Physically in real world, if somebody tells you that he directly observed black holes with telescopes that detect X-rays, light, or any other form of electromagnetic radiation... in the best case scenario, he is just joking... and the worst case scenario he has no clue what he is talking about.

So don't let the name fool you (a black hole is anything but empty space).

Theoretically, as the surface of your said person body nears an imaginary surface called the "event horizon," time on that body slows relative to the time kept by the observer far away; When the surface reaches the event horizon, time stands still, and the person can collapse no more - it is technically called a frozen collapsing object (this is just mathematical, the worst of all it has not yet been verified and will never be).

Back in the day, one would simply switch from Schwarzschild to Kruskal coordinates. "Objects falling into a black hole remain outside the event horizon in Schwarzschild coordinates but cross it in Kruskal–Szekeres coordinates." Quote from, Kruskal–Szekeres coordinates - Wikipedia. But this change in coordinates does not have-to-be smooth. Your observer is not always diffeomorphic to your victim. This is the catastrophe in smoothness theory that brought differential topology into physics. Please see: R.E. Gompf, J. Diff. Geom. 37, 199 (1993).

The infalling observer will reach the singularity in finite proper time. The proper time, as measured by the observer at infinity, is infinite. No problem, they aren't equivalent.

The mass contained in a black hole is proportional to its radius, so, as observers, of finite mass, fall into the black hole, its radius increases correspondingly. No problem there, either.

The confusion arises by not distinguishing what happens in space, with what happens in spacetime.

In space, the black hole is, just, an object whose mass is greater than the Schwarzschild bound, which means that the escape velocity is greater than the speed of light. Objects can orbit it or fall on it just like any other object.

And its mass and radius can be measured from far away, just like for any other object.

Thank you all for the inputs, but I'm not understanding any direct answers to the question "How does the black hole get bigger?" Thank you George Soli for getting me closer to the answer by mentioning Kruskal–Szekeres coordinates - Wikipedia. By reading that article I get the idea that matter falling into the black hole doesn't make it bigger in the sense of having more matter contained inside ("inside" means within the Schwarzschild radius). It gets bigger in the sense of having more matter outside but near the surface. My next question then is: Does matter added to the outside but near the surface increase the Schwarzschild radius? If the answer is yes then I have a problem because it means that the matter formally outside is now inside (which I thought is not possible). If the answer is no then I think my question has been answered. Is it yes or no?

Differential topology conjectures an answer to your problem. It's called the Brans conjecture. If I'm your victim that is not diffeomorphic to my outside self, after changing to Kruskal coordinates and finding myself inside the Schwarzschild radius, then your victim created differential obstruction to smoothness, gravitates, aka, has a topological mass but the topology did not change? But like Stam Nicolis said, "The proper time, as measured by the observer at infinity, is infinite. No problem, they aren't equivalent."

I'm still not getting a direct answer to the original question, and I'm not getting a yes or no to the question in my latest post. Please answer yes or no. I can understand yes or no.

The answer is NO. But quoting from the following link:

"One of the most common questions about black holes is how they can exist if it takes infinitely long (from the perspective of an outside observer) for anything to reach the event horizon... but it may not fully address the question, which can be summarized in terms of the following two seemingly contradictory facts:

(1) An event horizon can grow only if the mass contained inside the

horizon increases.

(2) Nothing crosses the event horizon in finite Schwarzschild

coordinate time."... The answers given are fun. I like the dust cloud answer,

"Now suppose a large concentric spherical dust cloud of total mass m surrounds the black hole is slowly pulled to within a shell of radius"...

https://www.mathpages.com/rr/s7-02/7-02.htm

Once more: Black holes are just objects, in space, for which the escape velocity is greater than the speed of light. When matter ``falls" in, the mass of the black hole increases-that's what ``falls" means-and the Schwarzschild radius does, too.

So called “black holes” fundamentally by no means are some “holes in spacetime”, as that the GR fundamentally wrongly postulates. As that rigorously scientifically proven in

the Shevchenko-Tokarevsky’s Planck scale informational physical model, 3 main papers are

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics ,

https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics ,

and [2023 Planck scale initial model of Nuclear Force in] https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force

[ the 2007 Planck scale initial model of Gravity and Electric Forces is also in

https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces]

- Matter’s spacetime is fundamentally absolute: it by no means can be impacted/affected by anything in Matter, and by no means can impact/affect on anything in Matter;

- and, as that rigorously scientifically shown in the whole model, concretely Matter’s spacetime with well non-zero probability is fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct).

Which fundamentally is nothing else than only some infinite “ empty container”, where everything in Matter is placed, exists, and happens.

More about what are “black holes” see section “Cosmology” in 2-nd link and the last link, if briefly – BHs are, of course, only some, though extremely exotic, but “ordinary” material objects, that have radiuses lesser than “Schwarzschild radius”, however no any “singularity” that would “perforate the spacetime” exist.

If a BH is large, it has inside extremely dense compact objects that has radius well lesser than the Schwarzschild one, and material objects that fall into BH move in the space between the objects surface and the “event horizon” surface quite analogously as they do that outside the event horizon. Though yeah, Gravity Force strength in this case is enormous, and a lot of specific physical events/effects/processes happen.

