Do black holes have singularities?
arxiv.org
arxiv.org
For all we know the universe decides to save memory and just not render anything there at all.
Don't get me wrong, I'm interested in hearing about some maximally elegant mathematical model which is consistent with the observations and the laws of physics on our side of the horizon. I just don't think I would then proceed to believe that what they described was a reality on the other side of that horizon.
1. https://en.wikipedia.org/wiki/Black_hole_information_paradox
Does the physicist believe that? If we get past popular culture which mangles modern science, the physicists are throwing around lots of random "what if" ideas and seeing where they go. If one is good, their idea is popular enough other physicists spend time thinking about if. If one gets lucky, then someone comes up with a way to test the theory (using the layman version of theory). If one gets REALLY lucky, the test doesn't lead to it being rejected.
Sometimes there an be a long gap between when a physicist first thinks of a theory and someone finds a way to test it. Some ideas are still untestable, but may be interesting enough that physicists will still try to dive deeper and see where the idea goes.
But do they believe it is the truth? While some might, I think most keep a sort "what if, maybe" vibe, even on the theories they spend time looking into. They are invested, but that doesn't mean the believe it is the truth, only that it is the model worth spending their time investigating.
One key idea to consider, science does not give truth, it gives the model that best fits all known data without any claim to if that model is true or false.
We have theories and experiments.
An experiment giving a result not in accord with the theory is an immediate disproof.
An experiment giving a result in accord with the theory is a confirmation possibly waiting for another experiment resulting in a disproof.
Proof exist only in mathematics.
Yes, prediction doesn't and can't contain information (in the technical sense) from the future, since by definition it's based only on what we know in the present.
> Do we have some ideas why rules of physics will be different in the future?
No. It's perfectly reasonable to assume that the rules of physics will be the same in the future. Just as it's perfectly reasonable to assume that they're the same inside a black hole. But in both cases we can't know.
In the technical sense the future _is_ driven purely by the information available in the present. It’s a function of t-1.
The only reason future should be different from prediction is if the set of information available to the predictor about the present is different from the actual set of information about the present.
The best way this word fits is that we can reason towards the conclusion that whether laws will change or not is an assumption.
Sure it can, you just have to be patient.
My sense is that we've got it flipped, and have so strongly embraced the 'realism' of quanta that we intuitively reject some of the more continuous features of GR, whereas if I was putting forward the candidate for the secondary 'rendering' side effect, it would be the conversation of continuous modeled things to discrete units for tracking state from interactions with free agents so optimized that erasing persistent information about the interactions converts back from discrete to continuous.
We've now seen that paradigm with procedural generated environments with deformable geometry where continuous seed functions convert to voxels that are tracked.
Maybe the foundation of existence is continuous and infinitely scaled, and it's only our own emulation of that foundation where there's conversion to discrete units and fundamental limits preventing any 'real' infinites?
I've never seen anything asserting this, and this is not what standard theories say. The idea is that with the right "key" you can recover the information that was encoded in the stuff that fell into the black hole. As far as I know there is no suggestion this gives you any information about what is going on inside it.
https://www.quantamagazine.org/new-calculations-show-how-to-...
I wouldn't put money on it being the case, but it's definitely "outside the event horizon" thinking and worth a read.
In any case the picture of time and space switching places inside a black hole is at best a rather deceptive simplification. The most important thing about the event horizon is that locally (i.e. to one falling in to it) nothing at all interesting happens at the event horizon.
Edit: The "swapping" you are referring to is an artifact of coordinate systems, not of space-time. Thinking something wild happens to space-time as you pass through the event horizon is the same as thinking that something wild happens to the Earth's geometry as you reach the north pole. Sure at the north pole there is no longer any meaningful direction other than "south" but thats an artefact of the coordinate system you're using, the pole is a normal point just like any other.
If you picture us in an X-Y plane (which somehow represents all 3 spatial coords), and "up" is the time dimension, then a black hole would be the X-Y plane deformed into a 90-deg "pipe" facing straight down. Once you are in the pipe, your "X-Y" is our "up-down", this is probably the "artifact" you are referring to.
This is not correct, there is no 90 degree bend. Space-time is locally Minkowskian ("flat") at the event horizon. It looks like a sharp 90 degrees turn in some coordinate system, just as when you walk in a "straight line" (a great circle if you prefer) over the north pole you go discontinuously from "walking north" to "walking south" even though your real motion is continuous.
The preprint linked to lays it out more technically if that's your jam:
https://arxiv.org/pdf/2207.06536.pdf
See section 6 on exterior vs interior measurements, and you can see the discussion in the FAQ about how measurements on the radiation after the Page time creates particles in the interior (which cites section 6 for more details). Then 8.2-3 goes more into what information about the interior can be known from observables in the fundamental description before and after the Page time. The "Previous attempts at an encoded interior" section in the discussion could help further clarify things.
It's not saying that it's trivial to see inside a black hole from the Hawking radiation, but it would be incorrect to characterize their model as saying that nothing about the interior can be known in measuring the Hawking radiation.
This is quite different from being able to probe the space-time structure inside (i.e. ask questions like is there a real singularity in there).
If you think about what you'd need there, you need the opposite of what they have in the FAQ, you would need operations in the interior to be able to create a particle on the exterior in order to build a "telescope" to look inside and I'm pretty sure this is ruled out even in this proposal.
