Mathematician Claims Black Holes Don't Add Up!

reply to post by S.J.Crothers


The length of the moving object is contracted by 1/gamma so your formulas are not quite right, but your conclusion of infinite density at the speed of light is correct.

Unfortunately the argument is circular. The conclusion that a speed equal to the speed of light is forbidden is precisely because it requires the object to have infinite energy.

However you can not say that a black hole has infinite energy since it's mass is finite and E = m c ^2 .

That doesn't mean that a black hole is perhaps possible. The question really is, is a black hole a valid solution of Einsteins general relativity tensor equation?

I think this author is arguing that it is not a valid solution.

reply to post by SevenThunders

You are incorrect. The formulae I have given are correct. And see the result of D = m/V.

The argument is not circular. Infinite density is forbidden by the Theory of Relativity because the fundamental postulate on the speed of light in vacuo requires that no material body can acquire the speed of light in vacuum. The singularity of the alleged black hole is infinite. It is a question of infinite densities. They do not exist. Furthermore, your claim that the black hole has a mass m is incorrect for other reasons. See the cited papers on this forum. So your writing of E = mc^2 in relation thereto is erroneous.

reply to post by Astyanax


Astyanax, your derision is futile, and the mark of a man who is not interested in scientific truth. All your irrational hot air and derision amounts to nothing but irrational hot air and derision, and is therefore of no account. You harp on your appeal to authority, the very same authority, with its PhD's, which is responsible, as I previously pointed out, for the black hole, big bang, gravitational waves and Higgs boson rot, and the misappropriation of vast sums of taxpayers' money for themselves. Furthermore, major elements in that ignoble group have indeed conceded that my arguments are correct. The entire Editorial Board of The International Journal of Theoretical Physics, amongst which sits Roger Penrose, has acknowledged that two papers I sent it for publication, contain no technical errors. Notwithstanding, that Editorial Board refused to publish the two papers and refused to give a reason for not publishing them, despite its admissions as to the accuracy of my arguments.

Here is the Editorial Board of the International Journal of Theoretical Physics:

www.springer.com...

Here are the two papers I sent it:

www.sjcrothers.plasmaresources.com...

www.sjcrothers.plasmaresources.com...

and here is the email correspondence in which the Editorial Board made its admissions:

www.sjcrothers.plasmaresources.com...

Now unless you provide rigorous proofs of your alleged invalidity of any of my arguments, howsoever you construe your claims, you are useless to science and a deliberate nuisance to this forum.

I'm indeed ignorant of your literary source, just as you are ignorant of the works of A. B. Patterson. But what has this got to do with the price of fish?

reply to post by mungodave


Dave,

The mystery resolved.

Steve.

I have for some time been following Crothers and his struggle to get his work objectively reviewed by someone sufficiently competent. The latter seems to be part of the problem. As you noticed, Michael, no-one in the academic theoretical physics community has had anything sensible to offer. Some pure mathematicians appear to have understood, though. I have over time come to believe that Crothers' capacity for analytical thinking and his mastering of differential geometry and the associated mathematics is extraordinary and quite unique. No wonder therefore if he gets frustrated when even some of those of world fame don't 'get it'. 

The 'Standard Model' rests on Einstein's General Theory of Relativity. That there were problems with it was known to Einstein himself, as well as other main players in the 'game' in the early years. There was at times quite heated debates. However, those who won the argument  turned out to be wrong and theoretical physics took a wrong turn, and it snowballed from then on. Hilbert's nimbus was blindingly high and Einstein himself was not combative. Physics stalled for now about 90 years.

What Crothers has done is not only to put the spotlight on several serious mistakes that were made in the early days, which by itself should earn him great respect, but he has also identified several additional problems with General Relativity which may well cause the complete collapse of it, and with it the entire edifice of the cherished 'Standard Model'. A theory which even with an arsenal of about 20 adjustable parameters is struggling to bend to fit observations. 

Crothers does not claim that he has a new theory. His claims are strictly limited to the mathematics and differential geometry applying to Einstein's Theory of Relativity and the consequences of correcting errors in mathematics and differential geometry. He has invited anyone so inclined to shoot him down in flames by proving his mathematics and differential geometry wrong. Nothing else. 

Enough has been said on this forum about the sad state of academic theoretical physics. The Crothers versus 'the Establishment' fight could have been dismissed as just another academic brawl initiated by some high principled fool. But to his great credit, Crothers refused to let himself be corrupted. 

For this, the taxpayers will owe him much but are yet to find out, but when they do, they will be enraged. If Crothers is correct, the LHC will find no Higgs Bosons. Billions of dollars squandered! And when the taxpayers find out that the academic establishment has conned their elected representatives to completely abdicate responsibility and guarantee political non-intervention, there will be electoral blood-letting! The Soap Opera will be over. 
Posted by MacMac

reply to post by S.J.Crothers

But the 'simple argument' you give above isn't anything like the full story, is it, Mr. Crothers?

