"Doesn't the angular momentum of a BH indicate that it is not a singularity, but an extended object?"

No. Electrons have spin, i.e. a form of angular momentum, and they are point-like, which means they don't have an extension.

Moreover, the singularity of a rotating black hole is extended, as it has the shape of a ring.

What rotates on formation of the black hole is mass-energy. Its angular momentum cannot be lost during contraction into the black hole, due to angular momentum conservation. After the mass-energy has dropped below the event horizon, the angular momentum of the object will still be present, but there is no way of knowing what precisely caused it, as no information gets out of the black hole. In particular, we do not have a theory telling us where the mass-energy will go (the singularity is not a part of spacetime) nor what it will turn into (this might be provided by a theory of quantum gravity). Presumably, if the singularity is washed out by quantum mechanics, the result may still be called mass-energy but be of an as yet unknown form (high-density quantum foam?).

K. Kassner ,

That is just a model which brings some results in QED, far from being real.

It would imply that electrons have a diverging mass/energy density.... that is to say that they are black holes themselves, since they are certainly smaller than their Schw radius...

Doesn't the angular momentum of a BH indicate that it is not a singularity, but an extended object?

Firstly if there is some angular momentum then you will have a ring singularity and not a point. So probably you can consider that the mass is rotating. However, when we are outside the event horizon, we can't know really what's happening inside the event horizon. So it's better not to consider the singularity completely in a standard classical way. Just assume that there is a property of blackhole called Angular momentum.

Now Just look at this from a completely different perspective. Suppose there is a spinning top. So it has angular momentum. Suppose there is a really huge blackhole event horizon and the top falls into the black-hole. In the top's coordinate system, it will not even realize that it falls inside the blackhole. it will keep on spinning as it was So it will still have the same angular momentum. Now an oserver who is outside the event horizon initially sees some angular momentum of the top. So after the top falls into the black hole (It will take infinite time in external coordinate system) the same angular momemntun will remain as it can't just vanish.

If angular momentum is conserved, where does the moment of the BH accretion disk go?

Firstly when you are saying that the angular momentum of a black hole is conserved you are not considering any accretion disk. So the angular momentum of the black-hole will be conserved.

Now suppose you are considering a stellar-mass black hole that has some orbiting partner and the black hole is accreting matter from the orbiting star. In such a case, the total angular momentum of the full system will get conserve.

Or suppose, two black hole collide and form a new one. The total momentum of the system will get conserved

It's the total angular momentum that is getting conserved, not the individual black hole angular momentum.

I am not a specialist but after me black holes are different than most think. first thing is that gravity can't escape a black hole.

secondly the singularity is only a process to transform the black hole into a white hole.

thus white holes rotate and spread material. this is the BH angular momentum.

To avoid confusion I must change the phrase

If angular momentum is conserved, where does the moment of the BH accretion disk go?

by

If angular momentum is conserved, where does the moment of the BH accretion disk go when it falls to the BH?

I suposse that the the mentioned ring structure for singularity comes from some black hole model. But it doesn't matter if the singularity is a ring, a disk, or a sphere. The point is that the singularity is not a point and the structure has to support gravitation through some mechanism, surely quantum. Is this correct?

How can a "nothing" have mass, rotate and have angular momentum ??

A very good point. I think the idea that a black hole contains a singularity is a very old conclusion based on the idea of the “pressureless dust” of a collapsing star. The assumption is made that there is no pressure resistance to the collapse and of course the mathematical model results in a singularity. If you take the more realistic assumption that matter such as neutrons cannot be crushed out of existence then the collapse of a star leads to a neutron star. It can then be shown that for neutron stars of greater than 3.4 solar masses an event horizon will form outside the surface of the star.

So it is the neutron star that is rotating as a result of a previous merger of neutron stars/black holes.