It just admits that the feasibility of this is ridiculous with my favorite line of the paper:
> Physically this seems absurd, as it allows a measurement inside a black hole to produce a record which stays outside, but we are not claiming that any effective-description observer could actually implement this unitary.
But I agree that there's a big difference between the plausibility of measuring the 'stuff' vs it's spacetime configuration - that was a great point.
I don’t want to dismiss it off hand because there’s all sorts of funky things out there, but “information encoded radiation” is something that I’d be pretty immediately and heavily skeptical of.
At least unless you can somehow reduce the data complexity dramatically without tainting the simulation, but that seems difficult to do when you're trying to work backwards to an unknown state. At least the pre-burnt piece of paper is known to exist alongside various rules of physics that we know - unlike in the black hole, where those rules all come with a "warrantry maybe void" asterisk.
The other thing I've wondered is how could you have a detector for those particles without interfering with your measurement (heisenberg's)? Your measurement apparatus will give off heat or very slightly change the shape of spacetime, thus interfering where your particles are detected :(.
But yes, if you have "collapsed the wave function", you don't have the information to "backtrack" anymore. But I don't think the information paradox is about this (although unsure why). AFAIU one problem is that black holes throw out even the statistical information available in the wavefunction.
What really bothers the quantum physicists is not a macro-scale unrecoverability, but the event of the loss itself. The equations of quantum physics do not have anywhere to "lose" information. If a black hole loses information, then that means there is some box you can draw in spacetime where the information goes in and doesn't come back out, and that necessarily implies that something in that box broke the fundamental equations of quantum mechanics.
I think you could analogize this issue into classical physics fairly well as finding a violation of the conservation of energy in a putatively classical system. (I have to qualify this because at it stands at the moment, conservation of energy is not absolute; at cosmological scales it seems to be violated by the expansion of the universe. So ignore that for the moment.) If someone produced a true perpetual motion machine, let alone one that actually provided over-unity energy, that would be a problem for classical physics because there is nowhere in the mathematics that energy can be produced in excess. It is written into the most fundamental formulations of the theories and backed by Noether's Theorem. Such a machine would mean that somewhere the laws of physics are being violated, and that would mean we have a hole in them. The quantum theorists are "worried" about quantum information loss in the same way a classical physicist is "worried" about over-unity machines. A real, physical quantum physicist or classical physicist might in fact be over the moon to discover such a thing; it would be a career maker and who knows what else might be implied by such a discovery. But the anthropomorphized theory that was just "violated" would be very "upset".
The other major relevant different being that the classical physics has those classic physics "in hand", in the sense that many real experiments on classic physics can be and are realized in the real world, and at this point, physicists as a whole do not take the idea that an over-unity machine is going to be produced very seriously. However, it is quite difficult to have black hole in hand to experiment on; such mathematical analogs as we have are intrinsically limited and probably quite likely to fail to exhibit the phenomena we're interested in. So there's a lot more "room" for problems to come from. Plus, classical physics already has very firmly built into it the understanding that it is only an approximation. Quantum physics is still struggling with that question; sure, we basically know it is incomplete, but we don't know exactly how to resolve that, so unlike classical physics where we know that technically, yes, it's predictions can be violated in certain ways at certain scales and we accept that, we're a lot more nervous about QM. Maybe the real theory of the universe would allow information destruction. In English, that sounds pretty harmless ultimately, like, I mean, OK, maybe that's a bit of an issue but who cares? But pushed through the aforementioned Noether's theorem it gets much more interesting considered from the mathematical point of view, and much more challenging.
The smallest perturbations in a chaotic system yield completely different results. The slit experinment for instance suggests that measurement changes the system.
Nothing.
To me, the resolution of the paradox — that the radiated field might contain some encoded information in it — is less weird than the alternative, which is that the information somehow disappears. Information being encoded in a field seems natural to me. There’s a tight interplay between energy, temperature, and information. It’s even right there in the first law of thermodynamics: dE = TdS + dW. (The S is the missing information about the system.)
But I think you're overcomplicating it. Think of it as a snapshot of an object as it crosses the event horizon. That snapshot is etched into the "surface" of the horizon and emits a pattern of radiation that corresponds to it.
It's pretty much the same as dropping a rock onto a planet and observing the crater from orbit. You left a mark on the surface and it emits a corresponding pattern of radiation.
The real crux of the matter is that we're starting to understand that information is a lot like energy. It's generally conserved in the same way, but black holes appear to destroy matter, energy, and information in a way that doesn't really add up.
So Hawking came up with the idea of Hawking radiation. It's a hypothetical way for a black hole to very slowly give back all of the matter and energy it's consumed in the form of particle radiation. If information is a conserved quantity like energy, Hawking radiation must also return all information consumed by the black hole.
Information theory is pretty interesting if you're the type of person who likes to think about black holes and cosmology in their free time.
AFAIK we haven't proven that Hawking radiation actually exists. It seems to work mathematically, but we'd have to go out and observe a black hole up close. It's also extraordinarily slow. As in, it would take the entire lifespan of the universe for a big black hole to evaporate into nothing. Ten to the power of hundreds of years. Just a hair shy of infinity.
And even you could always just pick a coordinate system with the origin right where the particle is, then its coordinates would trivially be zero. If you have several or moving particles and you want to keep the coordinate system fixed, then this will of course no longer work.
So even if spacetime is continuous and particles do move within it in continuous ways, the combination of Heisenberg's uncertainty principle plus the Plank length means we can never observe such continuity anyways.
