Should be pointed out that this is a critique of common popsci journalism tropes and not a fancy new research result. Anyone who has taken a graduate level class in General Relativity would have been able to tell you the same.
Or read Susskind's "The Theoretical Minimum: General Relativity". For a non-spinning blackhole at least, not only is the singularity not a point, it is a surface in time, not space (as the book explains, the space and time coordinates switch places as you cross the event horizon).
it might help to think of the singularity as not a point in space but rather a future that cannot be avoided. All possible paths through space and time, no matter what happens, will go towards the singularity.
Because it's very misleading. Time and space do not switch places past the event horizon. What happens is that the direction/path between an object and the singularity becomes a timelike dimension, and the direction that plays the role of time outside of the event horizon becomes a spacelike dimension. That is not the same as them swapping or that time becomes space and space becomes time not to mention that space has 3 dimensions and time has only 1 dimension so how could they even swap places.
Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time, specifically the amount of time left before you reach the singularity. It's not so mind blowing when you interpret it that way now is it? You can imagine many things in ordinary life that you use to measure time without claiming that time has literally swapped places with it. On a road trip, the number of kilometres to your exit tells you how long you have left, that's using space as a proxy for time... big deal. The notable difference between a road trip and a black hole is that on a road trip you could stop for a break, you could maybe take a detour, you could decide to go back home... and these would all break your use of space as a proxy for measuring time. Well with a blackhole you can't do any of those things, there is no going back, there is no detour, the relationship between the spatial direction towards the singularity and time is fixed and causal and there's nothing you can do about it.
The phrasing used is used almost certainly to evoke some kind of voodoo mind-blowing mystery that completely disappears when you get down to the more strict formalism.
> Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time
That's not correct. There is a relationship between the radial coordinate r you are at and the time it will take you, by your clock, to reach the singularity (at least assuming you are freely falling), but that relationship can't be described the way you are describing it.
To put the issue with what you say as starkly as possible: at any event inside the black hole's horizon, there are spacelike curves in every direction from you that will hit the singularity! So "the direction in space between you and the singularity" is not even well-defined.
To be clear, you are right that Susskind's statement is very misleading (I posted my own criticism of it upthread).
Am I understanding this right by thinking - if I was walking toward the black hole past the event horizon, and then I turned around, I would still be walking toward the black hole?
Once you pass the event horizon, every direction leads to the singularity in your future. Directions "away" from the singularity may still visibly show what things looked like outside of the event horizon before you fell in, but that is from your past. Heading in that direction will not get you back there anymore, you will only find the singularity along that path in your future.
Kerr spacetime contains closed timelike curves inside the inner horizon. You can reach them from the outside universe, but you can't escape back out.
Also, the region inside the inner horizon of Kerr spacetime is widely considered to be not physically reasonable, not just because of the closed timelike curves, but because the inner horizon itself is unstable--there is an infinite blueshift there which, it is believed, would cause it to be destroyed by the first tiny bit of incoming matter or radiation.
> if I was walking toward the black hole past the event horizon, and then I turned around
Note that, once you're inside the horizon, you can't "turn around" and go back outside again. You're inside the hole for good.
And once you're inside the hole, yes, no matter which direction in space you move, you're moving "towards" the singularity. But a better way to look at it is that the singularity is a moment of time, not a place in space. You're moving "towards" the singularity in the same sense as you're moving "towards" next Tuesday. You can't stop moving towards next Tuesday by changing which direction in space you move. The same is true for the singularity once you're inside the hole's horizon.
You can't turn around though. Everything goes toward the black hole. If you turned around, atoms would be moving away from, or at the least changing their direction in respect to the black hole. And that's not possible. You wouldn't even see anything because all light is going toward the center, and it wouldn't go into your eyes.
Unless you went in butt-first, but the path of the photons would have changed and would now be going toward the black hole, and everything would look probably all smushed together.
It's unfortunately misleading shorthand for what actually happens: space becomes timelike. It doesn't become time. All this means is that once you cross the event horizon, you can only ever move toward the center of the black hole, in the same way that outside of a black hole, you can only ever move toward the future. You might not take a direct route to the center, but no matter which way you move, you will be following a track that ends at the center.
The reason this phenomenon has a spooky-sounding name is that it also affects whether two objects can be causally connected. If you can only ever move closer to the center of the black hole, then there are (conceivably) other objects inside the event horizon that you can never have a causal relationship with.
But it doesn't mean that space and time literally switch places.
> the space and time coordinates switch places as you cross the event horizon
If Susskind's book does in fact say that, it's extremely disappointing to me, because, as a number of other GR textbooks will tell you (e.g., Misner, Thorne & Wheeler and Wald, the two great classic GR textbooks), the "switch places" is an artifact of a particular choice of coordinates (Schwarzschild coordinates), and does not represent anything physical. So it's not something that should be relied on. (Not to mention the confusion it causes when pop science sources repeat the statement and then draw all manner of wrong conclusions from it.)
The part about being "a surface in time" might be all right, assuming that by that he means "a surface representing a moment in time, not a place in space"--in more technical language, a spacelike surface. That is correct, and it's an invariant that does not depend on any choice of coordinates. But that invariant fact can be described without having to talk about the "switch places" thing at all.
Susskind's book does also mention that the event-horizon shenanigans are due to coordinates and not a physical thing. Certainly I'd trust what he says rather than me, so sorry if I was misleading.
(If anyone has the book, it is chapter 6 section "Interchange of Space and Time Dimensions at the Horizon" and the following section points out the singularity is a time (and you can't escape it (in a Schwartzschild model at least) just like you can't escape time). I'm sorry if my wording is still incorrect.).
Kruskal-Szeres coordinates indeed get rid of the wonky coordinate stuff at the event horizon, but if you look at the corresponding diagrams, you'll just end up with the same confusion, because the singularity is still a point (or rather surface) in the future instead of a point in space. The issue is that these diagrams are for eternal, static black holes, which cause diagrams to have these weirdly stretched infinite regions that are quite useful for understanding details of the math, but are highly confusing to laypeople. In fact these diagrams make it look like you'll always fall into the black hole at t=infinity, no matter how far you are away, when in reality you could orbit a static black hole pretty close for eternity.
