]. We have never observed any white-hole like object. But the point is, if you take your time-reversed object at the just-inside-the-bh-event-horizon radius away from the white hole's center, you'd get the correct reverse simulation. [0] https://en.wikipedia.org/wiki/White_hole https://en.wikipedia.org/wiki/White_hole
  - fallingfrog 3y ago
    This makes sense! Thank you
fallingfrog 3y ago
Here’s another wacky thing about black holes. It must be possible for one black hole to contain another. Imagine for example a tremendous supermassive black with a small stellar mass one falling into it. If the small one is free falling into the big one, then a few moments after crossing the event horizon it must still be in an inertial reference frame. So, one black hole can contain another. Perhaps, black holes contain a fractal where each black hole actually has many other smaller ones inside, and those have smaller ones in turn.
- quchen 3y ago
  > it [the small black hole] must still be in an inertial reference frame. Why? As soon as one’s center crosses the other’s Schwarzschild radius, the two merge and become a single hairless [1] black hole, no? Where does the »a few moments« come into play, and why would anything about the original black holes be retained? [1] https://en.wikipedia.org/wiki/No-hair_theorem https://en.wikipedia.org/wiki/No-hair_theorem
levn11 3y ago
PLEASE read this as this is literally about thinking of center of mass as existing in more than 0 dimensions. the book is called The Zero Point Paradox and has everything to do about singularities
Paul-Craft 3y ago
I think it's interesting that "black hole" is the least ambiguous phrase in the title of this paper. What even would be a "singularity," if we're talking about something beyond "this is where all our equations blow up to infinity?" What would it mean, then, for a black hole to "have" such a physical thing? Other people have said already in the comments that many physicists insist that "singularities" aren't a physical thing, anyway. But, that doesn't really remove much of the ambiguity, because there's still the question of what exactly it means that the equations blow up to infinity. Who knows? All I know is that I happened to be thinking about black holes at one point in grad school while I was also taking differential topology, and I realized that a rotating black hole would "smear out" a singularity at its "center" (whatever that means) due to frame dragging, resulting in a "ring singularity." And, lo and behold, there is such a thing, and it sort of works vaguely the way I thought it would: https://en.wikipedia.org/wiki/Ring_singularity https://en.wikipedia.org/wiki/Ring_singularity
- westurner 3y ago
  Mustn't Ring black holes also be fluid attractor system solutions? https://news.ycombinator.com/item?id=38370118 https://news.ycombinator.com/item?id=38370118 https://westurner.github.io/hnlog/ https://westurner.github.io/hnlog/ Ctrl-F "n-body" "Mathematicians Found 12,000 Solutions to the Notoriously Hard Three-Body Problem" (2023) https://news.ycombinator.com/item?id=37959364 https://news.ycombinator.com/item?id=37959364 https://westurner.github.io/hnlog/#comment-37959364 https://westurner.github.io/hnlog/#comment-37959364 : > Are all of the identified solutions (also) fluid attractor systems; and - if correct - shouldn't a theory of superfluid quantum gravity predict all of the n-body gravity solutions already discovered with non-fluidic numerical solutions? [...] > A sufficient theory of quantum gravity must describe n-body gravity within Bose-Einstein Condensates and also quantum levitation. ... > N-body gravity solutions with fluid vortices should predict all existing numerical n-body outcomes? > That so many things in space look fluidic - how many spiral arms are there on a nebula, [or a vortex due to a drain] all existing visual representations of black holes look like fluids, merging neutron stars look like emergent patterns from curl, too Shouldn't there be a corresponding solution with vorticity?
ngof 3y ago
I don't quite understand the Roy's Kerr argument. I have Hawking's and Ellis books in front of me and in chapter 8 they define very precisely what a singularity and they argue that finite length timelike or null geodisics incompleteness is the right concept to use when talking about singularities. quote Timelike geodesic incompleteness has an immediate physical significance in that it presents the possibility that there could be freely moving observers or particles whose history did not exist after or before a finite interval of time. This would appear and even more objectionable feature that infinite curvature and so it is appropriate to regard such a space a singular. endquote It is nice that Kerr's apparently found examples of geodesic incomplete spaces with bounded curvature and metric if I understand correctly, but I don't understand the "attack" on Penrose and Hawking work. At least in the book or in the original Penrose article they don't claim that geodesic incompleteness implies unboundedness of the metric or the curvature. On the contrary as far as I know they even argue (in the same book) that if the metric or the curvature is infinite at some point the manifold is not extensible and you could just remove the point from the manifold while with geodesic incompleteness the state of affair is worst cause you cannot in principle remove it. Finally I've never heard a physicist believes that singularities are real, they are just a symptoms that the theory reaches its limit.