I think the statement that you are implying here is not known to be correct. We have no idea if it is (theoretically) possible to measure the position of a particle to a precision of less than a Plank length. In some formulations of quantum gravity there are fundamental limits like this, but quantum gravity is difficult at best and sketchy at worst and none of those versions of quantum gravity is without their flaws.
If there's not enough energy in the universe to make the measurement, then there's no making the measurement no matter the theory of what would happen if there were more energy.
We could discuss the theory of what happens to a virtual photon going down a split path between Everett or another interpretation, but if we can't ever actually measure the virtual photon, then it's just theorizing around an unanswerable question. Which is part of what leads to "shut up and calculate."
We've known about the limitation in space for a while with the Plank length, and a similar limitation in time was discovered a year or two ago.
So while we have successful models for the universe that rely on the notion of continuous spacetime, our measurable version of it effectively has a minimum pixel size beyond which we fundamentally cannot get any more detail.
Fit the first time the other year I saw a psychics paper that actually presumed discrete spacetime based on simulation theory, which was pretty funny. I don't think the paper is that interesting beyond that aspect, but maybe you'll enjoy it given the presumption of discreteness: https://www.nature.com/articles/s41598-020-76301-0
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).
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.
If you try to naively apply the same procedure you would use to define volumes outside the event horizon, it's proportional to the lifetime of the black hole (infinite in the classical case) for the reason you note.
Of course the better way to interpret this is probably just that the interior volume of a black hole is ill-defined.
Every geodesic that crosses the horizon terminates at the singularity in a finite amount of time. If you fall past the horizon the singularity is in your definite future and in a finite amount of proper observer time your geodesic will end, at which point ... who knows what happens.
If you reject the theory because it makes unfalsifiable claims, you no longer get to claim they are unfalsifiable.
But in the end we all know that new physics need to be developed because the assumption is that there is only one reality and thus we should strive to reach a unifying theoretical model. Or are you suggesting there it is not possible to achieve a single theoretical model of reality?
And all true claims cannot be proven by science. Proof is the domain of logic and math, in science you can only falsify things.
I quoted this earlier I'll just quote it again for people who don't believe my second statement about science:
"No amount of experimentation can ever prove me right; a single experiment can prove me wrong." - Albert Einstein
So your statement, while not intentionally so, is pointless.
I think the main difference people are missing here is that everything beyond the event horizon hasn't ever been observed. And it's theorized to be unobservable.
That’s not what ‘falsifiable’ means. ‘Pi is irrational’ is falsifiable, in that if you can show me integer p and q such that p/q = pi, you would have demonstrated that statement to be false.
The fact we can show that no such p and q exist is what renders the truth of that statement proven. ‘Falsifiability’ of a statement is the property that makes the statement amenable to being evaluated for truth.
This is misunderstanding what falsifiability entails. A claim is falsifiable if one can, in principle, come up with experiments to disprove it. Just because a true claim will never be disproven by those experiments does not make it unfalsifiable. It could have been disproven, had it been false, and that is enough.
If your way of defining it is true then it's just a bad formal definition of falsifiability because you can make a sentence that sounds nonsensical like the one I made above. It means falsify and falsifiability are two different words with different definitions. When you look at the words they appear to be the same word with just different suffixes.
Let's examine the implications of your definition more carefully. If I falsify something. I either failed or succeeded at falsifying it. If there exists a thing that where all possible attempts at falsification will fail then it is still "falsifiable" because the attempt to falsify was possible??
If you are impossible to kill then you are still killable? If numbers cannot be divided by zero but it is still "divisible" by zero because I can make a fool hardy attempt at it?
From this I will say that my colloquial use of the term is actually better than your claim about the formal definition of falsifiability.
Better to use the word "observability". One cannot gather observable evidence to conduct an experiment. That's the key differentiator here.
So falsify refers to the result but falsifiability does not?
Reread my post, I don't think you read it fully. If falsifiability is defined as your claim then such a statement can be true:
"The Pythagorean theorem cannot be falsified but it is falsifiable"
Which sounds obviously nonsensical.
This is inconsistent with how we use the -able suffix in other words:
"The code cannot be extended but it is extendable"
I'm not referring to any official definition here, just pointing out the language problem that arises if we assume what you say is true. But here is the official definition anyway:
https://www.dictionary.com/browse/falsifiability
Which basically is pretty solid evidence for you being wrong. But at the same time I think you all are pulling some formalized definition from philosophy or something which probably has a different meaning defined for it. My argument is that the formalized definition is worse than the colloquial one in the English dictionary because the English definition is more logically consistent with the rest of the English language.
It's debatable which definition is more appropriate for this context. But assuming not everyone is a philosophy major I would say the definition in the English dictionary is more relevant.
falsifiability - the ability to be proven false. That's what it says in the dictionary.com link as well. It is not necessary for something to be false for the ability to prove it false to exist. That's "The chance of it happening was 100% because it actually happened" levels of word-twisting. I think it's a variety of begging the question, where you assume the outcome in your premises. If the coin flip lands on tails, the chance of it landing on heads was not 0%.
EDIT: Try this - substitute 'testable' for 'falsifiable' and see if that helps ease the dissonance.
No if something is true, it does not have the ability to be proven false. That's the obvious meaning at face value. Your definition is the one that's twisting things up here.
A person with no legs does not have the ability to walk. The implication of your logic is that a person with no legs can walk. Just like how a true statement can be proven false.