If you really want to get a picture of what is happening, you can look at Eddington-Finkelstein coordinates. In particular at a light cone field diagram around a collapsing shell of matter that turns into a black hole. Then this whole stuff suddenly makes sense without even going into the math. You don't just see how an event horizon can form out of nothing, you also see how gravity starts to bend your causal forward light cone (i.e. all points in spacetime with events that you could interact with in the future) inward in such a way that you will necessarily always fall closer to the center of the mass once you pass a certain line (aka the event horizon). No need to deal with those weird infinities or points in time suddenly lying on a different axis.
The great Roger Penrose (the same guy who also came up with some of the most confusing diagrams) published a beautiful, simple overview of exactly this stuff in Scientific American: https://www.wkbpic.com/wkbx/SA/1972/1972-05-01.pdf (starting on page 38)
Still one of the best things you can read if you don't just want the math.
This doesn't seem meaningfully different to me? Like the notion that the singularity is always in your future (because you can't escape it anymore past the event horizon) makes sense, the point of confusion is what are the implications?
Roughly the general public (including me) knows that gravity is meant to have some effect on the apparent passage of time, so it seems significant but under explained what it means to be in a region of space where all possible directions lead to the singularity.
It's not just that it's always in your future in the sense that you can't avoid it. It's that the reason you can't avoid it is that it's a moment of time, not a place in space. You can't avoid it for the same reason you can't avoid tomorrow. And which direction in space you move has no effect on whether or not you reach the singularity for the same reason it has no effect on whether or not you reach tomorrow.
>the notion that the singularity is always in your future makes sense
But it is just a mathematical artefact of weirdly chosen coordinates. In reality, the singularity is still just a point in space (or a line in spacetime), except that inside the event horizon all paths you are allowed to travel lead to it. There's no need for this whole "space turns into time" notion apart from the fact that you are guaranteed to hit it in *your* future as a local observer. And in Eddington-Finkelstein coordinates you can easily see that globally, things simply hit the spatial coordinates of the singularity at certain slices of coordinate time. Other coordinate systems make this whole process seem much more weird than it is.
> it is just a mathematical artefact of weirdly chosen coordinates.
No, that's not correct. The fact that the singularity is always in your future inside the horizon is an invariant, independent of any choice of coordinates.
> the singularity is still just a point in space
No, it's not. A point in space would be a timelike line in spacetime. But the singularity is a spacelike line in spacetime. That's a moment of time, not a place in space.
> There's no need for this whole "space turns into time" notion
That's true; that notion is an artifact of Schwarzschild coordinates. But that does not imply the other claims you are making.
> the spatial coordinates of the singularity
I'm not sure what you mean by this. It's true that, since the singularity is a spacelike line, you can treat a coordinate that varies along it as a "spatial" coordinate marking different spatial points on the singularity. But the singularity itself is a moment of time (as above, a spacelike line), so it is not a "place", and it does not have a particular set of "spatial coordinates". A spatial coordinate marking different points along the singularity is marking different points in space at a moment of time.
Just draw the geometry in Eddington Finkelstein coordinates and you will see everything I wrote above is true at the technical level if you read precisely.
No, everything you wrote is not true, in Eddington Finkelstein or any other coordinates. You wrote that the singularity is a point in space. It's not, no matter what coordinates you choose. It's a line in spacetime, but it's a spacelike line, and a spacelike line cannot describe a point in space. It can only describe a moment of time. No choice of coordinates can change that. (Similar remarks apply to your claim that the singularity always being in your future once you're inside the horizon is an artifact of a coordinate choice. It's not. It's just as true in Eddington-Finkelstein coordinates, or any others.)
That also makes your use of the term "spatial coordinates" questionable, as I already pointed out. The fact that the line r = 0 is vertical in an Eddington-Finkelstein spacetime diagram does not mean it's automatically a "point in space" or that r inside the horizon is automatically a "spatial coordinate". You need to look at the actual physics, not just the surface appearance of the diagram.
>You wrote that the singularity is a point in space
Because it is. Remember: space, not spacetime. Hence the remark in brackets in the original comment and my reminder to read precisely in the other one. And in Eddington Finkelstein it is most obvious that it is a point in space (i.e. it has spatial coordinate r=0 where r has the metric signature of a spatial dimension) that you can hit at various points in (global) time (and actually also in free falling observer time, but let's ignore that since it is not immediately obvious). You can literally trace incoming light rays crossing the event horizon and hitting the singularity at r=0 at a certain points in time in the diagram. This stuff is really not that weird once you choose less confusing coordinates. It only gets weird once you start asking what local observers can actually see, because from their perspective their relation to all other coordinates in spacetime gets really messy. That's probably where 95% of the confusion among laypeople comes from. But for that you can still resort to other coordinates which show it much better.
Sorry, you're just repeating the same wrong statement. I know you said "space", and I already explained that a spacelike line in spacetime cannot be a point in space. It can only be a moment of time.
You are quite correct that, since the singularity is a line in spacetime, different incoming light rays (or free-falling observers, for that matter) can hit it at different points. Depending on how you choose your coordinates, you can set it up so that those points have different "time" coordinates. But that doesn't make the singularity a point in space. It means you're running up against relativity of simultaneity--whether or not different events on a spacelike line (or more generally a spacelike surface) happen at the same time depends on your choice of coordinates. You can, in fact, choose coordinates in which all events on the singularity happen at the same time (for a "time" coordinate that is genuinely timelike--see below). The standard Penrose chart does that, for example.
You are also correct that a good choice of coordinates can make it easier to see certain properties of a spacetime geometry. But it can also make it harder to see other properties. In this case, your choice of Eddington-Finkelstein coordinates is making it harder for you to see why your claim that the singularity is a point in space is wrong, and why the things I said above are true.
For example, inside the horizon, the Eddington-Finkelstein "time" coordinate that you are using is not timelike. It's spacelike. In other words, it's not actually a "time" coordinate (even though it's labeled as such). It is actually a "space" coordinate! You should be able to see this by observing that the singularity is a spacelike line, and in E-F coordinates it's a vertical line--i.e., the only coordinate that changes along it is the "time" coordinate. That means the "time" coordinate must actually be spacelike there.
And, for extra confusion, the r coordinate in Eddington-Finkelstein coordinates is also spacelike, even inside the horizon (unlike in Schwarzschild coordinates, where it becomes timelike). So in this chart there is no coordinate that is timelike inside the horizon! That means any timelike curve inside the horizon must have more than one coordinate in this chart that changes along it (in the simplest case, a radial timelike curve, both the "time" and r coordinates must change along the curve).