WhitneyLand 3y ago
This is a paper by Roy Kerr who first found a solution for spinning black holes. This article explains the context and what’s being proposed: https://bigthink.com/starts-with-a-bang/singularities-dont-exist-roy-kerr https://bigthink.com/starts-with-a-bang/singularities-dont-e...
amai 3y ago
No, but a ringularity (https://en.wikipedia.org/wiki/Ring_singularity?wprov=sfti1#Traversability_and_nakedness https://en.wikipedia.org/wiki/Ring_singularity?wprov=sfti1#T...) .
infradig 3y ago
Thanks Roy for stating the obvious, someone needed to do it. Next: renormalization.
- amai 3y ago
  Problem is that gravity is generally thought to be non-renormalizable: https://arxiv.org/abs/0709.3555 https://arxiv.org/abs/0709.3555
- heyoni 3y ago
  For those of us that didn’t think anything about black holes was obvious, what’s up with Roy? He chasing clout or something?
  - defrost 3y ago
    He's got enough clout and awards for a soccer team already, his Marcel Grossmann Award has gravitas ... He's on the cusp of 90 and getting salty still hearing about singularities on pop sci TV shows I guess. From his conclusion: The author’s opinion is that gravitational clumping leads inevitably to black holes in our universe, confirming what is observed, but this does not lead to singularities. It is true that there are ”proofs” that the curvature of a non-rotating one is infinite at its central point. These all assume that matter is classical and that it satisfies whatever nineteenth century equation of state the proponents require to prove whatever it is that they wish to prove. Equations of state assume that all variables, such as pressure and volume, occur in the simplest algebraic fashion. This may be true for the low density laboratory or engineering experiments but perhaps not at black hole densities. The author has no doubt, and never did, that when Relativity and Quantum Mechanics are melded it will be shown that there are no singularities anywhere. When theory predicts singularities, the theory is wrong! A stellar example of Max Academic shade * ”airquotes” * "whatever nineteenth century" * "low density" .. "engineering"
    - slowmovintarget 3y ago
      So basically a swift whack on the chalkboard with a pointing stick, followed by "Pay attention, class!"
westurner 3y ago
"Do Black Holes Have Singularities?" (2023) https://news.ycombinator.com/item?id=38501546 https://news.ycombinator.com/item?id=38501546 : > SQS and SQG do purport to describe the interior topology of black holes.
crooked-v 3y ago
What would the implication of a no-singularity model be? Would it be that black holes just have a comparatively mundane ball of matter inside the event horizon?
- pantulis 3y ago
  There's an hypothesis for that! https://en.wikipedia.org/wiki/Fuzzball_(string_theory) https://en.wikipedia.org/wiki/Fuzzball_(string_theory)
- jonhohle 3y ago
  As someone with no formal experience in astronomy (other than a college for kids course in the 80s), that has been my mental model. Just a large enough mass with enough gravitational force to bend light/prevent light from leaving. There’s no hole, just a name describing what was originally observed.
  - Novosell 3y ago
    Mind you, black holes require high (infinite) density, but can exist at arbitrary mass. It'll just be smaller.
  - Sharlin 3y ago
    This is the 1800s classical, pre-relativistic idea of a "black hole". But it is mostly a coincidence that if you plug an escape velocity equal to the speed of light to Newton's equations, you get a body with a mass and radius equal to the mass and event horizon radius of a black hole. But given the incredible predictive success of general relativity, there's little doubt that actual black holes are not just "dark stars" but fundamentally relativistic objects: regions of spacetime so warped that time becomes spacelike and space becomes timelike. Note that Kerr most definitely does not disagree; the entire point of the Kerr metric is that it's a solution (set of solutions) to the Einstein field equations.
- pdonis 3y ago
  The kind of "no singularity" model Kerr discusses--where you have an object inside the inner horizon that replaces the ring singularity--is not actually viable. First, most physicists believe the inner horizon itself is not viable, because it is unstable against small perturbations, which any real hole will have (because there is always something falling in, even if it's just the cosmic background radiation). Second, it's not actually possible to replace the entire ring singularity with a non-singular object. However, there is a different type of "no singularity" model in the literature, called a "Bardeen black hole" (among other things), in which there is not only no singularity, but no event horizon. What appears to us as an event horizon is actually just an apparent horizon--a surface where, locally, light cannot escape, but which will not stay that way forever; eventually it will evaporate away (by a process similar to Hawking radiation), and everything that was trapped inside will come back out (though in hugely scrambled form). So there is nowhere in this spacetime that can't send light signals to infinity; it just takes a really long time for the signals to get out from some parts of it.
keithnz 3y ago
If you want a "laymans" brief... https://www.youtube.com/watch?v=nz55jONtFAU https://www.youtube.com/watch?v=nz55jONtFAU
- quickthrower2 3y ago
  Very good!
- mptest 3y ago