The statement also doesn't deal with probabilities. So your probabilistic analogy isn't relevant. When you say something can be falsified that is entirely different from saying that there's a probability something can be falsified.
>EDIT: Try this - substitute 'testable' for 'falsifiable' and see if that helps ease the dissonance.
Why?
Of course it helps. Because you chose a word with a different definition. I already know what you mean. You can leave the word as is, I still know what you mean and it's still logically consistent with your point.
I'm just pointing out the inconsistency with the linguistic aspect of your word choice that leaves it amenable for other people to interpret it differently. The original point is moot. We're talking about a linguistic problem here. Replacing the word is side stepping the original linguistic issue.
The pythagorean theorem is not an example of a falsifiable claim. It is a provable claim, the opposite of falsifiable. Though again, this has nothing to do with it being true or false. Bigfoot married Elvis is likewise a provable claim, a claim where evidence could be presented that would prove it true if it were true. The inverse, Bigfoot did not marry Elvis, is falsifiable, because evidence could be presented that would prove it false if it were false.
There's nothing nonsensical about it. Lots of things are extendable even when they're not extended, foldable when not folded, recyclable when not recycled, and falsifiable when not falsified. The colloquial definition is the same as the formal, you're the only one using it your way.
The lottery yesterday is not winnable by me because it was already won by someone else and because I already lost. That is a fact. That's a valid statement taken at face value. It's not nonsensical at all. There's no subtle word twisting here.
Do you actually go around saying the lottery was winnable after it was already won by someone else? Your example is the one that at face value seems more twisted.
You are also dealing with probabilities. Falsification by the word itself "false" deals with boolean logic. True or false. There is no probability here which you introduced with your "lottery" analogy. It's not really applicable because something can't be false if it has a probability of being true or false.
> Falsifiable doesn't mean proven false, it means able to be proven false, even if it isn't.
Again you're not addressing my point. I know what your definition IS. And I stated before, and I will state again that if we assume your definition is TRUE there is an inconsistency between the word "FALSIFIED" and "FALSIFIABILITY". This is a linguistic problem with your word choice.
But read your own statement carefully. Even your definition doesn't make sense. How can something have the ability to be proven false if it isn't false? That doesn't even make sense. What you mean is that a statement can be tested in attempt to be proved false. I'd be pedantic to hold you to that but I'm not. But I will hold on to the fact that the error you made in your language is a linguistic issue and not one with your logic. The linguistic issue is what I'm referring to here. That's the inconsistency I originally pointed out.
If something is falsified it is false. But by your definition it can be both falsifiable and not falsified and not false. I didn't say that YOUR definition made the statement nonsensical. I said it sounds nonsensical because the face-value definition makes it nonsensical. Which is equivalent to saying any average person will find it to not make sense because they defined the word traditionally while you defined the word differently.
>There's nothing nonsensical about it. Lots of things are extendable even when they're not extended, foldable when not folded, recyclable when not recycled, and falsifiable when not falsified. The colloquial definition is the same as the formal, you're the only one using it your way.
You're not getting it. It's not my way. It's you. You're extremely far away from understanding logic. We can tell from this statement here:
>Though again, this has nothing to do with it being true or false. Bigfoot married Elvis is likewise a provable claim, a claim where evidence could be presented that would prove it true if it were true.
In science and therefore reality as we know it there is no such thing as a provable claim. Nothing in reality can be proven. Falsification is the only methodology available to us. Read the first section here: https://www.wikiwand.com/en/Falsifiability I'll quote it:
"Popper contrasted falsifiability to the intuitively similar concept of verifiability that was then current in logical positivism. He argues that the only way to verify a claim such as "All swans are white" would be if one could theoretically observe all swans, which is not possible."
Which means you can't prove all swans are white. It's impossible. But you can falsify it by finding one black swan.
You'll also note on the same wikiwand page it says this as the second sentence: "A theory or hypothesis is falsifiable (or refutable) if it can be logically contradicted by an empirical test."
By definition a true statement can't be contradicted by an empirical test. So even the formal definition is inconsistent with your claim.
I entirely get how the word is used in the scientific community and what you are referring to but the formal definition here is just a poor choice made by Karl Popper or whoever it was who coined it and it doesn't mesh with the rest of English. It allows for wikipedia to mistakenly have a definition that by logic cannot be applied to true statements. If we just replace some words and apply that definition you get this:
"A true statement that is falsifiable by definition can be logically contradicted in a empirical test"
It can't man, let's be real here, don't twist it.
>Lots of things are extendable even when they're not extended, foldable when not folded, recyclable when not recycled, and falsifiable when not falsified.
Ok this. This is word twisting. It's almost deliberate. Nobody made any statements like this, you twisted the analogies slightly to fit your agenda. Let's make things more accurate here:
If something is can't be folded it is foldable. If something can't be recycled it is recyclable. If something can't be falsified it is falsifiable. These sound contradictory at face value. Ask anyone.
The ORIGINAL claim was this: "All true claims are unfalsifiable by definition."
A true claim is equivalent to a claim that can't be falsified. So I essentially said, "All claims that can't be falsified are unfalsifiable by definition" and you're saying that claim is wrong. Let's be real.
We're getting pedantic here, but ultimately the logic spells out that I'm right.
The leap that I'm raising an eyebrow at is the assumption that GR is applicable "inside" of a black hole. It's a very nice theory: it knows its boundaries. It's a little strange that we're trying to apply it on both sides of those boundaries, given that they are also our boundaries.
