The math is very difficult. More difficult even than that. When ever you are trying to explore the consequences of General Relativity, it is necessary to make some simplifying assumptions. Schwarzschild started with several such assumptions. First, he assumed a completely static system, one that doesn’t change with time. Second, that the mass in the system was spherically symmetrical. He also put the center of the black hole at the origin, and so on. All of these assumptions are there to make the math easier; they’re like using spherical cows in high school.

What Schwarzschild found was that this solution had two singularities. There was a singularity at the origin, and a singularity some distance away from the origin, at a radius which is proportional to the mass of the object. In both cases, some term of Einstein’s equations become infinite, and therefore seem to stop describing reality.

A couple of years later other physicists proved that by changing the coordinate system in a certain way, that second singularity would go away. That is, this singularity was merely an artifact of one of the simplifying assumptions that Schwarzschild started with, and didn’t represent any real feature of a real black hole. But the radius at which that singularity occurred is still relevant: it tells you how big the event horizon is.

Penrose and Hawking proved that the singularity at the center of the black hole cannot merely be a mathematical artifact. Penrose got his Nobel prize for that.

> Is the math referring to the center of gravity as the singularity? Because even a sub black hole mass object would have that.

Yes, the singularity at the center of a black hole is coincident with its center of mass. But not every center of mass is a singularity. Remember, we only have a singularity if some term of Einstein’s equations for General Relativity goes infinite. In a normal object nothing is infinite at the center of mass. That only starts to happen once the object is compressed into a black hole.

> Why is there an assumption that just after a mass becomes a black hole the matter inside it suddenly compresses further when the actual gravity of the object has only slightly increased?

There isn’t. This is the most common _conclusion_, based on the math. It’s not a starting assumption.

> Is there a maximum density of matter in the universe and if the black hole even reaches that?

Unknown. A neutron star is the densest object that can exist which doesn’t have an event horizon. Get any denser, and an event horizon forms which completely hides whatever happens next.

> Wouldn't you need that number to be infinite if the black hole itself is infinitely small?

Sure, if the mass all falls into the singularity, then the density of the singularity is infinite. There’s really no problem with that.

> If the black hole does have a mass inside it... Do the light particles trapped inside the black hole form a blanket around the existing matter?

This is a non–sequitur. It’s meaningless.

What is really going on here is that mass bends spacetime. This causes our path through spacetime to bend as well. All the gee–whiz effects of relativity, like time dilation, are a result of this bending. Time passes slower for an object moving quickly because its path has been bent so much that it is passing through less of the time dimension than it would otherwise. Light is moving so fast that it doesn’t pass through time at all; from the perspective of the photon no time at all passes between when it was emitted and when it was absorbed, no matter how far it traveled through the intervening space between those events.

Inside the event horizon of a black hole, the path of every object is bent towards the singularity. They’re bent so much that time and space swap roles. The singularity is inescapable not because something is dragging you towards it, but because it is literally in your future. From the outside it looks like the singularity is a place, but if you get close enough it becomes a time in your future, beyond which there is no more time. Everything outside the black hole is twisted around into the past, where you can never go. And, unfortunately for you, a stellar mass black hole is not very big. It’s only a few dozen miles to the center, and since we move through time at the speed of light, that is a very short timeline indeed. Your future ends very abruptly, probably faster than thought.

That’s why most people conclude that the matter is crushed into the singularity. How could it resist? You’re not going to brace yourself against the walls of the universe and prevent yourself from being dragged forward into the future, no matter how strong you are.

But, quantum gravity might change that picture slightly. It may be that the distance to the singularity grows the longer the black hole exists. It may in fact grow at the speed of light, meaning that while the volume of the black hole is not infinite, you never actually reach the singularity and go splat. Your time never actually runs out. You can find some lectures by Susskind about this on Youtube if you like.

> > Is the math referring to the center of gravity as the singularity? Because even a sub black hole mass object would have that.

> Yes, the singularity at the center of a black hole is coincident with its center of mass

I don't think this is accurate. Take Schwarzschild for instance: The singularity is not a place in space you can poke with a stick. It's a spacelike singularity, and it lies in the future of any observer unlucky enough to fall into the BH.