  Also, I'm just starting the book but I love the authors youtube videos and it seems germane, a brief history of black holes by dr becky smethurst seems to have decent reviews and her videos are great. Maybe check her out on youtube if you're more experienced but I'm finding her book fun as a layman
  - NegativeK 3y ago
    I just this week finished Dr. Smethurst's book. It was good stuff, but it does focus more on a black hole's interactions with its surrounding galaxy -- presumably because that's her specialization -- rather than things like firewalls and "is there a singularity." Would recommend.
- nirui 3y ago
  I just knew it's Sabine's video (I watched it last night) when I saw the name R. P. Kerr. I love her video too, though so far the only thing that I've learned from it is how to properly pronounce the word Einstein :DDDD Anyway here's another of her video which might be related to the one linked above: https://www.youtube.com/watch?v=-HHv3T4UHec https://www.youtube.com/watch?v=-HHv3T4UHec
winwang 3y ago
I didn't realize that Kerr was still alive and well! Similar to the feeling when I discovered that David Deutsch was on Twitter. Really incredible when names in physics textbooks are still around.
- passion__desire 3y ago
  I was surprised that Einstein's video and voice was preserved when I first saw him in a video. It never occurred to me to go out and check for such videos even though everyone holds him in high regard. This is also similar to the fact that I didn't know the top five contributions of Edward Witten, even though everyone considers him to our current generation Einstein. Only when I saw a video on that topic that I realized my folly, I should have sought such information actively. So much of our beliefs are formed through some kind of osmosis from the air. What works did Edward Witten do? https://www.youtube.com/watch?v=8xDSVeiVxMI https://www.youtube.com/watch?v=8xDSVeiVxMI
reidacdc 3y ago
Definitely not my field, but a colleague of mine in grad school who was doing GR stuff was convinced that black holes didn't have singularities. As I recall (it was a long time ago), it was mostly an aesthetic preference, he felt it was far more likely that at very high curvatures or energies or both, the domain of validity of GR would be exceeded, and Something Else would happen that preserved the theory in the low-curvature regime. It sounds like that's not even required, if I'm reading this right (did I mention it's not my field?), it sounds like even within GR, singularities are avoidable? Very cool.
- soundarana 3y ago
  Many physicists believe that no singularity can phisically exist in nature and that they are just our lack of a better theory.
  - boxed 3y ago
    Isn't an electron a singularity in this kind of sense? A mathematical point with some fields, and a certain mass.
    - layer8 3y ago
      An electron is a fluctuation of the electron field, not a singular point.
      - boxed 3y ago
        It certainly acts like a singular point if you measure it and have it scatter on stuff...
        layer8 3y ago
        The electron wavelength is around 4 picometers at low energies. The wavelength also imposes a limit on the resolution of electron microscopy, for example. The wavelengths are really small, but they are not zero.
__MatrixMan__ 3y ago
It has always struck me as kind of bizarre that we make assertions about what is beyond the event horizon of a black hole at all. Since no information can escape that place and reach us as evidence, all claims about it are unfalsifiable. For all we know the universe decides to save memory and just not render anything there at all.
- evanb 3y ago
  > Since no information can escape that place and reach us as evidence, all claims about it are unfalsifiable. The idea that no information can escape from the event horizon is model-dependent; it's a mathematical result from the assumptions of classic general relativity. If you operate with the assumption that the claim is true, it's fair to consider the other mathematical results of classic general relativity. That's why (some) people say there is a singularity. Of course, the point is that if GR isn't exactly but only approximately true to a deeper theory, is the claim about singularities also true in the deeper theory, or does the deeper theory resolve the singularities somehow? That deeper theory may also say that information escapes from the event horizon. For example, Hawking showed that semiclassical quantum corrections to GR means that black holes emit thermal (information-free) radiation. If we had a fully quantum theory of gravity people expect the evolution to be completely unitary and the information could ultimately be acquired (perhaps at enormous computational expense).
  - XorNot 3y ago
    We also know GR is incomplete because it cannot explain what happens in a black hole at the singularity. Objects within have to always be approaching it but never reach it (since then they would not be approaching it) but it has a finite volume in space, so they must eventually get there.
    - ben_w 3y ago
      Black holes have a finite volume on the outside, but I'd have to do an integral above my skill level to work out the volume inside; if I understand right, the radial direction and the time direction switch roles at the event horizon. Also, I'm not sure you need stuff to always approach without ever getting there: it's not clear what happens to quantum fields at a singularity, but if you no longer have time displacement symmetry you don't get energy conservation so stuff might just cease to exist.