For instance, here are the opening remarks in a discussion about precisely the point you have spent your life promoting. It is soon and rather comprehensively shot down. Interested parties may follow the thread in that forum, starting with the link I have provided, to discover just how much you, Mr. Crothers, have left out of your presentation above - how much you have, in fact, deliberately not told us.

The forest of equations and references to obscure mathematics in your own paper on the subject also reveals that your 'explanation' here was facile and tendentious.

Your paper is written and titled, I see, in your usual pleasant and tactful style. That style is also luminously on display in your reply to the poor editor who refused to publish it, as well as in various other fulminations preserved here.

Frankly, Mr. Crothers, you seem to be your own worst enemy. I'm sure I'm not the first to tell you this - if you have friends and loved ones, they must surely have told you the same, probably to the point where it sickens you to hear it. But they are right. It would be better for you to give up this Quixotic and futile quest of yours, and seek meaning and fulfilment down other pathways.

Very interesting. I'm gonna research this for sure

reply to post by mgmirkin


Agreed! Check out my thread here...

Black Holes Are A Myth!! A Fraud Being Perpetuated By A Coterie Of Scientists?

I had asked this question about the reality of Black Holes to Dr Michio Kaku on the ATS podcast, and he said that Black holes were real and scientifically proved! They are everywhere, millions of them and super massive BHs in the center of certain galaxies.

So it's back to basics again! The Dr ain't no pushover!

Cheers!

reply to post by Astyanax

Astyanax, again you appeal to authority and resort to abuse, and now you stoop so low as to try to implicate my family. Irrational and malicious to say the least. No matter what you say or who you cite, the fact remains that you have not given a proof that the simple calculation I have given is invalid. Since you claim that you have understood it, either provide a proof that infinite density is not forbidden by Special Relativity or admit that it is forbidden. It's that simple.

Your latest accusations are still unscientific drivel. I stated at the beginning of my relevant post that owing to its simplicity I gave the calculation, since 16 year olds can follow it, they having the required knowledge of algebra. Links to more detail were given by another forum member. Anybody can go there for all the details. You have admitted that you do not have the mathematical adequacy to understand my published papers, but that hasn't stopped you from insult and derision in a silly and futile attempt to discredit my scientific arguments. This forum is frequented by persons who, like you, are in general weak in mathematics, so I refrained from complicated mathematics. All your posts indicate that you are not interested in scientific discussion or scientific truth. You simply viciously and cowardly attack me personally without disclosing your true motive. It evidently annoys you beyond your self-control that I will not allow you to get away with impunity. Stand-over men like you don't go far, and always meet more than their match.

Anybody on this forum can think and decide for themselves if the simple calculation I have given is correct or not. They don't need you to decide for them. And they don't need “professors” and other “authorities” to decide for them. Despite what you might think, people can decide for themselves when given all the facts. They have now a simple fact before them. Anybody on this forum is invited to prove my simple calculation erroneous, if they think it wrong. So you too can now show us all precisely where my simple calculation is wrong, without introducing extraneous material or authority to mislead and deflect. You do some simple algebra, and try to think for yourself, instead of appealing to others to support your claims.

I also note that the PhD's that you are so quick and happy to praise are the very same who falsely claim that “Schwarzschild's solution” is Schwarzschild's solution, and who falsely claim that Schwarzschild's solution predicts black holes, despite the irrefutable fact that “Schwarzschild's solution” is not Schwarzschild's solution, and the irrefutable fact that Schwarzchild's solution actually precludes black holes, verifiable by simply reading Schwarzschild's original paper, which I have previously cited and provided a link to, but which you too ignored, as usual. Yet it is they who assert falsely that you would have us all believe and take on trust, in lieu of our own thought and verification. Like Galileo's professors, who refused to look through his telescope to verify for themselves the simple facts, irrationally clinging instead to their cherished dogma, you too refuse. Here yet again is Schwarzschild's real paper: www.sjcrothers.plasmaresources.com/schwarzschild.pdf

I will not respond to anything more you post here unless it's other than your usual disingenuous diatribe. If you will not provide a proof that my simple calculation is incorrect by showing us all where precisely my algebra is incorrect and if you refuse to admit that “Schwarzschild's solution” is not Schwarzschild's solution, then you are a hopeless case. I suspect that you will do neither, and will again just do your mischievous worst, bereft of scientific intent.

If the majority on this forum wish it, I will discuss with them all the salient facts which prove the black hole and the big bang entirely false.

It is unfortunate that so many are uninformed as to the true nature of the scientific method, and that the academic establishment with their peer review system is able to keep quiet what everyone should be screaming from the rooftops.