To the external observer, the black hole is perfectly spherically symmetrical.¹ The center of mass of a spherically symmetrical object is always right in the center. Right where the singularity would be, if it weren’t for the fact that to the inside observer the singularity is now in the future at the end of time.²

These types of coordinate changes are one reason why the subject is considered so hard.

¹ Except very briefly as two black holes merge. Or in the case of a rotating black hole. Or potentially during the formation of the black hole. But those are all complications and the subject is difficult enough.

² Except for the fact that the singularity might not actually exist if the interior of the black hole is growing without bound in the timelike direction. See ER=EPR.

Ah, but it's not! It's symmetrical in 3D, but not in 4D. So if you move close to the event horizon, the symmetry breaks.

> Time doesn't work inside black holes, we have no clue how that even works or if things are frozen or if it happens instantly. […] This isn't just the time paradox of near light travel, the math says that inside black holes you have an entire different dimension of time instead of our regular one

There is no such thing inside a black hole as "an entire different dimension of time." Yes, by the very definition of an event horizon, the coordinate chart of an observer at infinity cannot extend inside a black hole. Needing multiple coordinate charts is not really unusual, though. The two-dimensional sphere S² also requires at least two charts. All in all, time inside a black hole locally works the way it does outside a black hole. Yes, there might be interesting non-local effects like closed timelike curves but you can also have those outside.

> time inside a black hole locally works the way it does outside a black hole

That doesn't mean that it actually runs though, you can interpret the lack of possible shared reference of time as the black holes time either happens instantly, but also that it never ever happens and everything in it is stuck and time is frozen from our perspective. In the time frozen perspective the singularity would never form, all objects are frozen and never reach it.

Time doesn’t magically freeze inside of a black hole. That is a misunderstanding of what happens to light rays carrying the image of the infalling diver as they approach the event horizon. From the perspective of an outside observer, those light rays are slowed down more and more and light from the instant of crossing the event horizon never actually arrives; it appears to take an infinite amount of time to do so. The mistake is to think that the object is still there, hovering at the event horizon, for an infinite amount of time. The reality is that the diver notices nothing unusual as they cross the event horizon; they may not even be able to tell exactly when it happens. They certainly do not freeze in place forever.

> The reality is that the diver notices nothing unusual as they cross the event horizon

That doesn't mean that he actually crosses it from our reference frame. Relativity is all about understanding that time is relative, that applies here as well, except that there is no connection between the two reference frame unlike regular space, so we can't say anything about how time flows inside of a black hole from our perspective.

Basically what I am saying is, you can't say whether the singularity has actually formed, since your reference frame is just as connected to the instant anything fell into the black hole as it is connected to the end state of the singularity. That makes it just as valid to say that things freeze the instant they touch the black hole as to say that they merge with the singularity the instant they touch it, since both are equally valid viewpoints from our perspective.

You are correct that we just dont know what happens behind event horizont, from our perspective at least. Currently our best theory says nothing from inside can leak out, so in that spirit saying infalling matter ends up in singularity is as based in reality as it transforming into unicorns.

Regardless, its important to keep in mind that this is valid _only_ from our perspective, that from the perspective of infalling matter something _real_ happens, and that real thing that happens is probably not completely disconnected from rules we perceived in our own universe.

Throwing hands up and saying "we cant tell whats inside, so why are we even arguing about what we think happens there" is certainly a way to look at things if your only motivation is to find out whats happening inside, but that is not all we are after. We are trying to use all we currently know to reason about how the inside might look, any possibility, and try to work out backwards what unforseen implications it might have for our reality.

We are not saying that inside blackhole is sigularity, we are saying that, given our understanding of how outside looks, there might be a singularity inside. We also know the math that yields us this singularity is probably wrong (infinite), and actively are trying to figure out whats wrong with it. We are using this imaginated realoty to work backwards what we might have gotten wrong, and perhaps in this case its not even the roght way of thinking to solve this mystery; it just worked for us before, so we trying.

If you figure out whats actually happening there, and find some way to connect it to rules of our universe, everyone will cheer. If its by first discovering new effect in our universe that would elegantly fit into blackholes, or in the stroke of genius come up with a pure theory enlighting some real observations, nobody would care.