Nevermark 3y ago
If you naively apply Newton's force of gravity, between two masses at a distance, Fg = Gm1m2/d^2, you get an infinite force when a marble (mass 1) is at the center (distance = 0) of a planet (mass 2) Of course, this singularity is just a sign the equation doesn't capture all the details. The detail is the masses have radiuses, r1 and r2, and when the distance falls below either radius, the force of gravity for any mass's radius beyond d cancels out. When d = 0, Fg = 0. Similarly, the idea that general relativity's black hole singularity is real is also naive. A situation with massive gravity over tiny distances is going to require GR and QM to be united or otherwise reconciled (at a minimum!) for any chance of an accurate model. Lesson: Our equations break down because they are incomplete. Reality doesn't break down.
- dmarchand90 3y ago
  A fun fact is that even in humble fracture mechanics one gets singularities at the crack tip using standard elasticity theory. A bunch of funny mathematics is needed to get around this. And, of course, the reality is that at a certain point you hit the atomic level so the tip is always 'blunted' at least one atoms length.
  - jacquesm 3y ago
    > A bunch of funny mathematics is needed to get around this. I usually use a small drill to get around it. Works every time.
    - GTP 3y ago
      TIL that drills are excellent matematicians
      - otteromkram 3y ago
        They're great mathematicians, too.
- fsckboy 3y ago
  >If you naively apply Newton's force of gravity, between two masses at a distance, Fg = Gm1m2/d^2, you get an infinite force when a marble (mass 1) is at the center (distance = 0) of a planet (mass 2) and, for the people who might not have been exposed to the idea in a physics class, that marble at a distance from the planet has a potential energy, energy it would give up were it to be released and allowed to fall toward the planet. But, if instead you did work against the gravity to pull the marble farther away from the planet, that work would be saved up as an increase in the marble's potential energy. And that would continue till you pulled the marble infinitely far away, at which point the force of attraction would be 0 and the marble's potential energy would be zero. The only way this works is if the potential energy of the marble is a negative number, in which case maybe the singularity isn't such a bad idea
lordfrito 3y ago
Stupid layman question here. Apologies if my question "isn't even wrong". I have always had trouble reconciling the "tidal stresses rip everything apart" with the idea that "everything hits the center in finite time, thus infinite density and singularity". I mean, how can both be true? My understanding is that tidal forces are due to the gravity gradient being more and more severe as you near the center. That is, objects just a little bit closer to the center than you will be pulled more, and hence will accelerate towards the center faster than you are being accelerated (at that moment). Relatively speaking, they are moving away from you. Eventually the gradient is so severe even your atoms even get ripped apart. Everything accelerates at faster and faster speeds. This would imply that the "space" between matter increases indefinitely as you approach the center, right? Also, does this also apply to photons in say a light ray? Do the photons nearer the center pull away from the photons further out? If not, why not? And if so, then how can this be possible if all photons travel at same speed C? Is it that space is expanding inside the event horizon, faster than the speed of light? So anyhow, tidal forces seem to imply everything getting further and further apart from each other as you near the center. But the idea of a singularity is that "everything is in a single point of infinite density". So how can matter be getting ripped apart at the same time it's getting squooshed together? Also, wouldn't this apply to the original star that's collapsing? Meaning the particles inside the star are getting ripped apart as the black hole forms and they're drawn toward the center at faster and faster speeds. Is it possible that the particles in the star are also ripped apart by tidal forces, never reaching each other? I guess my question is, what forces the particles back together again? There must be deceleration involved, right? I feel like I'm missing something important.
- layer8 3y ago
  The issue with the singularity, and why it is a problem, is that the mathematics break down when a particle reaches the singularity, which it does after finite (proper) time, so we don’t know what happens to the particle after it hits the singularity. Physical objects falling towards the singularity get ripped apart, so their constituents reach the singularity at different times. We don’t know what happens at the respective moment they individually reach the singularity, but since there’s nowhere else they can go, we kind of assume that they’ll necessarily accumulate at the singularity, which therefore would be infinitely dense. But really the problem is that we have no functioning theory that tells us what actually happens at the singularity. In quantum mechanics, particles aren’t singular points, and instead have an extent corresponding to their wavelength. In that picture, it’s not possible for a particle to hit a singularity even as a limit.