Data Black Holes

Richard

We can consider this problem only at the surface of black hole, because the space inside black hole cannot be related to our space-time. The full energy at the surface of black hole is : Mc^2 = Mw + Mv_iu^i, where the first member is the purely gravitational energy and the second member is gravitationally-rottional energy (u_i is the velocity of its motion in the space and v_i is the velocity of rotation).

“…I think the idea that a black hole contains a singularity is a very old conclusion based on the idea of the “pressureless dust” of a collapsing star. The assumption is made that there is no pressure resistance to the collapse and of course the mathematical model results in a singularity…”

- that isn’t so in the standard official physics GR theory. The “singularity” is the concrete solution of the GR equations for some set of concrete specific parameters, i.e. gravitational mass and size [radius of spherical mass] of some material object, when on the having [Schwarzschild] radius “even horizon” surface the equations solution is singular – i.e. the “spacetime curvature” is infinite. So in the spacetime the “black hole in the spacetime” is formed, which has size/radius of the event horizon, and inside the “black hole” it is senseless to say about any “matter”.

Though really fundamentally the postulate in the GR that interactions in the systems “mass-spacetime-mass” are real, and these interactions are really observed gravitational interactions, is fundamentally wrong,

- and so fundamentally nothing can happen, and so nothing happens, with the Matter’s, fundamentally nothing else than, the fundamentally absolute, fundamentally flat, and fundamentally Cartesian, [5]4D spacetime with metrics (cτ,X,Y,Z,ct). Gravity fundamentally for sure is nothing else than the “fourth” – though non-existent in official physics – fundamental Nature force, which is similar in a few traits to the fundamental Nature E/EM force,

- and on the event horizon the Gravity field, though is extreme, changes smoothly, and no singularities exist. At that for extreme masses the Schwarzschild radius is rather large, and so really inside such “black hole” some compact material object is placed.

However that

“… If you take the more realistic assumption that matter such as neutrons cannot be crushed out of existence then the collapse of a star leads to a neutron star. It can then be shown that for neutron stars of greater than 3.4 solar masses an event horizon will form outside the surface of the star. So it is the neutron star that is rotating as a result of a previous merger of neutron stars/black holes.….”

- is really questionable claim; starting from the “an event horizon”, which doesn’t exist, and, at that, now official physics knows practically nothing about “neutron star phase of matter”, and if the “electron degeneracy” pressure rather possibly is rather correctly estimated, including the transition of matter from the “white dwarf” phase into “neutron star” phase, now it is unknown – at what gravitational impact some “neutron degeneracy” becomes to be insufficient to prevent further matter’s compression.

However that isn’t too essential in this case, since the compact objects can have enormous – much more than 3.4 solar masses – mass, as that “SMBH” in galaxies centers are, and so practically for sure “SMBHs” aren’t “neutron stars”,

- but, what is practically for sure is true in this case – the Matter’s basal laws of energy and angular momentum conservation act in this case as well, and the “black holes” rotate having some angular momentums, including this angular momentum increases when the accretion disk matter falls into the compact object.

More see the Shevchenko-Tokarevsky’s cosmological model https://www.researchgate.net/publication/355037416_The_informational_physical_model_cosmology , http://dx.doi.org/10.13140/RG.2.2.11088.64008; though to understand more the model it is necessary to read the whole informational physical model https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics ; https://arxiv.org/abs/0707.4657 ,

Cheers

Dear Javier Soto del Valle,

As others have said, they call it angular momentum based upon what they see outside the black hole. In particle physics they call particle spin angular momentum because they can't explain where the energy comes from to consider it real spin of the particle even though they can count the rotations of a proton.

The same thing is true for black holes IMO. It's spin is real, not just the fantasy of angular momentum. And the black hole's substance is not nothingness as in present theory but a presently unknown form of matter more dense than a neutron star. Although some have called it quark matter, it's substance is a condensed form of the background Zero Point Field, with its primary elements maybe millions of times smaller than a hypothetical quark IMO.