I wouldn't go so far as saying that applying GR inside a black hole is like applying GR in a critique of Star Wars, but I do think that that's the sort of distinction we're talking about here. Assuming the consistency of the laws of physics across separate universes might be kid of cool, but it's never going to be as justified as assuming their consistency within the same universe. And that's what the inside of a black hole is, supposing it exists: a separate universe, a place that will never be in our light cone.
(Or, GR is wrong, and we actually can get information from there, which would be interesting too, but I'm assuming for the present that GR will continue to make good predictions.)
EDIT: Oh, and there are people trying to do that, I think, but it's not that easy.
Careful readers and writers will observe that we do not. What physicists actually say is "IF this theory is true, THEN we can say this and that about what lies within a black hole."
Since at the moment we do not have any satisfactory theory that accurately describes black holes, every such if-then statement is known to be flawed, and a careful thinker will recognize these as being exploratory examinations of what theories imply, and a search for testable predictions, rather than dogmatic declarations of the true nature of the universe. Sometimes, for instance, you can explore a theory and determine that it makes contradictory predictions, which means you can toss that one out. Exploring mathematical hypotheses is a perfectly sensible use of research time.
However, careless readers, writers, and thinkers abound.
I think it is the general sense of physicists in general that there probably isn't a singularity in a black hole. There is almost certainly something there that is sensible under some theory. Extreme, sure, but sensible. It is relativity and derived theories that specifically yield singularities, but we also know relativity is not a complete description of the universe.
Even this article, if read carefully, is not saying "black holes do not in the real universe have singularities". It is saying something much more like "Previously physicists have accepted that IF the mathematics of Einsteinian relativity is true, THEN black holes have singularities. However, if you analyze the mathematics more carefuly, this IF-THEN does not in fact follow from the mathematics." It actually isn't a claim about the real universe, which is already known to not be purely described by Einsteinian relativity, but a claim about Einsteinian relativity qua Einsteinian relativity as a mathematical theory.
Of course, the whole reason anyone talks about singularities in black holes at all is precisely Einsteinian relativity in the first place. Quantum mechanics isn't the reason, nor any other alternate Theory of Everything that I know of. So if they are removed there, we are left with no reason to suspect singularities exist in any sense.
That still doesn't mean that we positively know what goes on under the event horizon. It would merely eliminate one "IF relativity THEN singularity" from our current discussion. Still progress in its own important way, but perhaps not as groundbreaking as a popular press treatment might claim.
Second, was general relativity falsified or are you referring to generally accepted speculation? If it was falsified, do you have a source?
I'm not making some whacky fringe claim here; this is actually completely mainstream physics. It just isn't as well understood by the laymen as it ought to be. The previous paragraph is a summary and you can get into lots of nuances and details and such, but in the end the underlying fact remains that at the moment nobody knows how to put relativity and QM together. We have several theories, none proved and all with problems, and there was even a new entrant this very week.
Relativity and QM are two of the best theories we've ever had in the world, in terms of the number of digits of precision they are accurate to... and in some sense that is one of the biggest problems with them. We know they don't go together as written, but to know how to weave them into something that covers both domains correctly, we either need real-world phenomena that they do not correctly predict, or the ability to do experiments in the regime where they disagree (which is why black holes are so interesting to physicists), and we're basically empty handed for both those things.
Could the inside of a black hole be an "observable universe"? I ask because our observable universe is a little smaller than its Schwarzschild radius. Ie could our edges be an event horizon too?
If LIGO is able to retrieve information from the insides of black holes that should be earth-shattering news, no?
Also I'm sure you already know that we can't prove anything to be true either in science and therefore reality, so basically the universe outside of the black hole is full of falsified statements and unprovable statements... and we just assert that some of those unprovable statements are true. For example: general relativity.
"No amount of experimentation can ever prove me right; a single experiment can prove me wrong." -albert Einstein
We can imagine a civilization made up for very sturdy physicists, so tidal forces inside the black hole don't rip them apart immediately. This civilization can enter the event horizon of the black hole, and observe what happens inside, make measurements, new theories, write papers, upload them to pre-prints, go to conferences, etc.
It is true that they cannot communicate with the outside world, but that may not bother them if there's enough of them that they can share their new discoveries with each other and have a society and satisfy their intellectual curiosity.
According to classical general relativity there are no stable orbits inside the black hole, so eventually this society will get arbitrary close to the singularity (or, to extremely large curvatures), so eventually they all would die, irrespective of how sturdy they are.
But this is also true outside the black hole, per our current best theories, we will all either get crushed in a big crunch (reverse of the big bang), or heat death as the Universe expands indefinitely. (Or, sooner, when the sun explodes, or sooner if an asteroid hits us, or global warming, or we nuke each other..)
The person entering the black hole does not perceive time freezing. How could he? Relative to himself he will enter the black hole but for him time outside of the black hole will accelerate at infinite speed well past the heat death of the universe forever in an instant. Then once the universe ends if there is an end, he will cross the threshold and move through the event horizon.
For the outside observer, it seems like nothing enters the event horizon. It seems like everything just gets infinitely close and redshifts and expands, and forms a giant low-energy redshifted enveloping pancake around the black hole.
But, from the perspective of the object passing through the event horizon, none of this happens, she passes through just fine.
Yes, relativity theory is weird as hell.
Yes, but due to the extreme time dilation, will they observe/experience the heat death of the universe prior to entering the black hole?