139 points by wrycoder 3y ago

What confuses me about black holes is that they appear to break time symmetry. Most equations in physics can be run forwards or backwards and the equations work the same. But if you imagine taking an object just after crossing the event horizon of a black hole, and then you were to flip the sign of its velocity vector so it was going backwards the way it came, you might expect the math to predict it to fly back out of the black hole. But, this can’t be right if nothing can escape the gravity of a black hole. Running the simulation backwards must not retrace the path it took when it went in. Doesn’t that break time symmetry?

r0uv3n 3y ago
No, classical general relativity is entirely time symmetric: time symmetry means here that if you have a solution for the equations that describe nature, then you still have a solution after you make the coordinate transformation t -> -t. This follows directly from the fact that the Einstein field equations involve only tensors and are thus diffeomorphism invariant. For the case of a black hole, the solution you get by reversing time describes a white hole., which is again an entirely valid solution to the Einstein field equations.
- fallingfrog 3y ago
  Ah I see! Time reversed, every path eventually exits the black hole. So it’s a different thing. Thank you
Ygg2 3y ago
Time symmetry can be broken. Just not Charge Parity Time symmetry. Also if you invert time, black hole behaves differently.
evanb 3y ago
Time reversal symmetry is probably the most subtle of the discrete symmetries. Suppose you have a video that follows the moon and the Earth from some distance but that no other celestial bodies are visible, for simplicity. If you reversed the orbit of the moon but didn't change the rotational sense of the Earth (sun rises in the east) then you could distinguish a video of that system from the original true-to-life video played backwards. Only if you ALSO reverse the rotational sense of the Earth (sun rises in the west) do you have a system that you can't distinguish from a backward true-to-life video. The same thing is happening in your scenario; if you want to apply time reversal, you'd better time reverse EVERYTHING relevant. Here, what you're missing is that you also need to time-reverse the black hole, which produces something called a white hole [0]. We have never observed any white-hole like object. But the point is, if you take your time-reversed object at the just-inside-the-bh-event-horizon radius away from the white hole's center, you'd get the correct reverse simulation. [0] https://en.wikipedia.org/wiki/White_hole https://en.wikipedia.org/wiki/White_hole
- fallingfrog 3y ago
  This makes sense! Thank you

fallingfrog 3y ago

Here’s another wacky thing about black holes. It must be possible for one black hole to contain another. Imagine for example a tremendous supermassive black with a small stellar mass one falling into it. If the small one is free falling into the big one, then a few moments after crossing the event horizon it must still be in an inertial reference frame. So, one black hole can contain another. Perhaps, black holes contain a fractal where each black hole actually has many other smaller ones inside, and those have smaller ones in turn.

quchen 3y ago
> it [the small black hole] must still be in an inertial reference frame. Why? As soon as one’s center crosses the other’s Schwarzschild radius, the two merge and become a single hairless [1] black hole, no? Where does the »a few moments« come into play, and why would anything about the original black holes be retained? [1] https://en.wikipedia.org/wiki/No-hair_theorem https://en.wikipedia.org/wiki/No-hair_theorem

levn11 3y ago

PLEASE read this as this is literally about thinking of center of mass as existing in more than 0 dimensions. the book is called The Zero Point Paradox and has everything to do about singularities

Paul-Craft 3y ago

I think it's interesting that "black hole" is the least ambiguous phrase in the title of this paper. What even would be a "singularity," if we're talking about something beyond "this is where all our equations blow up to infinity?" What would it mean, then, for a black hole to "have" such a physical thing? Other people have said already in the comments that many physicists insist that "singularities" aren't a physical thing, anyway. But, that doesn't really remove much of the ambiguity, because there's still the question of what exactly it means that the equations blow up to infinity. Who knows? All I know is that I happened to be thinking about black holes at one point in grad school while I was also taking differential topology, and I realized that a rotating black hole would "smear out" a singularity at its "center" (whatever that means) due to frame dragging, resulting in a "ring singularity." And, lo and behold, there is such a thing, and it sort of works vaguely the way I thought it would: https://en.wikipedia.org/wiki/Ring_singularity https://en.wikipedia.org/wiki/Ring_singularity

westurner 3y ago
Mustn't Ring black holes also be fluid attractor system solutions? https://news.ycombinator.com/item?id=38370118 https://news.ycombinator.com/item?id=38370118 https://westurner.github.io/hnlog/ https://westurner.github.io/hnlog/ Ctrl-F "n-body" "Mathematicians Found 12,000 Solutions to the Notoriously Hard Three-Body Problem" (2023) https://news.ycombinator.com/item?id=37959364 https://news.ycombinator.com/item?id=37959364 https://westurner.github.io/hnlog/#comment-37959364 https://westurner.github.io/hnlog/#comment-37959364 : > Are all of the identified solutions (also) fluid attractor systems; and - if correct - shouldn't a theory of superfluid quantum gravity predict all of the n-body gravity solutions already discovered with non-fluidic numerical solutions? [...] > A sufficient theory of quantum gravity must describe n-body gravity within Bose-Einstein Condensates and also quantum levitation. ... > N-body gravity solutions with fluid vortices should predict all existing numerical n-body outcomes? > That so many things in space look fluidic - how many spiral arms are there on a nebula, [or a vortex due to a drain] all existing visual representations of black holes look like fluids, merging neutron stars look like emergent patterns from curl, too Shouldn't there be a corresponding solution with vorticity?