Including the falling body moves with large Lorentz factor, and, since – as that rigorously proven in the SS&VT Gravity model above – Gravity field principally practically doesn’t contain energy, and so falling body is accelerated only by own energy, i.e. which is stored in the own body’s m0c2, m0 is the body’s rest mass. So its rest mass at motion to the BH center constantly diminishes [“gravitational mass defect”].

Both these effects result in that the intrinsic processes in the body slow down, but fundamentally nothing happen at that with time for anything – for the body itself and for any external observers on any distances. Eventually the body hits into central object having practically speed of light, increases the central object’s mass on m0; what other at that happens in the central object, including with the body, is fundamentally unknown in physics now.

More see the links above, to read reDzennn comments in

https://phys.org/news/2023-11-black-hole-paradox.html ,

https://phys.org/news/2023-12-ways-black-holes-energy-source.html

https://phys.org/news/2023-12-dense-quark-liquid-distinct-nucleon.html

it is useful as well.

Cheers

Seems like I'm not the only one enjoying this question.

After reading dear ''Sergey, Stam and George'', correct me if I'm wrong, I personally think that it all comes back to some extent to the same conclusion (I would join dear Edmonds in that exiperiment if and only if I have to play the role of the observer... I'm joking); the facts are:

*We can't directly observe a black hole (that's where the notions of proper-time and faster-than-light come into play), so there is no way whatsoever to assume that a black hole is getting bigger in a physical sense (the notions of visible/observable matter, space and time loose their cool to singularity).

*We can see how the strong gravity affects the stars and gas around a said black hole (that's where the notion of frozen collasping object might come into play), so there is a way to mathematically assume that it is getting larger in an informational sense (the notion of the invisible invites itself via dark-enery and/or matter).

*See that the only way to know we are in presence of a black hole must be indirect via the surrounding-gravitating stuffs, better say that any so-called black hole is just fundamentally a dynamically orbital system.

Thank you George Soli. I am sure that the link you provided answers the question, but the answer is a little deep and I need to study it some. I also see how it can be that such an obvious question is not anticipated and answered in every piece of literature that even mentions black holes. The reason is that the answer is complicated. The link you provided uses 9 pages to answer the question.

Thank you Olivier Hakizimana for pointing out that black holes are not directly observable. This helps me to understand the explanations given by others about the choice of coordinate systems. I naively thought that there is one unique time coordinate of a given event seen by a given observer so there is no choice of one kind of time coordinate instead of another for a given event and a given observer. Maybe I can understand that better now.

Thank you Sergey Shevchenko but I don't understand a single word of what you said so I will start paying attention to you if and when some of the smarter people on this thread concur with your claims. You would have more credibility without the claim "As that rigorously scientifically proven in..." Nothing in physics is rigorously proven unless a theory is proven wrong by a counterexample.

L.D. Edmonds

Crucial points highlighting the shortcomings of Astrophysics.

1. It is fundamentally wrong to assume, implicitly or explicitly, electrons, protons and ions to be non-interacting particles under any circumstances, especially under a high-density environment. It is well-known that electrostatic repulsion between two protons is 1036 times stronger than the gravitational force between them, yet in astrophysics of stellar cores, electrons, protons and ions are often assumed to be non-interacting for invoking the use of Electron Degeneracy Pressure and hydrodynamic Equation of State under high density environment.

2. Application of Fermi-Dirac Statistics to degenerate electrons, by treating them as non-interacting particles, to accelerate them to high kinetic energies through the action of Pauli's Exclusion Principle is fundamentally wrong. Electrons can never be accelerated to high kinetic energy without electromagnetic interaction in some or other form. The kinetic energy density of degenerate electrons can never be declared as the Electron Degeneracy Pressure just because their dimensions (ML-1T-2) are common, without incorporating a physical mechanism to enable electrons to exchange their momentum with protons and ions through elastic collisions.

3. Since the Astrophysics textbooks do not cover the theory of elasticity the students of Astrophysics are not prepared to handle the solid state of stellar cores or to work out stresses and strains in solid spherical bodies under self-gravitation. That is why Astrophysicists make use of invalid Electron Degeneracy Pressure and hydrodynamic Equation of State, by implicitly assuming all electrons, protons and ions to be non-interacting, and wrongly collapse solid iron stellar cores into Neutron Stars and Black Holes.

Article Black Holes are a Mathematical Fantasy, not a Physical Reality

Article Stellar Core Collapse Models are Erroneous and Misleading

Article Ionic Gravitation and Ionized Solid Iron Stellar Bodies

Thank you Gurcharn Singh Sandhu . I am a beginning student of modern physics (after a career as an engineer) and don't really know about this stuff but I had the idea that before a black hole is formed we have a neutron star. The gravity there (I thought) was strong enough to compress matter enough so that instead of electrons orbiting protons to make atoms, the electrons combine with protons to make neutrons. So all of the matter becomes a lot of neutrons. Is that correct?

Dear Edmonds, you surely know what probably ewaits you in modern physics: ''dealing with thousands if not millions of papers with different claims... guess what, in real world, probably most ''to not say all'' of them can not be tested or be falsified due to different reasons''.