> the singularity is still a point (or rather surface) in the future instead of a point in space.
It's a spacelike line on the Kruskal diagram, yes.
> The issue is that these diagrams are for eternal, static black holes
The full Kruskal diagram is, yes. But the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse of a massive body. That includes the singularity being a spacelike line, and there being spacelike curves inside the horizon that are infinitely long.
I agree that Eddington-Finkelstein coordinates can help with intuitions about this spacetime geometry as well.
It also is in Schwarzschild coords, so you've gained nothing with respect to the original issue from switching coordinates. Kruskal-Szeres really is only useful for demonstrating that the event horizon is not such a weird place, but it does nothing for the singularity at the center.
>the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse
The issue is even the limited diagram doesn't really show you that and the full one goes crazy with white holes. So not a good place if you don't want to confuse laypeople.
True--indeed, the statement that it's a spacelike line is an invariant, independent of any choice of coordinates. But it's a lot harder to see that in Schwarzschild coordinates.
> Kruskal-Szeres really is only useful for demonstrating that the event horizon is not such a weird place, but it does nothing for the singularity at the center.
I disagree, and I think many GR physicists would as well. Indeed, both classic GR textbooks, Misner, Thorne & Wheeler (1973) and Wald (1984) discuss Kruskal coordinates and their associated spacetime diagram (MTW in Box 31.2 and sections 31.5 and 31.5, Wald in section 6.4), and those discussions contain a good deal more than just showing that the horizon is "not such a weird place".
This article is great but the references to gravitational waves as if they were an observed fact (in 1972) was mystifying to me. It led me down a rabbit hole to Joe Weber, who is name-checked at the end of the Penrose article.
The way Brian Cox puts it, a singularity is a point in time: the end of time.
I have trouble really conceptualizing black hole physics, I just think of it as a mass so great that nothing, including light, can escape its gravity. Works for me.
The more interesting component is that black hole physics is almost an anti-free will zone.
Everywhere else in the universe with mass and energy you can do what you want (sort of). An event horizon throws a hard shroud over that and drastically reduces opportunities: your free will to use mass and energy is significantly curtailed (you must head towards the singularity).
The singularity in a non-rotating, non-charged black hole is as you say. It’s like in a finite amount of time you “run out of time”, like there isn’t any more time on that trajectory.
The singularity in a rotating black hole is entirely different but the interior of classical Kerr (rotating) black holes is one of the most controversial if inconsequential topics in theoretical physics because there are reasons to believe (without real proof mind you) the Kerr solution is unstable inside the inner event horizon so that whatever happens in there is not what that theory says.
And of course black holes are quantum objects which might actually have an “interior” entirely different from the classical picture.
If it signifies the end of time, then all the stuff in the black hole would need to no longer exist no? If anything is happening in the black hole, then time is still progressing, so nothing must be all that exists?
Time is change that happens in a continuous manner. It’s still possible to conceive of change happening in an unordered unpredictable way that is not like the smooth ordered time that we experience.
In a gravitational singularity spacetime breaks down. You could argue that time stops, but it’s also valid to argue that causality breaks down and we can no longer make any predictions about the future. Just because we don’t have a theory describing what could happen, doesn’t rule out that something could happen.
I think it's not even a valid critique of that and it's sort of playing games with what the definition of a singularity is to reach the claim that it's making. I think the topology of the singularity is not even a well defined question and certainly not well understood enough to bear the strong claims in the paper.
This is the opinion of most physicists, yes, but it does not in any way justify the GP's claims or cast doubt on anything that is said in the paper. Note that the paper talks explicitly about the limitations of GR as the singularity is approached and how a quantum gravity theory, if we ever find and confirm one, might fix those issues.
Unfortunately you are wrong. Everything the paper is saying about the singularity and its properties in GR, and more generally about the black hole solutions it describes, is well understood and has been for decades. The definition of "singularity" that the paper is using is perfectly fine, and its topology is perfectly well-defined. A good textbook treatment is that of Wald (1984).
Some of the things the paper points out are not emphasized in other sources, which is probably why the authors chose to write it. But there is nothing in the paper that is in the least questionable or ill-defined; it's all standard General Relativity as applied to the Schwarzschild and Kerr black hole solutions.
As someone with basically only popsci knowledge of black holes: people claiming it would be a literal point never made much sense - fundamentally, common sense (as much as it can apply here) dictates that you cannot compress particles to an absolute point.
Kind of, but not really.. though there are simple models with electrons as a point charge, a more accurate model involves the electron field describing the probability of an electron existing at any region in space (not to be confused with the electromagnetic field, the medium in which photons propagate).
Sure the position of an electron is not definite, but neither is that of a buckyball, but a buckyball has a shape we can describe, an internal structure we regard as extended over space, in a way that is separate from the indeterminacy of its center of mass position. This is unlike an electron, for which, if we set aside the uncertainty as to its center of mass, my understanding is that the only internal degrees of freedom it has left (in the Standard Model) are its spin and whether it is left or right handed, with no other structure to it.
It is in this sense that, AIUI, electrons are modeled as point particles.
Of course, that doesn’t mean that if we zoom in enough, probing at higher and higher energy scales, that it can’t turn out to have some non-zero fundamental size outside of just uncertainty in its center of mass position. I think string theory would say that at the string scale it would be a string.
But, AIUI, no experiment has shown it to have the kind of extent that would make it be called not a point particle (an extent in a sense beyond just uncertainty in COM position)
If you really treated them as points the theory would blow up because the electrostatic potential energy of a point charge is infinite. This is dealt with by “renormalization” which is roughly: assume the theory isn’t really valid all the way to a zero length scale and that we can average out everything that happens below some cutoff size and that it doesn’t really matter where we place the cutoff because the theory works the same if you change the cutoff and change the other parameters accordingly.
They are, but there are some interesting theories about their internal structure. Be aware that this is probably junk science but I have currently been enjoying this effort to describe them via the em field.
Points are a realist view - there's a real object there.
Although some physicists disagree, QM slants very anti-realist. There are no objects anywhere, no particles, no waves, only probabilistic interactions, some of which can be snapshotted into localised partially definite results.
So there are only interactions between probability distributions in space and time, and "particle-like events."
QM slanting anit-realist is because some prominent physicists like Neils Bohr gave the math that interpretation, and they were more persuasive than the realists like Einstein, Schrodinger, Everett.