Its just when we throw a mass, it keeps going. It makes more sense to think that it goes the same inside blackhole, but maybe not. We just dont know..

> Its just when we throw a mass, it keeps going

You wouldn't feel going through the event horizon of a large black hole, so I see no reason why that mass would somehow just collapse into a singularity.

Also the math for a black hole states that when the black holes density reaches below the density of the universe, the black holes event horizon will expand and encompass the whole universe, meaning matter doesn't even have to fall into the black hole, the black hole could just grow into the matter and then you don't even have a velocity you just have matter entering the black hole.

We know the two above are how the math for black holes work, none of those produce likely singularities, because there is no force compressing that into a singularity. So if singularities exists in black holes, it would just be some of them, and not all parts of the black hole would have to be a part of that singularity.

I am not arguing for certainty of singularity, quite the opposite. I stated that we seriously suspect the math yielding us that singularity is wrong, we just cant figure out anything more correct yet. Personally I think the geometry of spacetime inside blackhole gets all twisted up, bubbling like a boiling pot of water, but my guess is as good (probably worse) than anyone elses.

>when blackhole density falls below the density of the universe

Which one? The outside one? Density of whole universe? Its local surroundings? Are you counting unknown pressures of stuff we, for pure lack of understanding what the hell it even is, call dark energy/mass?

The "blackhole less dense than the rest of the universe" seem like just another mathematical artefact that couldnt, for any reason, exist in real world. Not saying thinking about it is wrong, but imho more could be gained by thinking "well it surely cant exist, so what mechanism are there that stops this", instead of "this math says that, so lets subdue our whole theory to it". Very same scenario as the singularity inside.

Just because math works for something doesnt mean it is like that. In science history we had plenty of equations that worked, until we discovered some edge case where it suddenly didnt. I think its safe to bet interiors of blackholes, or blackholes encompassing whole universe, are prime candidates for such edge cases where our pressumed math models just break down. The fact that our current math models are returning infinities, we are generally accepting that to be the case.

> but imho more could be gained by thinking "well it surely cant exist, so what mechanism are there that stops this"

Well, the universe Schwarzschild radius is massively larger than the universe itself, so math says we live in a black hole. It is true this might be a mathematical artifact, but it could also be how it actually works and the observations we make in our universe and about big bang is how a black hole looks on the inside.

I don't think you should just assume the math is wrong here and throw away those observations of the inside of a black hole. Sure you should be open to that being wrong, but at least to me that is far more believable and interesting to study, then you can try to connect what we observed about the big bang with a black hole etc.

If I go through enough of these forum discussions maybe I develop this long enough, and then maybe I'll take a serious attempt at solving the math to combine the two, since nobody else will do that. I was called a genius by both my physics and math professors, so it is possible I can solve it since I have good intuition for physics and good skills at math, most people who work in physics just have one of those, even though likely I'll fail, but it would be fun to try.

What makes me believe such an attempt could work is that it could lead to a different math for gravity and black holes at small scales, and thus lead to a unified theory of QFT and GR. If I manage to do that then I could convince physicists to adopt the new interpretation of GR. Current attempts of unifying those two has started from the QFT side and tried to incorporate current GR theories, but they all failed. But I haven't seen many try to attempt that from the GR side and unify that with QFT, so maybe that would yield some results.

Anyway, I don't think that professional physicists will solve this, since they are too occupied focusing on publishable results rather than solving the core issue. What I write here isn't publishable, so no physicists would even think about working on it.

It is how GR was invented by Einstein even though he wasn't a physics researcher, sometimes you need a big jump done by an outsider. GR wasn't on anyone's radar when Einstein suggested it, likely it would never have been discovered without Einstein, or at least take centuries. The gravity formula you get from GR doesn't need space time distortions to reproduce, so theoretical physicists would just update the gravity formula to match observations without creating a new interpretation of what that means.

Newtons gravity formula doesn't come with an interpretation, updating it to match new data is exactly what they did with dark matter and dark energy since it is just a formula, so I see no reason why gravity would be any different without Einstein's GR. Black holes would just be a part of that dark matter.

Edit: Anyway, for me it is fun to argue on forums, so that is the best way for me to think and develop theories. Typically I don't really believe what I say, so part of my posts is to find evidence for it and try to convince myself that what I say is true. So I refine things quite a bit in every discussion.