A black hole is where there is no solution to the Einstein equation, i.e. from the point of view of mathematics, this is not a solution, but a lack of meaning. Einstein advocated ridding the theory of singularities.

Preprint Einstein's Last Will

For all the perfection of general relativity, it has a weak point - this is the Einstein equation. His decisions will not obey the conservation law. Its solutions are nonsingular in strong fields. The fact is that Einstein was forced to simplify the equation of the gravitational field. He could not correctly enter into the equation the energy of the gravitational field, which should serve as a source of the field like any other energy.

I managed to solve this problem.

Preprint Gravitational Field Equation and the Structure of Black Holes

Preprint Exact equation of gravity field based on Einstein's separati...

Now the law of conservation of energy-momentum follows from the field equation. Instead of a singularity, there is a region with a catastrophically low speed of light (red line). While Schwarzschild's solution breaks off (blue line).

In fig. dependence of g00 on r/rg

Dear Valery Borisovich Morozov,

Looks like you have formulated some cool equations. Theoretical physics ain't easy as we both know, regards, Fprrest

Thanks for your links, Mr. Morozov.

There is great difficulty in describing the rotation of massive objects. The fact is that when the potentials of the gravitational field are close to the object, the time and speed of light is greatly slowed down. These are values close to zero. So the observed fast rotation actually turns out to be even faster. But there is a limiting speed, this is the speed of light. This limits the observed rotation rate to such an extent that rotating objects can appear stationary.

“…The matter inside a black hole is hugely compressed, very hot and has an immense pressure. It is a quark-gluon plasma (QGP), which is rotating very fast….”

- nobody knows what is the real extremely compact object’s “black hole” matter phase”, however practically for sure that isn’t a “quark-gluon plasma”, at least for large “BH”s, first of all “SMBH”; and the claim that this object is rotating very fast is too questionable as well. Though first time the gravitational collapses remnants indeed rotate fast, however for a lot of reasons the rotation slows. Moreover, the initial fast rotation appears if the collapsed object, say, a star, rotated fast enough; and if the collapsed object didn’t rotate, the remnant, also because of the angular momentum conservation, doesn’t rotate as well.

“... But within the framework of Einstein-Cartan theory (ECT) all your problems can be solved. There are no singularities any longer since there is a repulsive interaction caused by torsion (spin) in ECT which inhibits the formation of singularities. Consequently, the QGP is rotating very fast within a tiny region of space-time.….”

- the “BH” compact object fundamentally cannot be, and so isn’t, some “tiny region of space-time”, whereas really there cannot be any “singularities” in Matter at all. Including if an object doesn’t rotate, and so there is no repulsive interactions caused by torsion, there cannot be some “singularities”.

“…The fact is that when the potentials of the gravitational field are close to the object, the time and speed of light is greatly slowed down. ….”

- in Matter indeed there exist fundamentally the fundamental Nature force “Gravity”, and all/every material objects create nothing else than only gravitational fields;

- but at that such physical effects as “the time and speed of light is greatly slowed down” fundamentally by no means appear. Really fundamentally nothing happens with time in the Matter’s fundamentally absolute, fundamentally flat, and fundamentally Cartesian, [5]4D spacetime with metrics (cτ,X,Y,Z,ct), and nothing happens with the speed of light, c, which is equal c=lP/tP, where lP and tP are the size and flip time of the utmost fundamental Matter’s base - the [5]4D binary reversible fundamental logical elements [FLE].

More see the SS posts above and papers that are linked in the posts.

Cheers

There is no need to invent alternative hypotheses for general relativity. It is only necessary to carefully continue what Einstein began."There are no anomalies on the Schwarzschild radius. In general, the picture has become full-fledged physical but by no means simple. Both light and particles fall on such an object in a finite period of time. However, their return trip is also not an impossibility. (8) (PDF) Gravitational Field Equation in General Relativity. Available from: https://www.researchgate.net/publication/355078683_Gravitational_Field_Equation_in_General_Relativity [accessed Oct 20 2021]."