So far, I'm really enjoying this conversation, I would like to repeat to dear Sandhu or anyone else who feels concerned, and I would like Mr. Edmonds to judge by himself since he is an engineer.

''In an informational sense of understanding, a said black-hole is not a mathematical fantasy''.

The scientific answer “How do black holes get larger?” to the thread question is given in the SS post on page 1, a few notes else::

- in the SS&VT Planck scale physical model

[links see the SS post above, though more correctly that is proven in the SS&VT “The Information as Absolute” conception, recent version of the basic paper see

https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed, while the model is based on the conception,

- where the fundamental phenomena/notions, first of all in this case “Consciousness”, “Space”, “Time”, “Energy”, “Information”, “Matter”, which in the mainstream philosophy and sciences, including physics, are fundamentally completely transcendent/uncertain/irrational – and so, say, in mainstream physics everything in Matter, i.e. “space”, “time”, “spacetime” , “particles”, “fundamental Nature forces” – and so “fields”, etc., are fundamentally completely transcendent/uncertain/irrational also,

- and just so the GR is based on really transcendent fantastic – and wrong – postulates; and just so in the GR the fantastic “back”, “white”, “worm”, etc. “holes in spacetime”, are logically inevitably quite “scientifically legitimate”]

- the fundamental phenomena/notions above are rigorously scientifically defined, and it is rigorously proven that the really extremely exotic material objects “black holes” fundamentally aren’t something that perforate Matter’s spacetime making “hole in the spacetime” inside “event horizon” that has “Schwarzschild radius”, as that directly follows from the GR, and is written in innumerous corresponding mainstream physics publications. That is fundamentally impossible; including in this case that is impossible by the energy conservation law, which in the GR in this case is drastically violated.

Correspondingly “black holes”, despite that are really extremely exotic material objects, are only some material objects, which get larger if into a BH some other material object hits – as that happens mostly with all other “ordinary” objects, if some essential phase transitions don’t happen.

At that indeed, the “Schwarzschild radius” is some radius where because of really large Gravity field that is created by the BH central compact extremely dense material object, “ordinary”, i.e. that are observed in a rather weak fields, interactions of particles by other fundamental – Weak, Electric and Strong – Forces essentially differ from “ordinary” ones,

- and so now it is possible only in a zero approximation to describe what exists and happens inside “event horizon”, more see https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces , however, again, in this case it is necessary to read other papers in whole SS&VT model.

L.D. Edmonds

“…but I don't understand a single word of what you said so I will start paying attention to you if and when some of the smarter people on this thread concur with your claims.…”

- the SS&VT model and SS posts aren’t trivial, and so are intended for educated physicists, and even in this case to understand what is written in the model and the posts it is necessary to spend essential time. That is really necessary, and the time spending in this case is much more useful than spending time on reading of something else; and, of course, it is desirable to write concrete questions in posts in RG discussions, just for that RG platform, in principle exists.

Cheers

Well said dear Sergey... the only thing I would like to point out is that when it comes to black and white holes, the principle of conservation of energy and/or momentum must be violated, which so far seems like a taboo to even suggest... It's not the case anymore and shouldn't have been. This is why, dear Edmonds and most followers of this conversation, they need much more than just reading. Let me suggest that they need something they can test for themselves. Reminder: We can be an educated physicist but as long as we cannot explain a given concept to a six-year-old child, we still have to improve (not to say like Einstein "we don't understand it") .

Hello Olivier Hakizimana. You understand things that I have not been able to understand. I don't understand anything from Sergey but apparently you do. Specifically, what he said that you were referring to when saying "Well said dear Sergey...". Can you please explain that in terms that a six-year-old child can understand?

Dear Sergey should correct me if I'm wrong, he is basically trying to point out how complex the notion of black/white holes and/or wormholes is, since their existence requires the violation of the energy conservation principle... which makes most scientists skepitcal by the way.

At the same time, he is reinforcing the importance of the combination of different notions, typically that of ''information and energy at different scales''... which at the end of the day may require someone to be a phisicist in order to apprehend the complexity... before concluding that the notion of black/white holes and/or wormholes is inevitable.

And I suggest somthing fundamental, you yourself can test as an engineer so that you may draw your own conclusion.

Thank you.

I'm not happy with my understanding so far. Let me review the problem. According to a distant observer, it takes forever for a falling mass to enter a black hole. But a distant observer sees the mass contained in a black hole to increase in a finite amount of time. These statements seem contradictory. The fact that mass enters in a finite proper time does not change the fact that these statements seem contradictory. Therefore, when the question is how do we resolve this apparent paradox, the statement that mass enters in a finite proper time is not an answer to the question. The answer that I got so far, from a link from George Soli, talks about matter traveling backwards in time starting from an infinite future. I have no idea how to visualize "backwards in time from an infinite future" so I'm not happy with this.

I have a copy of (but am not yet familiar with) the book GRAVITATION by Misner, Thorne, and Wheeler (2017 edition) and would like to know what this book says about it. I look up "frozen star" in the index and it says "see black holes". I look up "black holes" in the index and find an enormous number of pages. I already spent hours going through some of these pages and have not yet found any mention of frozen stars. Can somebody please help me by telling me the page numbers that talk about frozen stars?