The agnostic view is it's just a mathematical model that makes accurate probabilistic predictions when measurements are made, which says nothing about what's really going on.
Of course treating particles as points is also mathematical.
Wouldn't it be both? Electrons occupy probability clouds, but the overall probabilities of things happening are summed over the whole cloud as if, at each point, the electron was a point particle at that point?
The question of "what holds it up?" is where that leads to. There's an interesting history of answering that question again and again - and the discovery of new types of stars each time.
A kugelblitz is a theoretical astrophysical object predicted by general relativity. It is a concentration of heat, light, or radiation so intense that its energy forms an event horizon and becomes self-trapped. In other words, if enough radiation is aimed into a region of space, the concentration of energy can warp spacetime so much that it creates a black hole. This would be a black hole the original mass–energy of which was in the form of radiant energy rather than matter
Rather than compressing particles, would you have difficulty with converting it to incredibly large amounts of energy that wraps space time into a singularity? If you packed enough photons into one spot, that energy would curve space time enough to form a black hole.
>Rather than compressing particles [...] If you packed enough photons into one spot
I haven't watched the video, but if we're compressing electrons, neutrons, or other fermions, I imagine if we want to keep compressing that down to an arbitrarily small radius, won't we pretty quickly find it favorable to shift those fermions to something else, probably photons, to respect Pauli exclusion?
Really, I don't know enough physics to figure out the reason why it shouldn't always end up in this incorporeal energy-curving-space situation either way, if we're compressing arbitrarily far.
But then you "fill up all the photon slots" too (not literally because they are not fermions, but they do spontaneously convert back into things like electrons at that density) and you can work around the Pauli exclusion principle by stacking your electrons at higher and higher energy levels.
Pauli exclusion isn't an impenetrable force field - as you say, it's just often more favourable to do something else than to work around it. Consider an iron atom with however many electrons though - all those orbitals except the inner one are electrons working around Pauli.
Common sense cannot be trusted on matters like these. Common sense is calibrated for reasoning over matters encountered in daily life. The further away we get from that, into more and more exotic phenomena, the less common sense can apply. Black holes are very far from the domain of common sense.
I always suggest looking at the quantum eraser experiment to see how bad common sense works with quantum mechanics. It's fairly simple but intuition fails most people when it comes to explaining how it works.
No need for funky stuff, just do the classic (lol) Young's slits experiment which should be more than enough oddness for anyone.
I was shown it at school, using microscope glass slides that we waved over a Bunsen burner running cold, to coat with soot. We then carefully etched parallel lines with a compass by hand. Our (~17 y/o) efforts were a bit random but we did get some smudgy banding results on the screen.
It was the '80s so safety razor blades were available but in a posh public school (UK version) aged ~17, compasses were everywhere and large old style razor blades were not - the modern style razor with one or two thin blades was a thing. We could have probably got some needles from matron for a finer point, than a compass.
Common sense - the experience gained from your common everyday experience of reality - does not apply in black holes.
Common sense would tell you they can't exist at all because you can't compress atoms - you have lived your entire life with atoms being entirely incompressible for the practical purpose of anything you do.
Leaning on common sense to discuss fundamental physics has been wrong since round about the start of the practice of physics.
Common sense actually says that atoms don't exist and if you squish cheese really hard you just get really hard and slightly smaller cheese, or maybe you invent a new type of dairy product.
My rather pop-sci understanding is that when you start playing around with relativity math, trying various masses and densities you hit something rather worrisome. As you approach some great, but still possible, value the plot goes infinite, the singularity. This is bad for the theory because going asymptotic like that usually indicates a fundamental problem in the math. But relativity does so well everywhere else... What if it could? And thus the black hole was born.
The easy thing to miss, and blew my mind when I read it. is that general relativity is the concept of space-time, emphasis on the time, and this is also compressed by the mass, so if this singularity can actually occur it would also take an infinite amount of time to fall into it. So nothing can actually enter it. From the point of view of an astronaut(deliberately ignoring all the other relativistic implications) flying directly toward the event horizon. As you approach you will quickly see the rest of the universe age and die. and if hawking radiation is real the black hole will evaporate in front of you before you can reach it.
Does time accelerate just for the astronaut approaching the black hole (meaning they would be witnessing the future) or does it accelerate for everyone (meaning approaching a black hole is going to make everything end quicker)?
My rather limited understanding is that. first there is a lot going on and due to the forces and gravitational gradients involved, matter itself probably would not survive the journey that close to the horizon. But ignoring that, When in compressed time, from the point of view of someone freefalling, timewise everything is normal, the rest of the universe has accelerated and in the case of a black hole has just aged out and died but you are fine. from the external point of view they are taking forever to get there.
Where my imagination fails(above my pay grade) is in the face of infinity, what are the implications of infinite time compression?(everything happens at once?)
I can only guess as well, infinite time compression might result in a big bang when it applies to everything. All black holes could lead to the same moment causing the bang.
There are a lot of curious coincidences between properties of black holes and properties of the whole universe that lead some physicists to the idea that they could be connected. There's also that Penrose diagram showing another universe beyond a black hole. (Seems like a copout to me though. Penrose diagrams are drawn in 1D space, so the black hole cuts the universe in half. If you had 2D or better space couldn't you just travel around behind the black hole to the other side of it?)
Time acceleration is dependent on the gravitational flux.
All objects within a given radius of the black hole (possibly modulo spin) would experience the same time dilation. Remote objects in the universe would not experience the dilation.
From the perspective of the astronaut falling toward the singularity, the rest of the Universe would age at an ever-increasing rate.
From the perspective of a remote observer, the astronaut falling toward the singularity would be experiencing time at an ever-decreasing rate.
The notion of relativity is that time-perception is relative, and dependent on acceleration, whether from motion (as on a spaceship) or from gravitational acceleration (as near a black hole). Objects in orbit around Earth, further from Earth's centre, and hence subject to reduced gravitational acceleration, age more quickly than objects on Earth's surface. This is actually measurable using atomic clocks, though the effect is quite small. It is sufficient that GPS satellites require time correction.
If outside observers could watch the astronaut clearly, the astronaut would look like they're slowing down to a stop at the event horizon. The astronaut would not see themselves freezing in time, but they would see everything outside of the black hole speed up.