If so, does it make sense to say they actually enter it in any meaning full sense from the perspective of our existence?
As in 'yes', they will enter the black hole, but they will enter it an infinite number of years from now when our universe "functionally" no longer exists.
Isn't this just another form of a particle with constant acceleration, accelerating to the speed of light? Yes, from their perspective, they reach it, but from our perspective, it will take an infinite amount of time and so we say they never can reach it from either our perspective or theirs? I don't see how this can be any different. Gravity is a constant accelerator.
(And note I'm calling out the constant acceleration case above for approaching 'C', not the increasing acceleration requiring 'exponentially increasing energy each second' case).
The person falling into the black hole will have time in the outside universe accelerate relative to him. It will get faster and faster and when he hits the event horizon we don't know what happens as that's the singularity where the math no longer works. We can speculate that time actually freezes but that leads to paradoxes.
It's true that infalling observers will experience outside time speeding up, and conversely outside observers will see infalling objects slow down. In fact, as they approach the Event Horizon, they would appear to experience diverging time dilation. So in effect, they become "frozen in time". But remember that you can always maintain two-way communication with light. The very fact that both the outside observer can always see the infalling person and the infalling person can always see the outside world imply there can be two-way communication all the way up to crossing the event horizon (which would take infinitely long for the outside observer). This ought to be enough to conclude the infalling person can in fact never reach the event horizon.
And the infinite passage of all external time is observed in a finite time by the infalling observer. All of the communication from the external observer is going to become a high frequency chirp at the event horizon, and the last message the infalling observer could send will take nearly an infinite amount of time to reach the external observer. And in the next instant of subjective time by the infalling observer they will be past the event horizon and unable to communicate any more.
If you have a classical black hole and you don't bother yourself with how it forms, though, there's no paradox, the paradoxical effects arise because the areas of space-time become completely unreachable and you're using coordinate systems which are not local.
From the perspective of the observer nothing enters the black hole. This is true.
From the perspective of the person entering the black hole he does enter it. It's because of time dilation.
Both of these statements are true according to theory as far as I know.
Side note, I watched this almost B movie called "time trap" and I feel like falling into a black hole would be just like the end of that movie. It really made me want to jump in a black hole.
The black hole evaporates at a finite speed relative to the outside observer. So someone falling in will by logic see this evaporation speed accelerate.
Before he touches the event horizon the black hole should have completely evaporated already so time never actually "freezes".
That's an interesting solution and resolves the paradox. When the black hole evaporates the reference frames become consistent again.
Sure, there's no evidence for this (yet?). But it'd be a nice solution to the paradox.
Itm similar to science fiction where time loops resolve through circumstance. If you go back in time to stop your birth you will inevitably instigate your birth instead of creating a paradox.
I'm this case if you try to freeze time by going into the black hole the black hole will inevitably be destroyed before you can get close enough to it to encounter the singularity.
What works did Edward Witten do?
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.
Struggles with the Continuum, https://arxiv.org/abs/1609.01421
Lots of issues spring from unphysical assumptions like continuous quantities, point-like objects and infinities. Quantum mechanics was the first step towards more discrete formalisms, and I think future physics will take further steps in this direction to eliminate these issues.
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://news.ycombinator.com/item?id=38370118
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://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?
Would recommend.
Anyway here's another of her video which might be related to the one linked above: https://www.youtube.com/watch?v=-HHv3T4UHec
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.
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.
A non-point mass only approximates to a point mass when you're not inside it. The gravitational effect of being inside a shell is nothing... so as d tends to zero the mass that's not a shell also tends to zero, so you actually get zero force.
I would note that reality is vacuously what reality is, regardless of model agreement. This however doesn’t mean reality isn’t weirder than we observe. That’s usually the first lesson you learn as you move beyond Newtonian physics.
Only if you have a point mass. There is no reason to believe that point masses exists, it all being fields makes more sense. Einstein himself scoffed at the idea of such singularities existing, so those singularities aren't part of the core theory, just one of the possible results. (Not saying Einstein has to be right here, just that he didn't envision such singularities to exist when he created the theory)
Why shouldn’t there be others?
For example, it is eternal, it's not the result of a collapse solution. As far as I know, no one has an analytic solution yet for black hole collapse of say a star in finite time.
For an outside observer, in fact I believe an infalling object into a black hole is never observed to reach the event horizon at all. Since the infalling object could communicate (using light) with the outside observer, there's a sense in which they must agree on whether the object has or hasn't crossed the event horizon -- in this case, the non-observation of crossing the event horizon must not be just apparent, because of this communication.
Since event horizons couldn't form in this case, then it should follow that a black hole cannot gain mass at all. I've yet to see a satisfactory debunk of those claims, at least at a level I could understand.
But that does not mean that reality does not also break down.
But reality as we normally experience it breaks down!
Advances in cosmology and physics have broken generations of our perceived realities.
What does that mean, though? Reality just is.
Our equations are just models of reality. They aren't reality.
And even if so, then what is the alternative? As far as I know, in terms of our knowledge of physics and philosophy, there is not a current alternative. We have no choice but to build models. We have no way of knowing what reality is.
If you're inside a planet, the layer of the planet that's farther from the center than you cancels out. So you need to take only the sphere that's deeper than you. By moving closer to the center, that sphere shrinks, so m2 also diminishes to 0.
So the total force magnitude smoothly reduces to zero the closer you get to the center.