ngof 3y ago

I don't quite understand the Roy's Kerr argument. I have Hawking's and Ellis books in front of me and in chapter 8 they define very precisely what a singularity and they argue that finite length timelike or null geodisics incompleteness is the right concept to use when talking about singularities. quote Timelike geodesic incompleteness has an immediate physical significance in that it presents the possibility that there could be freely moving observers or particles whose history did not exist after or before a finite interval of time. This would appear and even more objectionable feature that infinite curvature and so it is appropriate to regard such a space a singular. endquote It is nice that Kerr's apparently found examples of geodesic incomplete spaces with bounded curvature and metric if I understand correctly, but I don't understand the "attack" on Penrose and Hawking work. At least in the book or in the original Penrose article they don't claim that geodesic incompleteness implies unboundedness of the metric or the curvature. On the contrary as far as I know they even argue (in the same book) that if the metric or the curvature is infinite at some point the manifold is not extensible and you could just remove the point from the manifold while with geodesic incompleteness the state of affair is worst cause you cannot in principle remove it. Finally I've never heard a physicist believes that singularities are real, they are just a symptoms that the theory reaches its limit.

WhitneyLand 3y ago

This is a paper by Roy Kerr who first found a solution for spinning black holes. This article explains the context and what’s being proposed: https://bigthink.com/starts-with-a-bang/singularities-dont-exist-roy-kerr https://bigthink.com/starts-with-a-bang/singularities-dont-e...

amai 3y ago

No, but a ringularity (https://en.wikipedia.org/wiki/Ring_singularity?wprov=sfti1#Traversability_and_nakedness https://en.wikipedia.org/wiki/Ring_singularity?wprov=sfti1#T...) .

infradig 3y ago

Thanks Roy for stating the obvious, someone needed to do it. Next: renormalization.

amai 3y ago
Problem is that gravity is generally thought to be non-renormalizable: https://arxiv.org/abs/0709.3555 https://arxiv.org/abs/0709.3555
heyoni 3y ago
For those of us that didn’t think anything about black holes was obvious, what’s up with Roy? He chasing clout or something?
- defrost 3y ago
  He's got enough clout and awards for a soccer team already, his Marcel Grossmann Award has gravitas ... He's on the cusp of 90 and getting salty still hearing about singularities on pop sci TV shows I guess. From his conclusion: The author’s opinion is that gravitational clumping leads inevitably to black holes in our universe, confirming what is observed, but this does not lead to singularities. It is true that there are ”proofs” that the curvature of a non-rotating one is infinite at its central point. These all assume that matter is classical and that it satisfies whatever nineteenth century equation of state the proponents require to prove whatever it is that they wish to prove. Equations of state assume that all variables, such as pressure and volume, occur in the simplest algebraic fashion. This may be true for the low density laboratory or engineering experiments but perhaps not at black hole densities. The author has no doubt, and never did, that when Relativity and Quantum Mechanics are melded it will be shown that there are no singularities anywhere. When theory predicts singularities, the theory is wrong! A stellar example of Max Academic shade * ”airquotes” * "whatever nineteenth century" * "low density" .. "engineering"
  - slowmovintarget 3y ago
    So basically a swift whack on the chalkboard with a pointing stick, followed by "Pay attention, class!"

westurner 3y ago

"Do Black Holes Have Singularities?" (2023) https://news.ycombinator.com/item?id=38501546 https://news.ycombinator.com/item?id=38501546 : > SQS and SQG do purport to describe the interior topology of black holes.

crooked-v 3y ago

What would the implication of a no-singularity model be? Would it be that black holes just have a comparatively mundane ball of matter inside the event horizon?

pantulis 3y ago
There's an hypothesis for that! https://en.wikipedia.org/wiki/Fuzzball_(string_theory) https://en.wikipedia.org/wiki/Fuzzball_(string_theory)
jonhohle 3y ago
As someone with no formal experience in astronomy (other than a college for kids course in the 80s), that has been my mental model. Just a large enough mass with enough gravitational force to bend light/prevent light from leaving. There’s no hole, just a name describing what was originally observed.
- Novosell 3y ago
  Mind you, black holes require high (infinite) density, but can exist at arbitrary mass. It'll just be smaller.
- Sharlin 3y ago
  This is the 1800s classical, pre-relativistic idea of a "black hole". But it is mostly a coincidence that if you plug an escape velocity equal to the speed of light to Newton's equations, you get a body with a mass and radius equal to the mass and event horizon radius of a black hole. But given the incredible predictive success of general relativity, there's little doubt that actual black holes are not just "dark stars" but fundamentally relativistic objects: regions of spacetime so warped that time becomes spacelike and space becomes timelike. Note that Kerr most definitely does not disagree; the entire point of the Kerr metric is that it's a solution (set of solutions) to the Einstein field equations.
pdonis 3y ago
The kind of "no singularity" model Kerr discusses--where you have an object inside the inner horizon that replaces the ring singularity--is not actually viable. First, most physicists believe the inner horizon itself is not viable, because it is unstable against small perturbations, which any real hole will have (because there is always something falling in, even if it's just the cosmic background radiation). Second, it's not actually possible to replace the entire ring singularity with a non-singular object. However, there is a different type of "no singularity" model in the literature, called a "Bardeen black hole" (among other things), in which there is not only no singularity, but no event horizon. What appears to us as an event horizon is actually just an apparent horizon--a surface where, locally, light cannot escape, but which will not stay that way forever; eventually it will evaporate away (by a process similar to Hawking radiation), and everything that was trapped inside will come back out (though in hugely scrambled form). So there is nowhere in this spacetime that can't send light signals to infinity; it just takes a really long time for the signals to get out from some parts of it.