You could travel arbitrarily far into the future by getting close to a black hole's event horizon for a while without crossing it and then leaving, assuming you had the energy for it and you didn't get obliterated by all the mass and energy falling into the black hole in that timeframe.
I believe this is a misunderstanding based on inadequate coordinate systems, and that an astronaut would fall through the event horizon, die, and reach the singularity in finite time.
AFAIK from the outside point of view it takes infinite time. We see the falling object redshift to infinity (blackshift, really) and merge into the black sphere we observe.
But in the object's own time coordinates the math says it does hit the singularity. If you fell in you wouldn't die of old age before you hit it.
A particle is a region of space where it's probable that a certain kind of interaction will happen. I don't see any reason why they can't overlap infinitely and then squeeze to the Dirac delta function: certain to be here, no error bars. That is, apart from the Pauli exclusion principle. But you have to leave that one behind if you're dealing with masses beyond the TOV limit.
Of course I'm missing something here. I've taken QM and not GR so I would have this interpretation.
And if they didn't form a superconductor. I'm not sure why they would but if they did they would violate it. That's actually what makes superconductors superconducting - the really weird state where electron pairs act like bosons.
It's a complete violation of good sense to invoke common sense here. You talk about "particles" but that's not what the world is made of. Also, particle/wave duality. Also, any number of bosons can occupy the same position. Also black holes evaporate. And on and on.
I figure at least some of it comes from the idea that mathematically, a singularity is a point (e.g., in the graph of z=1/w, there is a singularity at the point w=0, and in the graph of z=(1-w)²/(1-w) there is a removable singularity at w=1 (that is, the function is undefined at w=1, but if you put a point at (1,0), the graph will be continuous and no longer have any holes in it). The fact that both have the same name and the similar behavior of a black hole singularity to a mathematical singularity¹ can lead people to make an incorrect assumption.
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1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.
They don't just have the same name, they are the same thing.
A Schwarzschild black hole has both: a removable singularity at the event horizon that is just an artefact of a particular choice of coordinates and a true non-removable mathematical singularity at r=0 where curvature really does go to infinity. It also wouldn't be much of an issue in classical physics, because this singularity is always hidden from outside observers, so the mathematical weirdness there can't screw with your normal predictions in space outside the black hole. The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions. This has opened a whole can of worms with a bunch of solution attempts, which are all sadly untestable for the foreseeable future.
OSM - slight generalization of Schwarzshild BH, where you take evolving spherically-symmetric mass distribution instead of point mass - shows that point singularity in the middle can be naked (aka observable), so it's not just QM that causes worms...
It is not difficult to construct geometries with naked singularities. Reissner, Nordström, Weyl and others individually came up with one long before Oppenheimer. You can also construct geometries where faster than light travel is possible. But all of these suffer from fundamentally unphysical energy conditions. Quantum mechanics may change the picture because it allows weirder energy states than normal physics because everything fluctuates. But it is unknown if and how this actually affects gravity.
> The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions.
How is this any different than classical? Isn't it still just an ~impossibility hidden behind an event horizon in either model?
With our current understanding, baryon and lepton number are not conserved as a black hole radiates. I think this is a better demonstration of the incompatibility with classical and quantum mechanics.
Baryon and lepton number conservation are what's called "accidental symmetries" in the standard models, meaning there is no real underlying symmetry that would conserve them. In fact many extensions of the Standard Model don't, while still retaining unitarity. The problems already start once you try to calculate any time evolution of anything, because the Hilbert operator not being unitary means that everything breaks. Even the total energy in a closed system might vanish or blow up to infinity. You can't calculate anything under these conditions.
This is like saying the Riemann zeta function is only defined for real numbers. You can always extend the singularity mathematically by incorporating new axioms.
My point is, it’s not super meaningful to argue whether a black hole has an inside.
Even without quantum mechanics, black holes are trouble:
Approximately everything in nature rotates. Including black holes. Schwarzschild blockholes do not rotate. Rotating black holes are much more complicated and don't necessarily shield their singularity behind an event horizon.
Rotating black holes are described by Kerr geometries and have more than one event horizon, but still have their singularities hidden from anyone outside behind their inner horizon.
> 1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.
Well, the Ricci curvature scalar blows up to infinity, which is obviously unphysical.
The curvature scalar can be physically evaluated by measuring the volume of a small ball of freely falling test particles and comparing to its volume in flat spacetime.
If this unbounded state were asymptotic then it wouldn't be unphysical, but a freely falling particle reaches the singularity in finite time. A freely falling observer crossing the event horizon could in principle perform this measurement as they approached the singularity, and general relativity could no longer describe their measurements.
Okay — you’re still not explaining what actually breaks, just repeating they could measure over and over.
Please say what you specifically believe is unphysical about the situation — what trajectory reaches the singularity in finite time and why specifically is that unphysical?
My understanding is that you have a cusp singularity that is actually an infinite spike, ie, distance to the singularity is unbounded; that is, no matter how small a circle/sphere around the singularity, you have an infinite diameter. And so you will need to be much more explicit about where the problem lies.
> No complete and precise definition of singularities exist in the theory of general relativity,
So which is it? It can't both be trivial to any grad student but also an open question. And things like naked singularities aren't proven to not exist either.
Also, general relativity is a classical, geometric-only theory. It seems obvious that better understanding what a black hole's singularity is would require quantum mechanics because the singularity is effectively what's "left over" of the physical material once you go beyond a neutron star.
I'm sorry but this is blowing my mind. What???
Also read Nick Gorkavyi: The Oscillating Universe: Einsteinian Cosmology of Black Holes and Gravitational Waves
[1]: https://www.youtube.com/watch?v=O_2vnb_eVGE
Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time, specifically the amount of time left before you reach the singularity. It's not so mind blowing when you interpret it that way now is it? You can imagine many things in ordinary life that you use to measure time without claiming that time has literally swapped places with it. On a road trip, the number of kilometres to your exit tells you how long you have left, that's using space as a proxy for time... big deal. The notable difference between a road trip and a black hole is that on a road trip you could stop for a break, you could maybe take a detour, you could decide to go back home... and these would all break your use of space as a proxy for measuring time. Well with a blackhole you can't do any of those things, there is no going back, there is no detour, the relationship between the spatial direction towards the singularity and time is fixed and causal and there's nothing you can do about it.
The phrasing used is used almost certainly to evoke some kind of voodoo mind-blowing mystery that completely disappears when you get down to the more strict formalism.