Thank you Robert A. Phillips

I'm not happy with the answers given so far (see my two most recent posts for an explanation of why) and am going to guess at the answer. Please tell me if you agree. The guess is as follows.

The analysis that predicts an infinite time (as seen by a distant observer) for an object to fall into a black hole is a limiting case that becomes exact in the limit as the mass of the falling object approaches zero. It is a limiting case because the analysis does not recognize that the falling object adds mass to the system and increases the size of the black hole. The limiting case is an accurate approximation for a small but greater than zero mass of the falling object for some finite amount of time, but the solution cannot be extrapolated into the infinite future. I am guessing that a modified analysis (I don't know how to do this analysis so this is only a guess), that recognizes that the falling object adds mass to the system, will predict that it enters the black hole in some finite time. Does anyone know whether or not this is correct?

The observer deduces the increase in mass via the gravitational field.

People that complain about mainstream theory agree with each other on only one point, that mainstream is junk science. There is absolutely no agreement between them as to what the correct science is. Also, many complaints about mainstream are due to a lack of understanding.

I have been involved in many forums and learned that the more respectable complainers of mainstream theory are those that admit that they do not have the answers so their mission is just to complain. Less respectable complainers are those that haven't learned the subject very well and believe that they are qualified to discuss it because they don't know any better. The least respected people are those that live in some fantasy world of their own imagination. Eventually, I expect, there will be a gifted person that will produce a better science. But I don't think that person is participating in this forum.

This discussion got distracted from the points that I care about. Since I am the one that asked the question of this thread, I should be allowed to decide what I care about. To bring the discussion back on topic (I hope the distractions will not continue) I will repeat some things with the intention of restarting the thread from here.

I'm not happy with my understanding so far. Let me review the problem. Mainstream textbook theory says that, according to a distant observer, it takes forever for a falling mass to enter a black hole. But the mainstream theory also says that a distant observer also determines that the mass contained inside a black hole (with the mass deduced by gravity together with the radius of an event horizon that distinguishes inside mass from orbiting mass) can increase (via accumulation of more matter) in a finite amount of time. These statements seem contradictory. The fact that mass enters in a finite proper time does not change the fact that these statements seem contradictory. Therefore, when the question is how do we resolve this apparent paradox, the statement that mass enters in a finite proper time is not an answer to the question. So some of the answers that were given in this thread are not satisfactory. Another answer, that I got from a link from George Soli, talks about matter traveling backwards in time starting from an infinite future. I have no idea how to visualize "backwards in time from an infinite future" so I'm not happy with this.

I am a student presently attempting to learn mainstream textbook theory so I am looking for an answer to my question that is obtained from mainstream textbook theory. If an answer is given outside of mainstream theory then, even if that answer is convincing, I will still be looking for an answer within mainstream theory because I expect such an answer to exist but I don’t know what it is and I want to know. Just for my own education, whether or not I should want to know, I still want to know.

Now I am going to guess at the answer to my question in the hopes that someone can tell me whether or not the guess is correct. The guess is as follows.

The analysis that predicts an infinite time (as seen by a distant observer) for an object to fall into a black hole is a limiting case that becomes exact in the limit as the mass of the falling object approaches zero. It is a limiting case because the analysis does not recognize that the falling object adds mass to the system which affects the metric tensor that affects space-time geometry with the result being an increase in the size of the black hole. The limiting case is an accurate approximation for a small but greater than zero mass of the falling object for some finite amount of time, but the solution cannot be extrapolated into the infinite future. I am guessing that a modified analysis (I don't know how to do this analysis so this is only a guess), that recognizes that the falling object adds mass to the system and affects the metric tensor which affects space-time geometry, will predict that it enters the black hole in some finite time. Does anyone know whether or not this is correct?

Another way to help me is as follows. I have a copy of (but am not yet familiar with) the book GRAVITATION by Misner, Thorne, and Wheeler (2017 edition) and would like to know what this book says about the topic. I looked up "frozen star" in the index and it says "see black holes". I looked up "black holes" in the index and found an enormous number of pages. I already spent hours going through some of these pages and have not yet found any mention of frozen stars. Can somebody please help me by telling me the page numbers that talk about frozen stars?

I'd advise any student attempting to learn mainstream textbook theory to think by themselves before parrot style answering (some who think are scientists are really only good in that - parroting other ones work). Any real scientist is - and stays - critical. For the rest of his life, including all own ideas and (maybe) even so against all of mainstream.

This is as mainstream has shown to be - sooner or later - be replaced by some new mainstream, after undenieable new (experimental or theoretical) knowledge has been worked out by someone (creative).

Such happened for sure over now literal many thousands of years, so why should it be suddenly no longer true for today and the future? It is exactly true, so to all with very high iQ sole based on photographic memory - try to understand what you (believed) you have “learned“ - who ever wrote so (Planck, Einstein, Feynman … no-one is unfailable).

Thank you Robert A. Phillips

I have no objections to thinking for myself. I have a published history of that as seen in my peer-reviewed publications introducing the ADC charge-collection model as an alternative to the popular concept of a "funnel". It took many years for me to make my concepts become the new mainstream (getting peer-reviewed acceptance against the old mainstream required a lot of work and very convincing arguments). What I do object to is not thoroughly learning the mainstream first before criticizing it. Many criticisms I have seen in RG threads are due to a lack of understanding. Worse yet, these criticisms are used as an excuse for not thoroughly studying the mainstream (which, admittedly, is not an easy study because of the enormous amount of detail that has been worked out by many brilliant people over the years). The only way to properly appreciate the strengths and limitations of mainstream is to first get a very good understanding of what it is. That is what I am trying to do in this thread.