Seems perfectly reasonable, if a bit useless.
If you somehow made a spherical hole in the middle of the earth and placed a cup of water inside the hollow (anywhere inside, doesn't have to be the centre) it will just sit there: Newtonian gravity is 0 inside a uniform spherical shell of mass. (Einsteinian gravity is probably mostly 0 but you'll get frame dragging effects if the shell is rotating I would imagine.)
You can do the maths to prove this yourself if you want.
In the ISS the air pressure is artificially kept at a certain level. To make a proper comparison, you should check what water would do outside of the ISS.
The context of my original comment was someone expecting that a cup of water at the centre of the earth would explode due directly to gravitational effects. This is wrong, as I pointed out.
Even on the surface of the earth it is the air pressure that prevents the water boiling off instantly, not gravity itself. On the surface of the earth that air pressure is due to the effect of gravity on the atmosphere, but you can supply that air pressure by a number of other means in other places. The air pressure inside the ISS is not there due to gravity after all! I suggest to you that if we can posit a hole at the centre of the earth, then we can fill it with air at 1atm if we want to - we are in the realm of mathematical models here, not reality after all :)
Moving the experiment to a zero-gravity environment doesn't change the pressure considerations much.
>If you’re surrounded by an equal amount of mass in every direction
Which is a reasonable approximation for being 'out in space', but perhaps not an entirely intuitive one.
And never mind the pressure from all of the mass around you ;)
I usually use a small drill to get around it. Works every time.
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
That's wrong. If you actually stick to newtonian physics (because the picture changes completely in GR), then you can define the potential arbitrarily at infinite distance. Since a body with finite density will see a finite variation in gravitational potential, you could just define the potential at infinity such that it is zero at its lowest point by adding a constant. That's because forces in physics arise from the potential field's gradient - not the field itself. So any constant will just disappear in the derivative. Now, if you go to GR, the story becomes a lot more complicated, since gravitational potential energy isn't even well defined.
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.
No. The "distortion" doesn't prevent things from falling in; it helps things to fall in. The event horizon, heuristically, is the point at which the "helping things to fall in" becomes strong enough that even outgoing light can't overcome it.
There are many complexities that this type of model will not account for and it's worth noting that higher dimensional geometries don't "play nice", in that your visual intuitions will mislead you. Such as the stretchy fabric model is a 2D spacetime fabric stretching into a 3rd dimension that is otherwise not accessible by those flatlanders who experience a pulling force but do not see where that fabric is stretching into. Similarly we can not think of a black hole (or any mass) as a 3 dimensional version of a hold because it is "stretching" into higher dimensions, but the result of this distortion is the gravitational force we feel. Even this is a great oversimplification. If it helps you can think instead think of gravity as an inter-dimensional spaghetti monster that invisibly grabs everything and the closer you are to it the harder it is able to pull (just like you!). That might help remind you that the analogy is incomplete and unrealistic at some level.
I'd generalize the abstracted phenomena here and make sure that when anyone is listening to a scientific explanation they understand that it is incomplete (compared to the level of current understanding or prevailing hypotheses/theories). Truth has a lower limit in complexity and often the complexity is rather high. Physicists __love__ simple theories (they call it "elegant") and the whole goal is to make things as simple as possible. But obviously that threshold is rather high considering the level of math physicists do. So keep that in mind when hearing explanations because if it can be explained to your grandma, you're losing a lot of information. Even if as distilled as possible. (Also, Einstein never said if you understand something you can explain it to a layman. Not sure where that came from but it is a silly notion without addendums akin to what has been said here)
So take analogies for what they are, but do not rely on them as complete or even "good enough" models. They're explanatory aids, not explanations. Maybe scientists can do better on this, but it's a tough job already and requiring being a scientific communicator (to the masses) is too high of an expectation. Scientists are still people too and our brains are small and time is limited. We can only do so much lol
Also keep in mind that from the perspective of someone falling in, there's nothing particularly noticeable as you cross the event horizon.
Only relative to static observers, i.e., observers who are hovering at a constant altitude above the horizon. But there is no such observer at the horizon, so no observer ever sees the infalling object going past them at the speed of light.
> So to external observers they slow down.
No, that isn't the reason they appear to slow down to external observers. This is curved spacetime and you can't use your intuitions from Special Relativity, since that is only valid in flat spacetime.
The reason the infalling object appears to slow down to an external observer is that the light it emits takes longer and longer to get back out to the external observer, because of the way spacetime is curved.
> I think of black holes as onions, everything approaches the event horizon and then (to external observers) get frozen at the edge, until the black hole gets bigger.
This view is wrong. Things fall into the hole. They don't pile up at the horizon. They appear to slow down as they approach the horizon, but that is an optical illusion created by the curvature of spacetime.
The dilation gets pretty extreme, you could watch suns be born and die as you fall in.
So I've heard that before, but let's say you are slowly spiraling into a supermassive black hole with very low tidal forces near the event horizon. You get close to the event horizon. Light can't escape. You stick your hand into / past the event horizon. Seems like a pretty definite discontinuity in "noticeability", if one second you can see your hand and move it around, and the next you can't see it and can't yank it back.
Now if you are falling in your hand never disappears, it's just that your body would accelerate into the black hole a little faster than your hand is accelerating because you are pulling back on your hand. But your hand never could have a negative velocity (moving away from the blackhole) no matter what you do.