That's not correct. There is a relationship between the radial coordinate r you are at and the time it will take you, by your clock, to reach the singularity (at least assuming you are freely falling), but that relationship can't be described the way you are describing it.
To put the issue with what you say as starkly as possible: at any event inside the black hole's horizon, there are spacelike curves in every direction from you that will hit the singularity! So "the direction in space between you and the singularity" is not even well-defined.
To be clear, you are right that Susskind's statement is very misleading (I posted my own criticism of it upthread).
You can avoid a coordinate, for example by choosing not to go there, or revisit another one repeatedly.
A black hole on the other hand doesn't have that: you cannot revisit old locations - attempting to do so moves you closer to the singularity.
Also, the region inside the inner horizon of Kerr spacetime is widely considered to be not physically reasonable, not just because of the closed timelike curves, but because the inner horizon itself is unstable--there is an infinite blueshift there which, it is believed, would cause it to be destroyed by the first tiny bit of incoming matter or radiation.
Note that, once you're inside the horizon, you can't "turn around" and go back outside again. You're inside the hole for good.
And once you're inside the hole, yes, no matter which direction in space you move, you're moving "towards" the singularity. But a better way to look at it is that the singularity is a moment of time, not a place in space. You're moving "towards" the singularity in the same sense as you're moving "towards" next Tuesday. You can't stop moving towards next Tuesday by changing which direction in space you move. The same is true for the singularity once you're inside the hole's horizon.
Unless you went in butt-first, but the path of the photons would have changed and would now be going toward the black hole, and everything would look probably all smushed together.
The reason this phenomenon has a spooky-sounding name is that it also affects whether two objects can be causally connected. If you can only ever move closer to the center of the black hole, then there are (conceivably) other objects inside the event horizon that you can never have a causal relationship with.
But it doesn't mean that space and time literally switch places.
If Susskind's book does in fact say that, it's extremely disappointing to me, because, as a number of other GR textbooks will tell you (e.g., Misner, Thorne & Wheeler and Wald, the two great classic GR textbooks), the "switch places" is an artifact of a particular choice of coordinates (Schwarzschild coordinates), and does not represent anything physical. So it's not something that should be relied on. (Not to mention the confusion it causes when pop science sources repeat the statement and then draw all manner of wrong conclusions from it.)
The part about being "a surface in time" might be all right, assuming that by that he means "a surface representing a moment in time, not a place in space"--in more technical language, a spacelike surface. That is correct, and it's an invariant that does not depend on any choice of coordinates. But that invariant fact can be described without having to talk about the "switch places" thing at all.
(If anyone has the book, it is chapter 6 section "Interchange of Space and Time Dimensions at the Horizon" and the following section points out the singularity is a time (and you can't escape it (in a Schwartzschild model at least) just like you can't escape time). I'm sorry if my wording is still incorrect.).
That's good. However:
> Interchange of Space and Time Dimensions at the Horizon
This still seems misleading to me, because "Dimensions" makes it seem like it's not just an artifact of coordinates--but it is.
If you really want to get a picture of what is happening, you can look at Eddington-Finkelstein coordinates. In particular at a light cone field diagram around a collapsing shell of matter that turns into a black hole. Then this whole stuff suddenly makes sense without even going into the math. You don't just see how an event horizon can form out of nothing, you also see how gravity starts to bend your causal forward light cone (i.e. all points in spacetime with events that you could interact with in the future) inward in such a way that you will necessarily always fall closer to the center of the mass once you pass a certain line (aka the event horizon). No need to deal with those weird infinities or points in time suddenly lying on a different axis.
The great Roger Penrose (the same guy who also came up with some of the most confusing diagrams) published a beautiful, simple overview of exactly this stuff in Scientific American: https://www.wkbpic.com/wkbx/SA/1972/1972-05-01.pdf (starting on page 38)
Still one of the best things you can read if you don't just want the math.
Roughly the general public (including me) knows that gravity is meant to have some effect on the apparent passage of time, so it seems significant but under explained what it means to be in a region of space where all possible directions lead to the singularity.
It's not just that it's always in your future in the sense that you can't avoid it. It's that the reason you can't avoid it is that it's a moment of time, not a place in space. You can't avoid it for the same reason you can't avoid tomorrow. And which direction in space you move has no effect on whether or not you reach the singularity for the same reason it has no effect on whether or not you reach tomorrow.
But it is just a mathematical artefact of weirdly chosen coordinates. In reality, the singularity is still just a point in space (or a line in spacetime), except that inside the event horizon all paths you are allowed to travel lead to it. There's no need for this whole "space turns into time" notion apart from the fact that you are guaranteed to hit it in *your* future as a local observer. And in Eddington-Finkelstein coordinates you can easily see that globally, things simply hit the spatial coordinates of the singularity at certain slices of coordinate time. Other coordinate systems make this whole process seem much more weird than it is.
No, that's not correct. The fact that the singularity is always in your future inside the horizon is an invariant, independent of any choice of coordinates.
> the singularity is still just a point in space
No, it's not. A point in space would be a timelike line in spacetime. But the singularity is a spacelike line in spacetime. That's a moment of time, not a place in space.
> There's no need for this whole "space turns into time" notion
That's true; that notion is an artifact of Schwarzschild coordinates. But that does not imply the other claims you are making.
> the spatial coordinates of the singularity
I'm not sure what you mean by this. It's true that, since the singularity is a spacelike line, you can treat a coordinate that varies along it as a "spatial" coordinate marking different spatial points on the singularity. But the singularity itself is a moment of time (as above, a spacelike line), so it is not a "place", and it does not have a particular set of "spatial coordinates". A spatial coordinate marking different points along the singularity is marking different points in space at a moment of time.
That also makes your use of the term "spatial coordinates" questionable, as I already pointed out. The fact that the line r = 0 is vertical in an Eddington-Finkelstein spacetime diagram does not mean it's automatically a "point in space" or that r inside the horizon is automatically a "spatial coordinate". You need to look at the actual physics, not just the surface appearance of the diagram.