I see that we have returned to distractions. The philosophy of what we should care about. I am trying to ask a technical question. Can we please focus on the technical question and put the philosophy in another thread? The technical question is rephrased in my post before this one.

This is exactly one among other misleading notions from mainstream media, they are just selling everyone that nothing can exceed the speed of light... the coin paradox disapproves of it.

Any falling visible body must be accelarating, which means neither the velocity nor the distance can be constant with respect to the observer ( note that a straight line trajectory does not exist in nature, that assumption if not an illusion is due to human-being's vision limitations that naturally creats the horizon; one might like it or not ''still everthing is fundamentally either orbiting or is connected to something in a given orbit'').

Therefore the issue highlighted by dear Edmonds is still technically relevant and that's why the notion of these so-called black holes needs to be redefined... Although it is not bad to follow the crowd, one still need to think outside the box to see the full picture.

Edmonds's questions are well described for anybody who followed this topic since the beginning... unlike you, dear Robert, no one else is questionning the scientific effectiveness of those questions... that's a fact.

Plus... I would like to let you know that the notion of ''the front or back side'' can not be applied on black holes whatsoever (we are not talking about the sun... you're making me look like a clown... hahahaha).

Shouldn't be an issue for a scientist to say I don't know or don't underestand, before making flawed confirmations on the effectiveness of the coin paradox, ask yourself if you would have failed or passed the question in the SAT test below:

https://www.nytimes.com/1982/05/25/us/error-found-in-sat-question.html

"Front or back side" I said "Front or Side"... still the same logic anyway.

Honestly, you should feel sorry for yourself (even a high school student wouldn't selfcontradict on the notion of acceleration... hahahaha).

I'm not surprised that the coin paradox misunderstood by mathematicians who wrote the SAT-test questionnaire, has no value for you...what a genius!

I would like to bring this discussion back on topic. Some of the distractions were about whether I should or should not be attempting to understand mainstream theory. I claim that the only way to appreciate the strengths and limitations of the theory is to first understand it. That is what I am trying to do. To get back on the topic I care about (as the one that asked the question that started this thread) I will repeat some things again.

I'm not happy with my understanding so far. Let me review the problem. Mainstream textbook theory says that, according to a distant observer, it takes forever for a falling mass to enter a black hole. But the mainstream theory also says that a distant observer also determines that the mass contained inside a black hole (with the mass deduced by gravity together with the radius of an event horizon that distinguishes inside mass from orbiting mass) can increase (via accumulation of more matter) in a finite amount of time. These statements seem contradictory. The fact that mass enters in a finite proper time does not change the fact that these statements seem contradictory. Therefore, when the question is how do we resolve this apparent paradox, the statement that mass enters in a finite proper time is not an answer to the question. So some of the answers that were given in this thread are not satisfactory. Another answer, that I got from a link from George Soli, talks about matter traveling backwards in time starting from an infinite future. I have no idea how to visualize "backwards in time from an infinite future" so I'm not happy with this.

I am a student presently attempting to learn mainstream textbook theory so I am looking for an answer to my question that is obtained from mainstream textbook theory. If an answer is given outside of mainstream theory then, even if that answer is convincing, I will still be looking for an answer within mainstream theory because I expect such an answer to exist but I don’t know what it is and I want to know. The only way to appreciate the strengths and limitations of the theory is by having a thorough understanding of it, which is what I am trying to do.

Now I am going to guess at the answer to my question in the hopes that someone can tell me whether or not the guess is correct. The guess is as follows.

The analysis that predicts an infinite time (as seen by a distant observer) for an object to fall into a black hole is a limiting case that becomes exact in the limit as the mass of the falling object approaches zero. It is a limiting case because the analysis does not recognize that the falling object adds mass to the system which affects the metric tensor that affects space-time geometry with the result being an increase in the size of the black hole. The limiting case is an accurate approximation for a small but greater than zero mass of the falling object for some finite amount of time, but the solution cannot be extrapolated into the infinite future. I am guessing that a modified analysis (I don't know how to do this analysis so this is only a guess), that recognizes that the falling object adds mass to the system and affects the metric tensor which affects space-time geometry, will predict that it enters the black hole in some finite time. Does anyone know whether or not this is correct?

Another way to help me is as follows. I have a copy of (but am not yet familiar with) the book GRAVITATION by Misner, Thorne, and Wheeler (2017 edition) and would like to know what this book says about the topic. I looked up "frozen star" in the index and it says "see black holes". I looked up "black holes" in the index and found an enormous number of pages. I already spent hours going through some of these pages and have not yet found any mention of frozen stars. Can somebody please help me by telling me the page numbers that talk about frozen stars?

I don't understand why you Robert A. Phillips

As any wise would build a golden bridge for an unworthy opponent to retreat... I 'd say ''my intentions weren't about denigrating dear Robert.''