Dear @Shevchenko:

It may be that a process dissipates part of the angular momentum, but not all. That is too much energy to be dissipated. Due to its conservation, a reduction in the radius, either of the collapsed object or of the accretion disk that falls on the BH, the substance that makes up the black hole must rotate very quickly, but without at any time its "edge" exceeding the speed of light.

As @Santanu Das suggested in an answer in this same thread, the singularity could be a ring. This answer is consistent with the magnitude of the angular momentum and with its conservation. Although in my opinion, this ring would not be a singularity, but an element of non-zero volume.

As you can see, I am quite upset by singularities :-)

What is more important is the conservation of angular momentum, as is the conservation of energy. All theories about BH should be subject to these two laws.

Greetings

Dear @Soto del Valle:

“…It may be that a process dissipates part of the angular momentum, but not all. That is too much energy to be dissipated...”

- that essentially isn’t correct. The mechanisms of losing by compact extremely dense objects of angular momentum aren’t clear completely now, but that is well observable – pulsars are observed as slowing their rotation rate even on ~years time intervals, what is an jiffy in cosmological scale; and, again, if a “black hole” was formed at collapse of some non-rotating mass, as that, say, seems happened at forming Milky Way SM”BH”,

- which was formed yet at Beginning as a “seed” of future galaxy, which rather probably was some non-rotating dense local region of primary particles, which practically for sure were Planck mass particles, or something that doesn’t differ from PMP particles essentially, and which rotates now seems with a small rate. More see the Shevchenko-Tokarevsky’s cosmological model, the links are given in the SS post 5 days ago now.

‘….As @Santanu Das suggested in an answer in this same thread, the singularity could be a ring. This answer is consistent with the magnitude of the angular momentum and with its conservation. Although in my opinion, this ring would not be a singularity, but an element of non-zero volume.…..”

- again, in Matter any singularity, including [standard in official physics] “spherical”, “ring”, etc., cannot exist fundamentally; and, besides, not only a singularity, but even non-singular “material”, i.e. having energy, momentums, etc., elements of non-zero volume of the Matter’s [5]4D spacetime fundamentally cannot exist as well. The spacetime is fundamentally nothing else than [5]4D “empty container”, where material objects exist, change and interact by Forces, and any “element of non-zero volume” is nothing else than some element of non-zero volume of the emptiness,

- though yeah, every material object occupies some element of non-zero volume.

“…"There are no anomalies on the Schwarzschild radius. In general, the picture has become full-fledged physical but by no means simple. Both light and particles fall on such an object in a finite period of time. ….”

- that in “Both light and particles fall on such an object in a finite period of time”, and what is “the Schwarzschild radius”, is written in many SS posts and linked SS&VT papers on the RG soon 10 years already – that is rigorously proven in the papers; including in yesterday post relating to that “the time and speed of light is greatly slowed down”; it seems as even interesting – there are or not in (8) (PDF) some references on the papers?

Cheers

Stefan Bernhard Rüster, I have a couple of questions about "... QGP is rotating very fast within a tiny region of space-time."

In the phenomenon known as the BH at the center of a galaxy, rotational speed, at times a significant increment of the speed of light hurls the QGP toward the spherical shell primarily along the axis of rotation. Simultaneously, inbound matter and EM energy are inwardly drawn toward the BH due to immense gravitational forces - again, heightened along the galactic plane (in the hole of an AGN).

Assuming there's any merit to the above assumptions...

Is the tiny region you mention where the QGP is heightened located along the horizon's rotating spherical shell, more intense in graduated degrees as the galactic plane is approached?

Also, narrow jets are frequently observed from the centers of these holes vertical to the galactic plane. Why are the dynamics behind the reasons these jets are created?

Because of the rapid rotation and angular momentum becoming greatest at the event horizon's spherical edge, could this mean that at the center of a BH that mass might actually approach zero?