keithnz 3y ago

If you want a "laymans" brief... https://www.youtube.com/watch?v=nz55jONtFAU https://www.youtube.com/watch?v=nz55jONtFAU

quickthrower2 3y ago
Very good!
mptest 3y ago
Also, I'm just starting the book but I love the authors youtube videos and it seems germane, a brief history of black holes by dr becky smethurst seems to have decent reviews and her videos are great. Maybe check her out on youtube if you're more experienced but I'm finding her book fun as a layman
- NegativeK 3y ago
  I just this week finished Dr. Smethurst's book. It was good stuff, but it does focus more on a black hole's interactions with its surrounding galaxy -- presumably because that's her specialization -- rather than things like firewalls and "is there a singularity." Would recommend.
nirui 3y ago
I just knew it's Sabine's video (I watched it last night) when I saw the name R. P. Kerr. I love her video too, though so far the only thing that I've learned from it is how to properly pronounce the word Einstein :DDDD Anyway here's another of her video which might be related to the one linked above: https://www.youtube.com/watch?v=-HHv3T4UHec https://www.youtube.com/watch?v=-HHv3T4UHec

winwang 3y ago

I didn't realize that Kerr was still alive and well! Similar to the feeling when I discovered that David Deutsch was on Twitter. Really incredible when names in physics textbooks are still around.

passion__desire 3y ago
I was surprised that Einstein's video and voice was preserved when I first saw him in a video. It never occurred to me to go out and check for such videos even though everyone holds him in high regard. This is also similar to the fact that I didn't know the top five contributions of Edward Witten, even though everyone considers him to our current generation Einstein. Only when I saw a video on that topic that I realized my folly, I should have sought such information actively. So much of our beliefs are formed through some kind of osmosis from the air. What works did Edward Witten do? https://www.youtube.com/watch?v=8xDSVeiVxMI https://www.youtube.com/watch?v=8xDSVeiVxMI

reidacdc 3y ago

Definitely not my field, but a colleague of mine in grad school who was doing GR stuff was convinced that black holes didn't have singularities. As I recall (it was a long time ago), it was mostly an aesthetic preference, he felt it was far more likely that at very high curvatures or energies or both, the domain of validity of GR would be exceeded, and Something Else would happen that preserved the theory in the low-curvature regime. It sounds like that's not even required, if I'm reading this right (did I mention it's not my field?), it sounds like even within GR, singularities are avoidable? Very cool.

soundarana 3y ago
Many physicists believe that no singularity can phisically exist in nature and that they are just our lack of a better theory.
- boxed 3y ago
  Isn't an electron a singularity in this kind of sense? A mathematical point with some fields, and a certain mass.
  - layer8 3y ago
    An electron is a fluctuation of the electron field, not a singular point.
    - boxed 3y ago
      It certainly acts like a singular point if you measure it and have it scatter on stuff...
      - layer8 3y ago
        The electron wavelength is around 4 picometers at low energies. The wavelength also imposes a limit on the resolution of electron microscopy, for example. The wavelengths are really small, but they are not zero.

__MatrixMan__ 3y ago

It has always struck me as kind of bizarre that we make assertions about what is beyond the event horizon of a black hole at all. Since no information can escape that place and reach us as evidence, all claims about it are unfalsifiable. For all we know the universe decides to save memory and just not render anything there at all.

evanb 3y ago
> Since no information can escape that place and reach us as evidence, all claims about it are unfalsifiable. The idea that no information can escape from the event horizon is model-dependent; it's a mathematical result from the assumptions of classic general relativity. If you operate with the assumption that the claim is true, it's fair to consider the other mathematical results of classic general relativity. That's why (some) people say there is a singularity. Of course, the point is that if GR isn't exactly but only approximately true to a deeper theory, is the claim about singularities also true in the deeper theory, or does the deeper theory resolve the singularities somehow? That deeper theory may also say that information escapes from the event horizon. For example, Hawking showed that semiclassical quantum corrections to GR means that black holes emit thermal (information-free) radiation. If we had a fully quantum theory of gravity people expect the evolution to be completely unitary and the information could ultimately be acquired (perhaps at enormous computational expense).
- XorNot 3y ago
  We also know GR is incomplete because it cannot explain what happens in a black hole at the singularity. Objects within have to always be approaching it but never reach it (since then they would not be approaching it) but it has a finite volume in space, so they must eventually get there.
  - ben_w 3y ago
    Black holes have a finite volume on the outside, but I'd have to do an integral above my skill level to work out the volume inside; if I understand right, the radial direction and the time direction switch roles at the event horizon. Also, I'm not sure you need stuff to always approach without ever getting there: it's not clear what happens to quantum fields at a singularity, but if you no longer have time displacement symmetry you don't get energy conservation so stuff might just cease to exist.