Unfortunately, He can't help but humiliating himself... next time, he will make sure ''he at least understands basic notions before playing the phisicist.''

Robert A. Phillips

Robert A. Phillips

Continuim theory, the basis of this question and all such discussion about relativity, does exist only in the mind of mathematicians. No continuum, no Zeno. And no Albert, unfortunately. But now exact constants of nature, able to be fed from iSpace theory into (more or less, value wise) correct QED (QM) instead of the (21 or so) by now only (CODATA) measurement based constants of nature like e, h, FSC, me, R, …, G, H0 and Planck constants:

Preprint iSpace - Quantization of Time in iSpace-IQ Unit-System by 1/...

And while we’re at it - the foot and the mile are the physically most stupid (imperial) defined units one can possibly think of - in mph your question on the cars is indeed unsolvable, but not due to non-existing Zeno, but due to intrinsically unknowable human artefact part of mile and foot with respect to quantum based entities like proton radius or electron radius (a0 and re).

It’s like asking for the length of the coastline of UK - unsolvable as such is fractal - in assumed continuum. In iSpace-SI and with this SI it’s exactly convertable into intrinsically human artefact free iSpace-IQ units, which is due to extremely clever definition of the SI Meter and the speed of light really being constant (in what RT defines a reference frame). Here Albert was completely correct. And with the QM related photo effect - of course - he got his Nobel for, and rightly so. He never got a second one for theory of relativity, and rightly so.

Suppose the falling object is moving on the straight line through the black hole center that is perpendicular to the line connecting the observer to the black hole center. Does your analysis Robert A. Phillips

I believe that the metric tensor (which is used to construct the Christoffel symbols, which construct the equation for geodesics) was constructed in such a way so that a trajectory along any line radially outward from the black hole center has the same solution when the radial coordinate is expressed as a function of coordinate time. This means that the approach to the event horizon is only asymptotic even if the trajectory is perpendicular to the line of sight.

I asked a technical question that started a thread that degenerated to the topic that we should not try to understand mainstream theory. Any post that says that mainstream is wrong, or that we should think for ourselves, gets recommendations from people that don’t understand the theory and are searching for ways to take pride in their ignorance. Most of the “independent thinking” I have seen in RG threads are fantasies invented by people that don’t understand the theory (not all, some people understand the theory and have valid complaints, but most are in this category). They get praised for going against mainstream when they are actually useless distractions. Is mainstream so wrong that there is nothing there worth learning? If so, this is not a flattering statement for the many brilliant people that contributed to the theory over the years. There is something worth learning because all successful modern technology comes from it. Of course theories evolve and the mainstream gets replaced. But I say that you should understand the theory first, then complain about it. Don’t discourage people from trying to learn it.

Can we now please focus on the technical question of this thread?

Robert A. Phillips

Robert A. Phillips

I give you a more simple pixel based example, do you relkay and easily understand iSpace:

Two (virtual) cars of one pixel (voxel) „size„ drive next to each other. One is (say) 50 pixels ahead, and driving 3 pixels per time quantum, the other is faster and driving (say) 8 pixels per time quantum in the exact same direction.

With Zeno and continuum without a quantum of time, the second „faster one“ would indeed never reach the first one, as such has moved infinitesimal ahead of whatever the second one catches up.

But quantum of time and discrete space does not allow for (mathematical only) nonsense like that (infinitesimal length, there is no infinity and there is even no zero, but we all learned at school there would be.

Just look on your Monitor it TV TFT screen and you will understand what primary quantization of time - and with this everything by unavoidable intrinsuc nature of physical relations - actually means.

The second car will simply catch up 8-3=5 pixels with every step (quantum of time!!) and if their sistance between was initially (say) 50 after 10 steps the second catches up and after 11 steps the second has bypassed the first started (slower) „car“ or pixel.

That simple, no magic needed here.

You're welcome, Robert ( Robert A. Phillips

Robert A. Phillips

Here is another simple way (that doesn't refer to work done) to make my point that falling objects with greater than zero rest mass do not approach the speed of light (as seen by an outside observer) as they approach the event horizon. The simple answer is that the approach to the event horizon is asymptotic, so a trajectory along a radial line starts to slow down when the object is sufficiently close to the event horizon.

Communications with you have been unproductive (I'm no closer to the answer to my technical question) since they started, and are a major distraction, so I will not continue with them. Based on past experiences with disgruntled people on RG threads I expect you will want to have the last word. You can have the last word in your next post. It will be the last word because I will not reply to it.

➡Why can't a journalist playing the great physicist get enough of humiliating himself?

Response: Just urgue for the sake of arguing (The same method currently used by most of mainstream media to make things look bigger, since the number of views counts first).

Many thanks to dear Christian and dear Edmonds for their well-articulated points of view... unfortunately, dear Robert is sucking your energies like a black hole ... I'm not joking... hahahahahaha.

➡Now, Edmonds' main question becomes: ''let's assume dear Robert is a black hole and is getting bigger (larger)... , how does dear Robert get bigger (larger)?''

Comment: From Edmonds' point of view, all we know is that a portion of information was physically introduced into Robert's brain (can be dubbed the photon sphere)... but how did the information reach Robert's mind (can be dubbed the event horizon) if the latter is not physically reachable?