Because it is. Remember: space, not spacetime. Hence the remark in brackets in the original comment and my reminder to read precisely in the other one. And in Eddington Finkelstein it is most obvious that it is a point in space (i.e. it has spatial coordinate r=0 where r has the metric signature of a spatial dimension) that you can hit at various points in (global) time (and actually also in free falling observer time, but let's ignore that since it is not immediately obvious). You can literally trace incoming light rays crossing the event horizon and hitting the singularity at r=0 at a certain points in time in the diagram. This stuff is really not that weird once you choose less confusing coordinates. It only gets weird once you start asking what local observers can actually see, because from their perspective their relation to all other coordinates in spacetime gets really messy. That's probably where 95% of the confusion among laypeople comes from. But for that you can still resort to other coordinates which show it much better.
You are quite correct that, since the singularity is a line in spacetime, different incoming light rays (or free-falling observers, for that matter) can hit it at different points. Depending on how you choose your coordinates, you can set it up so that those points have different "time" coordinates. But that doesn't make the singularity a point in space. It means you're running up against relativity of simultaneity--whether or not different events on a spacelike line (or more generally a spacelike surface) happen at the same time depends on your choice of coordinates. You can, in fact, choose coordinates in which all events on the singularity happen at the same time (for a "time" coordinate that is genuinely timelike--see below). The standard Penrose chart does that, for example.
You are also correct that a good choice of coordinates can make it easier to see certain properties of a spacetime geometry. But it can also make it harder to see other properties. In this case, your choice of Eddington-Finkelstein coordinates is making it harder for you to see why your claim that the singularity is a point in space is wrong, and why the things I said above are true.
For example, inside the horizon, the Eddington-Finkelstein "time" coordinate that you are using is not timelike. It's spacelike. In other words, it's not actually a "time" coordinate (even though it's labeled as such). It is actually a "space" coordinate! You should be able to see this by observing that the singularity is a spacelike line, and in E-F coordinates it's a vertical line--i.e., the only coordinate that changes along it is the "time" coordinate. That means the "time" coordinate must actually be spacelike there.
And, for extra confusion, the r coordinate in Eddington-Finkelstein coordinates is also spacelike, even inside the horizon (unlike in Schwarzschild coordinates, where it becomes timelike). So in this chart there is no coordinate that is timelike inside the horizon! That means any timelike curve inside the horizon must have more than one coordinate in this chart that changes along it (in the simplest case, a radial timelike curve, both the "time" and r coordinates must change along the curve).
It's a spacelike line on the Kruskal diagram, yes.
> The issue is that these diagrams are for eternal, static black holes
The full Kruskal diagram is, yes. But the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse of a massive body. That includes the singularity being a spacelike line, and there being spacelike curves inside the horizon that are infinitely long.
I agree that Eddington-Finkelstein coordinates can help with intuitions about this spacetime geometry as well.
It also is in Schwarzschild coords, so you've gained nothing with respect to the original issue from switching coordinates. Kruskal-Szeres really is only useful for demonstrating that the event horizon is not such a weird place, but it does nothing for the singularity at the center.
>the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse
The issue is even the limited diagram doesn't really show you that and the full one goes crazy with white holes. So not a good place if you don't want to confuse laypeople.
True--indeed, the statement that it's a spacelike line is an invariant, independent of any choice of coordinates. But it's a lot harder to see that in Schwarzschild coordinates.
> Kruskal-Szeres really is only useful for demonstrating that the event horizon is not such a weird place, but it does nothing for the singularity at the center.
I disagree, and I think many GR physicists would as well. Indeed, both classic GR textbooks, Misner, Thorne & Wheeler (1973) and Wald (1984) discuss Kruskal coordinates and their associated spacetime diagram (MTW in Box 31.2 and sections 31.5 and 31.5, Wald in section 6.4), and those discussions contain a good deal more than just showing that the horizon is "not such a weird place".
A Fleeting Detection of Gravitational Waves
https://physics.aps.org/story/v16/st19
Gravitational wave blues
https://aeon.co/essays/how-joe-weber-s-gravity-ripples-turne...
I have trouble really conceptualizing black hole physics, I just think of it as a mass so great that nothing, including light, can escape its gravity. Works for me.
Everywhere else in the universe with mass and energy you can do what you want (sort of). An event horizon throws a hard shroud over that and drastically reduces opportunities: your free will to use mass and energy is significantly curtailed (you must head towards the singularity).
If you don’t have enough upward velocity to escape earths gravity, hitting the ground is also inevitable.
The singularity in a rotating black hole is entirely different but the interior of classical Kerr (rotating) black holes is one of the most controversial if inconsequential topics in theoretical physics because there are reasons to believe (without real proof mind you) the Kerr solution is unstable inside the inner event horizon so that whatever happens in there is not what that theory says.
And of course black holes are quantum objects which might actually have an “interior” entirely different from the classical picture.
In a gravitational singularity spacetime breaks down. You could argue that time stops, but it’s also valid to argue that causality breaks down and we can no longer make any predictions about the future. Just because we don’t have a theory describing what could happen, doesn’t rule out that something could happen.
Some of the things the paper points out are not emphasized in other sources, which is probably why the authors chose to write it. But there is nothing in the paper that is in the least questionable or ill-defined; it's all standard General Relativity as applied to the Schwarzschild and Kerr black hole solutions.
It is in this sense that, AIUI, electrons are modeled as point particles.
Of course, that doesn’t mean that if we zoom in enough, probing at higher and higher energy scales, that it can’t turn out to have some non-zero fundamental size outside of just uncertainty in its center of mass position. I think string theory would say that at the string scale it would be a string.
But, AIUI, no experiment has shown it to have the kind of extent that would make it be called not a point particle (an extent in a sense beyond just uncertainty in COM position)
https://quicycle.com/understanding-electrons/
And the video essay on the subject https://www.youtube.com/watch?v=hYyrgDEJLOA (Huygens Optics: Williamson & Van der Mark electron model | Are electrons made of light?)
Although some physicists disagree, QM slants very anti-realist. There are no objects anywhere, no particles, no waves, only probabilistic interactions, some of which can be snapshotted into localised partially definite results.
So there are only interactions between probability distributions in space and time, and "particle-like events."
No pointy objects, and no need for them.
The agnostic view is it's just a mathematical model that makes accurate probabilistic predictions when measurements are made, which says nothing about what's really going on.
Of course treating particles as points is also mathematical.
History of the Universe : What Is Hidden In The Core Of A Neutron Star? - https://youtu.be/YoYjkNQ27T8
That video goes into it... without getting mathy at any point.