"Black holes" are areas where Einstein's equation does not work. Has no solution. This area lies outside of science, it is not physics. Any hypothesis about what's inside and how it moves is equally meaningless. On the other hand, alternative theories also lack solid ground. The answer to these questions is only in general relativity. In the extension of the theory to the region of large fields.

Perhaps I managed to get a gravitational field equation suitable for large fields, but there is no black hole. There is another strange object with an extremely low speed of light.

Preprint Gravitational Field Equation and the Structure of Black Holes

A black hole is an object, the observed time on the surface of which stops. According to Zelmanov's theory of physical observables, this effect occurs in two cases: 1) the body does not rotate, but its radius is equal to the Hilbert gravitational radius r_g = 2GM / c ^ 2, where M is the mass of the black hole, 2) for a rotating black hole the condition is satisfied: w + u_iv ^ i = 0, where w is 3-dimensional gravitational potential, u_i is 3-dimensional translational speed of the object, v ^ i is 3-dimensional speed of rotation of space. A black hole of the first type can capture other bodies by the force of its gravitational field. In the second case, rapidly rotating stars can pull other objects into their vortex - dust, nearby stars, etc.

I see no perspective in alternative, non-metric theories. The main problems can be solved without going beyond general relativity. The main problem is the conservation law. After solving this problem, the singularity problem is automatically solved.

Instead of a set of hypotheses, the problem of dense objects is solved. Instead of fantastically low values ​​of the potential, filling this interval gives a reasonable distribution of matter in this region. Of course, we can only guess about the equation of state of matter.

Perhaps we will not see a significant difference between neutron stars and denser objects, since the sizes of neutron stars are close to the calculated critical radius of the gravitational field rc ≈ 3rg.

The minimum gravitational potential is -c2.

The substance will change the picture. The nearly horizontal red line will rise. The amount by which the horizontal line rises is determined by the equation of state. Strictly speaking, a horizontal line is not horizontal, with or without matter (point source).

And what does a singularity physically constitute ? A hole ? A singular point of infinite density ? Mathematically anything goes but if its sensible is another question . The first is fantasy/fiction , and the second is absurd . I feel so certain i'd bet my life there is a finitely dense object of immense density , representing a next stage of what we learn in intro-astro . And it rotates ! Think about an ice dancer - when they pull their arms in the spin ever faster . The same is happening to a black star . I think if we know the size , mass and masdistribution of the star before collaps , and we know how much goes in and how much out , by its new rotation velocity we should be able to calculate the new size/mass distribution of the black star .

When I asked the question, I still didn't know about the Kerr models. But in these models the singularity is a ring. It seems absurd to call a ring "singularity". Black holes, strange as they may seem, are subject to the same physical laws as the rest of the Universe. So, in effect, I also think that black holes are non-point objects and not infinitely dense.

The ideas of @Valery Borisovich Morozov are interesting.

Thank you very much for your reply, Hanna.

I am with you mate .

Just because electron's are singular points in some theory does not mean they are physically singular points or singular in physical reality , but i believe it is well known that they are non-singular objects . Mind you , all restmatter is just a standing wave , so not a singular point .

Likewise just because we write theory to excuse the singular hole , does not make it physical .

I just see you wrote this question in October and i even replied to it before and 100% can't remember , but some days ago i had the idea that conservation of (angular) momentum proves black holes are stellar objects of finite size being able to calculate that size from conservation . Interestingly i found the conservation of angular momentum to imply the conservation of the nonzero magnitudinal sum of sum_i dm_i*v_i , because if the latter would be allowed to go to zero i.e. by opposite velocities cancelling to standstill , then angular momentum would be zero , but so if angular momentum is conserved , this nonzero dm*v sum must be . Just found it interesting .

Dear Dr Javier Soto del Valle . See the following useful RG link: Article Energy and angular momentum flow into a black hole

Kindly see also the following good link : https://www.sciencedirect.com/topics/physics-and-astronomy/rotating-black-holes