That wouldn't really happen. When people say that light cannot escape, they don't mean that a beam of light can't pass the horizon heading outwards, they mean that the curvature of spacetime is such that the photons will always curve back around and fall back into the hole.
Locally, the horizon will look more or less the same to you, except at high curvature you'll start to see Doppler shift of light from outside vs. inside. At extreme curvature, an arm pointed towards the singularity will look red shifted and an arm pointed away from the singularity will look blue shifted. Although at this level of curvature, you'd already be ripped apart so you wouldn't really notice anything at all.
Space isn't distorted at the event horizon and you wouldn't notice any effects from crossing it - other than no longer being able to see the outside universe.
Technically, in GR gravity is the distortion of spacetime, it does not have independent existence that acts on spacetime. It's mass that distorts spacetime.
> SQS and SQG do purport to describe the interior topology of black holes.
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?
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.
Also if you invert time, black hole behaves differently.
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.
This article explains the context and what’s being proposed:
https://bigthink.com/starts-with-a-bang/singularities-dont-e...
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.
From whose perspective? Two astronauts, a watcher and a faller, have two very different experiences.
> Do the photons nearer the center pull away from the photons further out?
I believe their wavelengths increase toward infinity. They don't move more quickly away from one another but, rather, become red shifted.
But I'm just a layman so my guess is as good as yours.
Right, that's sort of my point. If the experiences differ outside the event horizon, they must differ even more inside the horizon. Imagine Astronaut "A" who is closer to the horizon gets pulled in first, and is accelerating faster than Astronaut "B" outside the horizon.
Once A is inside the horizon, B can never interact with A again. I would assume this is true even after B crosses the horizon later on -- they both accelerate but tidal forces keep them moving further and further apart. Even though both are inside the horizon and heading in the same direction (center), at no point do they ever slow down or "catch up" to each other. B still can't interact with A, as A was infinitely redshifted already. Would seem they're always cutoff from each other.
> I believe their wavelengths increase toward infinity. They don't move more quickly away from one another but, rather, become red shifted.
Red shifted from the point of an observer looking towards the center of the black hole (anyone looking away from the center sees the outside universe blue shifted).
Red shifted light from far away stars implies an expanding universe. Wouldn't red shifted light looking at the center of a black hole imply that the space between the observer and the center of the hole be increasing as well??
So increasing wavelength = increasing curvature = space expansion?
I guess my naïve interpretation is that, while you can never get out of the black hole (you can't outrun the pull towards the center), at the same time you can never hit the center as things closer to it get further and further away from you. Would seem to me that there is expansion of space inside a black hole, maybe it's this that prevents a true singularity from forming?
> 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?
In that model, yes. If you take GR literally (and personally I wouldn't), space itself is distorted and matter falling in falls infinitely far. (There is an argument that this itself prevents a true singularity from ever forming: there is an eternally collapsing pseudosingularity that is getting smaller and smaller and denser and denser, but the denser it is the more time-dilation it undergoes and so the collapse can never finish in finite time, at least for an outside observer).
> 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?
You can't really talk about photons in the context of GR, but yes, from the perspective of an infalling observer, light from an entity behind you gets increasingly redshifted and eventually the two of you are accelerating away from each other faster than light can reach, like a "big rip" in minature.
> 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?
From the outside it's a point. But from the inside it's an infinitely large volume of space. (Again, if you take GR literally)
> From the outside it's a point.
If I understand what you're saying, it's that from the outside it wants to be a point, but can never quite get there in (our) finite time. So we just see a big red shifted "frozen in time" black hole event horizon. Evaporates maybe in the future, but point is we never actually get a singularity on our side of the horizon.
> From the inside, it's an infinitely large volume.
This makes sense to me, more than a singularity existing. On the inside everything is ripped apart as space infinitely expands.
So doesn't this imply there is no singularity on either side of the event horizon then?
It's as if the "wanting" to be a singularity on our side of the horizon is countered/balanced by frozen time. And on the other side of the horizon, from the particles point of view you can't freeze time. So instead the singularity is countered by infinitely expanding space to prevent just this sort of thing from happening. Is this some sort of relativistic time/space conservation law?
It's like the extreme gravity trying to create a particle singularity just ends up expanding the space between the particles instead. Hmmm. We know that at relativistic speeds, trying to accelerate a particle to C leads to time slowing down. In this case too much gravity trying to create a singularity leads to space expansion instead?
Are these just two sides to the same coin. Frozen time = infinite space depending on your relativistic point of view??
Sort of like the cosmic censorship hypothesis, just extended from "no naked singularities exist" on our side of the universe, to "no singularities exist" on the other side as well.
Did I get that right, or did I butcher it?
Right. Bear in mind that's only one school of thought, and not the most mainstream one.
> Is this some sort of relativistic time/space conservation law?
> Are these just two sides to the same coin. Frozen time = infinite space depending on your relativistic point of view??
Separation is Lorentz invariant. But there's no general theorem here AFAIK, at least not a known one, though the behaviour certainly rhymes.
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.
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!
* ”airquotes”
* "whatever nineteenth century"
* "low density" .. "engineering"
My read is that he is disappointed that certain lines of research that could have come from his original publication of the black hole solution that is named after him, did not actually get pursued by the community. He describes at least some of them in the paper. Unfortunately, for reasons that I have pointed out elsewhere in this discussion, I don't think the kinds of models he appears to be interested in are actually viable physically, however interesting they might be mathematically.
None of this is obvious to physicists, so if it is to you I'd suggest publishing.