Those of us who are true pioneers do not have it easy. Lies, deception, ego battles for fame are all a part of the history of mainstream theories. False attributions, deluded perceptions of original work which are purposely propagated instead of the actual work...

S.J. Crothers in the post above gives Schwarzschild's solution as one example of this. "Hubble's Law" is in my opinion another great example of the type of deception and treachery which can take place in order to promote one viewpoint over another and pass it off as science.

Hubble discovered an empirical relationship between luminosity and redshift. This was interpreted by others as a relation between distance and velocity, so that it could be incorporated as 'evidence' which supported recent solutions in gravitational cosmology. Hubble himself said that is only one interpretation of the empirical observation, and that it isn't necessarily the correct one. But others passed it off as being the correct interpretation and the one the Hubble supported (he did not.) Yet today, the theoretical interpretation of Hubble's Law is touted as evidence in favor of the big bang while its empirically observational counterpart is relegated to the dust bin of hidden truth.

There are so few true scientists left, their voices so drowned out by the 'technician' mindset: take what is touted as truth for granted and continue along that line with no questions asked. It is sickening.

The worshiping of the mainstream scientists is quite disheartening as well. Einstein this and that, Hawking what a genius (and don't try to say he isn't or you will look like someone who hates the disabled...)

Is it any wonder that science goes through what Hannes Alfven called the 'Cosmological Pendulum"? Periodic changes in thought from what he termed Actualistic Cosmologies to Prophetic Cosmologies. Big Bang is what is classified as Prophetic, plasma cosmology is Actualistic. Paradigm shifts seem to swing back and forth between the two types.

And then there are the 'there are no paradigm' types, claiming that science does not work within paradigmatic frames.

After years of debate and attempting to teach the truth, one can adapt the feeling that it doesn't really matter any more. Why bother showing people reality when they simply disrespect the attempt and spit on the truth? I used to be one of such high hopes for humanity.

I can't blame the individual entirely however, as most are simply stuck in the system unable to see beyond its edges. The pure mind is unable to spit on the truth. The conditioned mind is unable to see it. It is a shame that it is so difficult for people to break through their conditioning.

It doesn't add up because we don't yet understand the universe completely.

S.J. Crothers,

Upon reading your website I find that Marcel Brillouin wrote a mathematical proof that shows the invalidity of Black Holes.

I just now realized something worth sharing. His SON, Léon Brillouin, is the mind behind what is known as Brillouin Scattering. This type of radiation scattering (though more specifically a form called Forward Brillouin Scattering, FBS) is what in my own personal research came to light as the most likely candidate for electromagnetic redshift phenomena in space (which is actually a plasma.)

FBS answers the question of how light can redshift via a scattering mechanism while maintaining a forward direction (which is often taken as impossible by the mainstream crowd.) It has been empirically proven as a valid mechanism in laboratory experiments shooting light through a plasma. It only takes some scaling laws to see that it is applicable in outer space to some extent, thereby allowing for alternate interpretation of Hubble's original empirical observation.

I find it invigorating and neat to some extent that the father disproved black holes, and the son unwittingly stumbled upon what could be the real mechanism behind redshift of radiation in space. Outstanding!

(By the way the information I just shared (about FBS and redshift) was a tiny summary of a paper I once submitted only to have rejected of course. This was several years ago, by now it could be understood by a wider range of people that FBS plays a role in redshift. Though maybe this isn't understood, those interested should do their own research, and perhaps submit papers. I'm not out for credit as I'm used to not getting it, I just want the truth to be known for future generations.)

edit: of course I could be completely insane and entirely wrong about FBS being a possible mechanism behind redshift. But I'm OK with that, because unlike most mainstream scientists, I KNOW that I am not omniscient!

[edit on 15-9-2008 by Ionized]

reply to post by S.J.Crothers


Just checking your formulas for a second.

Define the usual
gamma = 1/sqrt(1-v^2/c^2)

Note that gamma -> infinity as v -> c.

The moving object as seen in the rest frame sees a mass increase and a length contraction. Thus

m = m0 * gamma
length = l0 / gamma

But the length is only contracted in the direction of motion. I believe the orthogonal cube parameters are not contracted.

density = m / (length * l0^2) =
(m0 / l0 ^3) * gamma^2

Is that what you got? Maybe it is, so I stand corrected.

We agree that the density becomes infinite. But so what? The argument is circular because the speed of light barrier is assumed so that a particle can not have infinite energy.

Energy density is in fact the T00 component of the stress tensor in general relativity, but there is nothing to suggest that it can't be allowed to have a singularity from a strict mathematical sense. In fact since the left hand side involves a bunch of derivatives, a singularity would occur in the tensor for any discontinuities in the space time metric.

Again the real question is, can you satisfy the equation using a solution that involves a singularity? As we know some Green functions of important PDE's, have singularities. Whether that can be a real process in the physical world, I don't know. My suspicion is that it is in fact impossible, but is a practical approximation to a run away positive feedback loop as mass collapses and the density increases.