Response: From Christian, until proven otherwise, only experiments on dear Robert can tell (we're still yet directly analysing his genius brain ''to not say a frozen brain'').

Impolite, sarcastic personal assaulting replies are a full no-go on any scientific platform like RG - this is not stubborn Facebook for „wannabe“ profilation, ok

Hope such is the last clear word on this required to state the obvious.

Will report further derails like above to RG site management and L. D. Edmonds please have my excuse for both deviating from your rightly so stated core question (on black hole relativity) and more so from not being able to answer such - seemingly simple, but then of course not - hence very good revealing question you asked. I’ll for myself stop here.

I agree with Christian... although to be able to think, sometimes one has to take the risk of being offensive... I'm sorry for the inconvenience caused.

The scientific answer to the thread question is given in SS posts on pages 1,2.

Cheers

Sergey Shevchenko said that he answered the question but I need an interpreter. I can understand the vocabulary and math in introductory-level and intermediate-level textbooks on relativity. If the answer can be explained in that vocabulary I can understand it. I expect the existence of an answer that can be put in that vocabulary but I don't know what it is and I want to know. Is there anyone that is able to understand Sergey's answer and able to explain it to me so I understand it? Is there anyone on this thread that is able to understand Sergey's answer?

As a reminder I will review the question. Mainstream textbook theory says that, according to a distant observer, it takes forever for a falling mass to enter a black hole. But the mainstream theory also says that a distant observer also determines that the mass contained inside a black hole (with the contained mass deduced by gravity together with the radius of an event horizon that distinguishes inside mass from orbiting mass) can increase (via accumulation of more matter) in a finite amount of time. These statements seem contradictory. The fact that mass enters in a finite proper time does not change the fact that these statements seem contradictory. Therefore, when the question is how do we resolve this apparent paradox (which is my question), the statement that mass enters in a finite proper time is not an answer to the question. So some of the answers that were given in this thread are not satisfactory. Another answer, that I got from a link from George Soli, talks about matter traveling backwards in time starting from an infinite future. I have no idea how to visualize "backwards in time from an infinite future" so I'm not happy with this.

I am a student presently attempting to learn mainstream textbook theory so I am looking for an answer to my question that is obtained from mainstream textbook theory. If an answer is given outside of mainstream theory I will appreciate it (if it is convincing and not someone's invented fantasy) but I will still be looking for an answer within mainstream theory because I expect such an answer to exist but I don’t know what it is and I want to know. I want to know because the only way to appreciate the strengths and limitations of the theory is by having a thorough understanding of it, which is what I am trying to do.

Now I am going to guess at the answer to my question in the hopes that someone can tell me whether or not the guess is correct. The guess is as follows.

The analysis that predicts an infinite time (as seen by a distant observer) for an object to fall into a black hole is a limiting case that becomes exact in the limit as the mass of the falling object approaches zero. It is a limiting case because the analysis does not recognize that the falling object adds mass to the system which affects the metric tensor that affects space-time geometry with the result being an increase in the size of the black hole. The limiting case is an accurate approximation for a small but greater than zero mass of the falling object for some finite amount of time, but the solution cannot be extrapolated into the infinite future. I am guessing that a modified analysis (I don't know how to do this analysis so this is only a guess), that recognizes that the falling object adds mass to the system and affects the metric tensor which affects space-time geometry, will predict that it enters the black hole in some finite time. Does anyone know whether or not this is correct?

Another way to help me is as follows. I have a copy of (but am not yet familiar with) the book GRAVITATION by Misner, Thorne, and Wheeler (2017 edition) and would like to know what this book says about the topic. I looked up "frozen star" in the index and it says "see black holes". I looked up "black holes" in the index and found an enormous number of pages. I already spent hours going through some of these pages and have not yet found any mention of frozen stars. Can somebody please help me by telling me the page numbers that talk about frozen stars?

Usually, the first way physicists solve a problem is one of the most insightful ways. Use a vertical object of length L that penetrates the Schwarzschild radius and compute the ordinary tidal forces that the object experiences. Yep, they are ordinary tidal forces, and you only need to change coordinates to escape the seeming nonphysical artifacts at the Schwarzschild radius.

Needham, Tristan. Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts (p. 321). Princeton University Press. Kindle Edition.

Thank you George Soli. I'm having trouble connecting to the literature page you indicated but maybe I'm getting the idea. The math analysis I learned that predicts the "forever fall time" says nothing more about the coordinates except that the metric tensor has a particular form expressed in terms of them. It never was clear to me that these are the coordinates actually used by a distant observer. The actual coordinate system (I think) uses an ordinary clock to determine the time of arrival of a light signal and combines this with some estimate of a spatial distance to an object to deduce the time of an event. It never was clear to me that this is the same coordinate system that the metric tensor is expressed in terms of in the math analysis. The idea I'm getting from you is that the coordinate systems are not the same, and the distant observer actually sees falling objects enter the black hole (the ones that enter instead of orbit) in a finite amount of time. Do I have the correct idea? If so then my question has been answered.