I got a good idea: Nothing ever passes the event horizon, rather as an object gets close to the event horizon the combined Schwarzschild radius of the black hole and the object will at some point cover the object, meaning the event horizon would expand and engulf the object instead of the object moving through it.

This would totally change the math around the event horizons, since then space doesn't need to be connected between the interior and exterior of the hole. The outside of the hole still would work the same, but as the hole bends space to engulf objects rather than objects moving through space to enter the hole you get a very different way to look at the interior.

Not sure how the math for that would work, but it is fun to think about. Also this is obviously true, for any particle that point would happen before it enters the current radius, so the hole expands out, even if it is by an extremely small amount that is still enough to change the math around the event horizon singularity.

Edit: The main thing this changes is that now the particle doesn't have to accelerate to the speed of light as it passes the event horizon, as the event horizon expands to cover it rather than it accelerating through. As you can understand that is a massive change, it means that space inside the black hole could remain sane without breaking GR. The infinite time dilation you get at those gravity levels is why the math for space and time inside of black holes is so strange, remove that and you can get back to sanity.

Then we could assume that the interior of the black hole looks just like our universe, since our universe is smaller than its Schwarzschild radius. Basically we want to show that the interior space time of a black hole can be relatively flat.

The problem to solve then is to calculate what happens at the edge of such a universe, and try to match that with what happens at the edge of a black hole, since those two would be the two sides.

To unify that with QFT you'd have to include the particle collapse (or entanglement if you want to use the many worlds wording), where the quantum field would collapse to where the particle suddenly is inside the black hole instead of outside. I have long theorized that there is no way to unify the theories without using quantum collapses, so black holes could engulf particles via quantum field collapses only.

The math for such collapses isn't fully established though, so it would need to have more theories on the quantum side as well. But at least that means nobody has developed a theory like this yet.

The main calculation would be to calculate the probability of a particle collapsing into the black hole over time, by calculating how large part of the particle field is inside the critical area were it would be inside the new black hole radius. The particle and the black hole would get entangled for a bit where it is both inside and outside the black hole at the same time, and then the field collapses and it is fully inside.

I think that can actually work! Then the black holes event horizon is a natural quantum effect, which could potentially provide the missing link between the two.

> That doesn't mean that he actually crosses it from our reference frame.

This specifically is an incorrect understanding. All events happen in all reference frames. There are no situations where an event that happens in one reference frame fails to happen in another. At worst (or best, depending on how you view it) we can disagree about the _order_ of events, but not which events actually happened.

It’s not that the crossing fails to happen. It’s just that, from the outside it takes an infinitely long time to happen and, for the diver’s perspective, it’s the universe outside that ended really quickly.

There is no disconnection between the interior of the black hole and the exterior. They are smoothly and continuously connected, and the “normal” axis of time blends seamlessly with the “bent” axis of time inside the black hole. That’s why orbits are so weird outside the black hole.

You’re simply wrong about this.

So how long does it take for a thing to enter the singularity as seen from our reference frame? If you say there is no way to answer it, then you say that I am right, so I'd like to see a link to a formula saying how long that takes from our point of view.

I studied up to a masters in physics, I've seen the math, I don't believe there is a way to calculate that, there is no way to compare time inside with time outside.

Edit: I'd love to see such a formula if there is one btw, so if you know there is one please link!

I'm not sure what you mean by "enter the singularity". Once an object has crossed the event horizon, its light rays can no longer reach us. From an outside perspective, the time required would be based on the object's orbit and when it intersected with the event horizon.

When you say "thing", it's more like photons. While thought experiments of a diver falling into a black hole are fun to ponder, nature isn't so gentle.

The corona, tidal forces, magnetic fields--and other factors--would obliterate matter into a stream of subatomic particles and light before crossing the event horizon. So the concept of a "thing" moving inside a black hole is likely misguided.

  It’s been called one of the most extreme physical environments in the universe.
  Strong magnetic fields threading the inner accretion disk extend out of it,
  creating a tenuous, turbulent, billion-degree cloud. Particles in the corona
  orbit the black hole at velocities approaching the speed of light. It’s a source
  of X-rays with much higher energies than those emanating from the accretion
  disk, but astronomers are still trying to figure out its extent, shape, and
  other characteristics. [0]

NASA provides a fantastic overview here [0].