One of the bits that you're having trouble with is the compression of matter to a point. There's a theoretical type of black hole known as a kugelblitz - https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics)
Rather than compressing particles, would you have difficulty with converting it to incredibly large amounts of energy that wraps space time into a singularity? If you packed enough photons into one spot, that energy would curve space time enough to form a black hole.I haven't watched the video, but if we're compressing electrons, neutrons, or other fermions, I imagine if we want to keep compressing that down to an arbitrarily small radius, won't we pretty quickly find it favorable to shift those fermions to something else, probably photons, to respect Pauli exclusion?
Really, I don't know enough physics to figure out the reason why it shouldn't always end up in this incorporeal energy-curving-space situation either way, if we're compressing arbitrarily far.
Finding a tame enough special case was how Hawking discovered his radiation.
Pauli exclusion isn't an impenetrable force field - as you say, it's just often more favourable to do something else than to work around it. Consider an iron atom with however many electrons though - all those orbitals except the inner one are electrons working around Pauli.
I'm not a physicist either.
I was shown it at school, using microscope glass slides that we waved over a Bunsen burner running cold, to coat with soot. We then carefully etched parallel lines with a compass by hand. Our (~17 y/o) efforts were a bit random but we did get some smudgy banding results on the screen.
Your pair of razor blades is a great solution.
Common sense would tell you they can't exist at all because you can't compress atoms - you have lived your entire life with atoms being entirely incompressible for the practical purpose of anything you do.
Leaning on common sense to discuss fundamental physics has been wrong since round about the start of the practice of physics.
That's because a lot of the ordinary mass in the universe is ionised or in other weirder states.
The easy thing to miss, and blew my mind when I read it. is that general relativity is the concept of space-time, emphasis on the time, and this is also compressed by the mass, so if this singularity can actually occur it would also take an infinite amount of time to fall into it. So nothing can actually enter it. From the point of view of an astronaut(deliberately ignoring all the other relativistic implications) flying directly toward the event horizon. As you approach you will quickly see the rest of the universe age and die. and if hawking radiation is real the black hole will evaporate in front of you before you can reach it.
Where my imagination fails(above my pay grade) is in the face of infinity, what are the implications of infinite time compression?(everything happens at once?)
So time is localised? I’m not sure what localised time means but I’m hoping the question makes sense.
All objects within a given radius of the black hole (possibly modulo spin) would experience the same time dilation. Remote objects in the universe would not experience the dilation.
From the perspective of the astronaut falling toward the singularity, the rest of the Universe would age at an ever-increasing rate.
From the perspective of a remote observer, the astronaut falling toward the singularity would be experiencing time at an ever-decreasing rate.
The notion of relativity is that time-perception is relative, and dependent on acceleration, whether from motion (as on a spaceship) or from gravitational acceleration (as near a black hole). Objects in orbit around Earth, further from Earth's centre, and hence subject to reduced gravitational acceleration, age more quickly than objects on Earth's surface. This is actually measurable using atomic clocks, though the effect is quite small. It is sufficient that GPS satellites require time correction.
You could travel arbitrarily far into the future by getting close to a black hole's event horizon for a while without crossing it and then leaving, assuming you had the energy for it and you didn't get obliterated by all the mass and energy falling into the black hole in that timeframe.
See https://physics.stackexchange.com/questions/82678/does-someo...
But in the object's own time coordinates the math says it does hit the singularity. If you fell in you wouldn't die of old age before you hit it.
Of course I'm missing something here. I've taken QM and not GR so I would have this interpretation.
What do you mean by “particle” here? This kind of handwaving is fundamentally classical, and breaks down in the presence of quantum physics.
And if they didn't form a superconductor. I'm not sure why they would but if they did they would violate it. That's actually what makes superconductors superconducting - the really weird state where electron pairs act like bosons.
⸻
1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.
They don't just have the same name, they are the same thing.
A Schwarzschild black hole has both: a removable singularity at the event horizon that is just an artefact of a particular choice of coordinates and a true non-removable mathematical singularity at r=0 where curvature really does go to infinity. It also wouldn't be much of an issue in classical physics, because this singularity is always hidden from outside observers, so the mathematical weirdness there can't screw with your normal predictions in space outside the black hole. The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions. This has opened a whole can of worms with a bunch of solution attempts, which are all sadly untestable for the foreseeable future.
https://en.wikipedia.org/wiki/Oppenheimer–Snyder_model
How is this any different than classical? Isn't it still just an ~impossibility hidden behind an event horizon in either model?
My point is, it’s not super meaningful to argue whether a black hole has an inside.
So does spacetime exist in some frames of reference but not others because those frames disagree on the radius of the apparent event horizon?
Also note that in general an event horizon doesn’t require a singularity.
What I’m trying to say is that there is nothing special about the region of space near the event horizon.
Approximately everything in nature rotates. Including black holes. Schwarzschild blockholes do not rotate. Rotating black holes are much more complicated and don't necessarily shield their singularity behind an event horizon.
why does it matter that it is not 'visible' for anyone?
If a problem is not able to influence anything, even in theory, then by definition, it cannot possible influence any testable predictions we have.
Well, the Ricci curvature scalar blows up to infinity, which is obviously unphysical.
https://en.wikipedia.org/wiki/Scalar_curvature#Relation_betw...
Please say what you specifically believe is unphysical about the situation — what trajectory reaches the singularity in finite time and why specifically is that unphysical?
My understanding is that you have a cusp singularity that is actually an infinite spike, ie, distance to the singularity is unbounded; that is, no matter how small a circle/sphere around the singularity, you have an infinite diameter. And so you will need to be much more explicit about where the problem lies.
You say that and yet this thread is full of people arguing about it, and there's an entire Wikipedia article on this: https://en.wikipedia.org/wiki/Gravitational_singularity.
In fact, that article says:
> No complete and precise definition of singularities exist in the theory of general relativity,
So which is it? It can't both be trivial to any grad student but also an open question. And things like naked singularities aren't proven to not exist either.
Also, general relativity is a classical, geometric-only theory. It seems obvious that better understanding what a black hole's singularity is would require quantum mechanics because the singularity is effectively what's "left over" of the physical material once you go beyond a neutron star.
What do you mean by not exist? If you postulate the right black hole with a naked singularity, it would have a naked singularity.
> It seems obvious that better understanding what a black hole's singularity is would require quantum mechanics
If you postulate a classical black hole, it won't require quantum mechanics to understand.