L.D. Edmonds,

- as to what you don’t understand in SS posts - see also two reDzennn comments, 3 and passages, in comments section [option “Load comments at the article bottom”] in https://phys.org/news/2023-11-black-hole-paradox.html , the comments thread isn’t too heavily spammed;

- however if you really is a student, then really scientific understanding of what really black holes are would be for you wrong – since you are teaching in accordance with mainstream physics, which is too far from real science in this case. So if you will tell something as that is in SS posts, you will be a rather bad student in your, say, university;

- as to “Frozen stars” see https://en.wikipedia.org/wiki/Hypothetical_star, that is a next fantastic mainstream physics mental construction; but so full stop fantastic, that even in the mainstream that is an exotic fantasy; so don’t spend time on anything that relates to these “stars”.

Cheers

Thank you Sergey Shevchenko but I think I got the answer from George Soli. I'm just waiting for confirmation from him that my interpretation is correct. Also, the Wikipedia mention of a frozen star is not the kind I was thinking of. I was thinking in the context of a black hole with a material layer stuck (frozen in the radial coordinate) next to the event horizon because it can't penetrate. I don't need that discussion any more.

I guess I am a bad student for studying mainstream theory. But it seems to me that this is a good place to start, because we get the benefit of the works of many brilliant people over the years, and we look for improvements only after we understand the theory so that we know where the improvements are needed. Since I don't yet have a good understanding of mainstream theory I am still working on that first step. Of course the first step of a good student would to study you first, instead of Einstein or Feynman or Dirac or any of those dumb people, but I don't understand anything you say so I can't be a good student.

The link you provided talks about an information paradox but does not address the apparent paradox of my question. The answer from George Soli does.

I'm getting sick of these spam distractions of what I should be trying to understand and should not be trying to understand. Some people like poetry, some like the color blue, and I would like to understand mainstream theory out of curiosity. Call me an historian. I should not have to defend that. I am not going to reply to any more posts on that topic. Most of this thread is that spam and it needs to stop.

One more history thing. Einstein was very upset that people wanted to call his theories "relativity" theories. Einstein would have preferred "absolute" theories, the absolute being the local proper time on your watch between point A and point B as you travel between them. That proper time is the interval ds^2 that is the "absolute" that everybody agrees on.

Thank you George Soli but I'm still asking if my interpretation of your previous answer is correct. My interpretation, stated in the post immediately after you posted your answer, implies that a distant observer sees matter falling into a black hole (crossing the event horizon) in a finite time. The question I am asking is what a distant observer sees. Does he see matter entering the black hole in a finite time? Asked in more detail, is my interpretation of your answer correct? I should point out that when I say "see" I don't mean a literal visual image. I mean "determine" which can be done via gravity from the black hole together with making a distinction (via the event horizon) between contained mass and orbiting mass.

Yes, an observer outside an event horizon can see an object of length L that exists on both sides of that same event horizon. Watch a black hole merge with a star from far away, to be safe, and notice that a bigger and more massive black hole forms with the merged star clearly inside the bigger event horizon.

Thank you George Soli. You answered my question. I assume that, as with my posts, when you say "see" you mean "determine". Matter outside the event horizon can be literally visually seen while matter inside can be determined via gravity from the black hole. The important point, and answer to my question, is that, according to a distant observer, matter can enter a black hole in a finite time.

Now that my question has been answered according to mainstream theory I'm no longer concerned with distractions so now I invite everyone (that wants to) to continue this thread by complaining about how wrong mainstream theory is. I'm happy to learn something about that now that I know what the mainstream theory says.

I'm afraid even mainstreams actually desagree with George's answer.

-In the best case scenario, the said answer is an hypothetical computation (far from being the observation of nature, reason why dear Edomonds is ajusting the vocabulary by saying ''determine instead of seing or watching'').

-In the midium case scenario, dear George is confusing the photon sphere with the event horizon (I would personally agree to disagree).

-In the worst case scenario, the answer is mistakenly talking about seeing beyond the event horizon and even NASA would disagree (https://science.nasa.gov/universe/10-questions-you-might-have-about-black-holes/).

At the end of the day, when dancing with a bear ''you don't decide when the dance is over'' (one may like it or not, but that's how it is with big scientific questions, they still stand until something new is discovered and commonly accepted... hahahaha).

Hello Olivier Hakizimana, I know from past experience that George does not spend a lot of time arguing with people so it is unlikely that he will defend himself but I can defend him at least on the use of the word "see". He was responding directly to one of my questions. While writing that question it was in my mind that "what an observer sees" means "what an observer is aware of". Like "I see" means "I understand", or "I see said the blind man". I realized too late (after posting the question) that this is a bad choice of words because "see" also means a visual perception. It was a bad choice of words but what was done was done. George was giving a direct answer to my question using the same (bad) vocabulary that my question used. His use of the bad vocabulary is more justified than my original use of it because his answer came after I explained the intended meaning of that vocabulary.

I know from past experience that George has an enormous amount of knowledge and understanding (you might want to check his RG profile to appreciate that) so I pay attention to what he says.

Dear Edmonds, it is undeniably already known: ''we all make mistakes whatever our profiles''... so by admitting the slight misuse of vocabulary, you turn out to be a very smart physicist more than you might be thinking... thank you, I so far enjoyed the topic and I wish you good progress... Regards.

Thank you for the compliment. As a return compliment to you, you seem to understand the Sergey posts when I cannot, so you are smarter than me.