A few resources to check out: Sean Carrol, PBS Space Time, Ask a Spaceman, and Why this Universe are all great resources--and frequently do deep dives into this topic.

[0] https://science.nasa.gov/universe/black-holes/anatomy/

> Time doesn't work inside black holes…

Time and space work exactly the same inside the black hole as outside, they just swap places. One dimension that was spacelike is bent into becoming timelike. Closer to the center becomes further in the future, and outside the event horizon becomes part of the past. The singularity at the center of the black hole is now the literal end of time. Nothing exists past the end of time; you hit that singularity and you cease to exist.

From the outside, all that we can detect is the mass of the black hole. Or rather, all we can detect is some gravity pulling us in, as if there were mass inside. Einstein proved that all gravity is just the curvature of spacetime. Your body is bending the fabric of spacetime right now!¹ When you dive into a black hole, the curvature you are causing is added to that of the black hole, so that the black hole grows exactly as if your mass still existed inside of it. But really you ceased to exist when you hit the end of time at the singularity.

But of course that is how we _used_ to think of it, up until a decade or two ago. As Susskind would say, ER=EPR. Spatial connectivity (which Einstein and Rosen wrote a paper about) is exactly the same thing as quantum entanglement (which Einstein, Podolsky, and Rosen wrote a completely different paper about in the same year). I won’t try to recapitulate one of his lectures (since you can just watch one; see <https://www.youtube.com/watch?v=31fVea8_OAw> for a recent example, but there are others), but the result is that the spacetime inside the black hole grows without bound, and you never actually reach the end of time. You cannot go back, but neither do you go splat. The matter that was once a star is somewhere ahead of you in that growing region of spacetime, forever in your future.

¹ Note all possible “yo mamma” jokes for future reference.

Let me rephrase: The time we measure with our clocks from the outside doesn't apply inside of black holes. There is no way to say whether any singularity has ever formed or ever will form even according to the math, since time inside of them isn't the kind of time we can measure from the outside.

If you go inside of it the math says that now your clock inside of the black hole can still function, but that also means you are no longer connected to time outside of the black hole, so you can't say whether anything actually happens inside of them from our perspective, all the math says is what it would be like for someone inside.

You need to make extra assumptions about what it means to have a disconnected time reference frame to say anything.

> - Why is there an assumption that just after a mass becomes a black hole the matter inside it suddenly compresses further when the actual gravity of the object has only slightly increased?

Yeah, that seems like an important thing to address. Black holes don't even have to be high density, or have much matter in the center at the time of formation. If you arrange enough big chunks of metal into a spherical-shell constellation, then drop them all toward their mutual center, they can reach the threshold to become a black hole before they even start colliding. What happens around that time, and what specifically does "singularity" mean (because I see people using it in very different ways).

> - Is there a maximum density of matter in the universe and if the black hole even reaches that?

> - Wouldn't you need that number to be infinite if the black hole itself is infinitely small?

Black holes are the benchmark for maximum density. The event horizon is always exactly at the limit. By "black hole itself" do you mean something other than the event horizon?

But that maximum density depends on size, smaller things can be denser and bigger things have to be less dense.

> What happens around that time

I can imagine it's something stupidly energetic. If you don't want them turning into a hot ball of neutrons first you're either going to have to spend a lot of energy keeping them apart or they are going to be orbiting a virtual center and it will take far longer for them to reach the center singularity than you expect. This will follow the laws of the 3(+) body problem so you won't be able to calculate a perfect impact, so the birth of the singularity will be shrouded in very high energy particles escaping.

Nature abhors a naked singularity.

It wouldn't be naked, there would be an event horizon.

Even approaching the critical density, barely anything would be escaping.

But if it's really really big, there wouldn't need to be any notable spaghettification.

> If you arrange enough big chunks of metal into a spherical-shell constellation, then drop them all toward their mutual center, they can reach the threshold to become a black hole before they even start colliding.

When I say "black hole itself" I imagine any combination of mass at it's center that provides enough density to form a gravitational pull that will trap light.