Nevermark 3y ago

If you naively apply Newton's force of gravity, between two masses at a distance, Fg = Gm1m2/d^2, you get an infinite force when a marble (mass 1) is at the center (distance = 0) of a planet (mass 2) Of course, this singularity is just a sign the equation doesn't capture all the details. The detail is the masses have radiuses, r1 and r2, and when the distance falls below either radius, the force of gravity for any mass's radius beyond d cancels out. When d = 0, Fg = 0. Similarly, the idea that general relativity's black hole singularity is real is also naive. A situation with massive gravity over tiny distances is going to require GR and QM to be united or otherwise reconciled (at a minimum!) for any chance of an accurate model. Lesson: Our equations break down because they are incomplete. Reality doesn't break down.

dmarchand90 3y ago
A fun fact is that even in humble fracture mechanics one gets singularities at the crack tip using standard elasticity theory. A bunch of funny mathematics is needed to get around this. And, of course, the reality is that at a certain point you hit the atomic level so the tip is always 'blunted' at least one atoms length.
- jacquesm 3y ago
  > A bunch of funny mathematics is needed to get around this. I usually use a small drill to get around it. Works every time.
  - GTP 3y ago
    TIL that drills are excellent matematicians
    - otteromkram 3y ago
      They're great mathematicians, too.
fsckboy 3y ago
>If you naively apply Newton's force of gravity, between two masses at a distance, Fg = Gm1m2/d^2, you get an infinite force when a marble (mass 1) is at the center (distance = 0) of a planet (mass 2) and, for the people who might not have been exposed to the idea in a physics class, that marble at a distance from the planet has a potential energy, energy it would give up were it to be released and allowed to fall toward the planet. But, if instead you did work against the gravity to pull the marble farther away from the planet, that work would be saved up as an increase in the marble's potential energy. And that would continue till you pulled the marble infinitely far away, at which point the force of attraction would be 0 and the marble's potential energy would be zero. The only way this works is if the potential energy of the marble is a negative number, in which case maybe the singularity isn't such a bad idea

lordfrito 3y ago

Stupid layman question here. Apologies if my question "isn't even wrong". I have always had trouble reconciling the "tidal stresses rip everything apart" with the idea that "everything hits the center in finite time, thus infinite density and singularity". I mean, how can both be true? My understanding is that tidal forces are due to the gravity gradient being more and more severe as you near the center. That is, objects just a little bit closer to the center than you will be pulled more, and hence will accelerate towards the center faster than you are being accelerated (at that moment). Relatively speaking, they are moving away from you. Eventually the gradient is so severe even your atoms even get ripped apart. Everything accelerates at faster and faster speeds. This would imply that the "space" between matter increases indefinitely as you approach the center, right? Also, does this also apply to photons in say a light ray? Do the photons nearer the center pull away from the photons further out? If not, why not? And if so, then how can this be possible if all photons travel at same speed C? Is it that space is expanding inside the event horizon, faster than the speed of light? So anyhow, tidal forces seem to imply everything getting further and further apart from each other as you near the center. But the idea of a singularity is that "everything is in a single point of infinite density". So how can matter be getting ripped apart at the same time it's getting squooshed together? Also, wouldn't this apply to the original star that's collapsing? Meaning the particles inside the star are getting ripped apart as the black hole forms and they're drawn toward the center at faster and faster speeds. Is it possible that the particles in the star are also ripped apart by tidal forces, never reaching each other? I guess my question is, what forces the particles back together again? There must be deceleration involved, right? I feel like I'm missing something important.

layer8 3y ago
The issue with the singularity, and why it is a problem, is that the mathematics break down when a particle reaches the singularity, which it does after finite (proper) time, so we don’t know what happens to the particle after it hits the singularity. Physical objects falling towards the singularity get ripped apart, so their constituents reach the singularity at different times. We don’t know what happens at the respective moment they individually reach the singularity, but since there’s nowhere else they can go, we kind of assume that they’ll necessarily accumulate at the singularity, which therefore would be infinitely dense. But really the problem is that we have no functioning theory that tells us what actually happens at the singularity. In quantum mechanics, particles aren’t singular points, and instead have an extent corresponding to their wavelength. In that picture, it’s not possible for a particle to hit a singularity even as a limit.