After all according to quantum mechanics there are no point masses, but only a probability fuzz. Since quantum mechanics and general relativity contradict each other something has to give. My guess is general relativity is flawed in some way.

Einstein's General Theory of Relativity is not only challenged by Crothers' findings. 

That the speed of light is isotropic was taken as a fact based on the presumed 'null' result of the 1887 Michelson-Morley experiment. However, very compelling research by Professor Reginald Cahill at Finders University in Australia has revealed flaws in both the Michelson-Morley 1887 apparatus, and in the theory used to evaluate the obtained data. Cahill has very thoroughly reviewed a series of later experiments by others and he has also devised his own experiments, all in very good agreement. The 1887 experiment was after all not a 'null' experiment. The speed of light is anisotropic and the anisotropy appears to have a measurable direction in relation to a 3-space frame. The solar system appears to be moving through a 3-space at 420±30 km/s in the direction RA=5.5±2 hrs, Dec=70±10°S. Go here for the details: . 

As if the above was not shocking enough, Cahill has recently published a research paper in which he is challenging the concept of 'Spacetime'. Go here for this paper: . The concept of 'Spacetime' was the result of the efforts to devise a formalism which could accommodate the idea of the isotropy and invariance of the speed of light in vacuum. It appears now that Lorentz and Einstein were on the basis of the incorrectly interpreted Michelson-Morley experiment coming at the problem kind of backwards. 

The proponents of the 'Standard Model' are not amused. To dismiss Crothers was easy. No PhD, no affiliation, no kowtowing to the exalted and uncouth language. Just an Australian nobody. Cahill on the other hand is a full Professor at a respected University. But he is dabbling in fringe science instead of Mainstream Physics. And for some unknown reason, his papers are rarely seen in the major journals but are published in odd places. And he is never seen on the telly or in 'New Scientist'. Timid man. 

Could those two guys be right? Oh Dear God, please let my bedside alarm clock ring now. 
Posted by MacMac

reply to post by SevenThunders

For our general readers I limit mathematical argument. There is nothing in what follows that is beyond all on this forum. I use only algebra. You have reproduced the very same equations I gave, so you say:

“We agree that the density becomes infinite. But so what? The argument is circular because the speed of light barrier is assumed so that a particle can not have infinite energy.”

My argument is not circular. Einstein’s postulates for Special Relativity are:
(a) the speed of light in vacuo is the same for all inertial frames, (b) the laws of physics are the same for all inertial frames. It follows from these postulates that infinite energy is forbidden or equivalently that no material body can acquire the speed of light in vacuo. Equivalently, it follows that infinite density is forbidden, as the simple calculation shows. Thus, Special Relativity forbids infinite density, and since General Relativity cannot violate Special Relativity by definition, it too forbids infinite density. When you write E = mc^2 for a black hole of finite mass m you amplify the contradiction in the black hole, because you have then an infinite density associated with a finite energy, which violates Special Relativity. So not only does the alleged black hole violate Special Relativity by virtue of its infinitely dense singularity, it also has an infinite density associated with a finite energy, which is contrary to Special Relativity, and hence contrary to General Relativity too, since the latter cannot violate the former. Thus the infinitely dense singularity of the black hole violates the Theory of Relativity, and so the black hole is forbidden by the Theory of Relativity.

You remark: “My guess is general relativity is flawed in some way.” You are right. Here is why. Ric = Rij = 0, by definition, describes an empty Universe. Einstein requires that The Principle of Equivalence and the laws of Special Relativity must manifest in his gravitational field. But they cannot manifest in a Universe that by definition contains no matter! Similarly, for Ric = 0 there is no energy density because the energy-momentum tensor is set to zero by hypothesis (there is no matter present). So Ric = 0 cannot describe Einstein’s gravitational field – it violates Einstein’s physical requirements for his gravitational field. According to Einstein, matter is the cause of the gravitational field and the causative matter is described by an energy-momentum tensor, which is coupled to geometry by his field equations, so that matter causes spacetime curvature (his gravitational field). Qualitatively his field equations are: Geometry = -k matter where matter is described by the energy-momentum tensor and -k is a constant. The geometry is described by Einstein’s tensor, Gij (subscripts i,j = 0,1,2,3) and the energy-momentum tensor is Tij. So Einstein’s field equations are:
Gij = -kTij. Since Ric = 0 cannot describe Einstein’s gravitational field, Einstein’s field equations cannot reduce to Ric = 0 when Tij = 0. In other words, if Tij = 0 (i.e. there is no matter) then there is no gravitational field. Consequently Einstein’s field equations must take the form
Gij /k + Tij = 0. This is an identity (the left and right sides of the equation are always zero). The Gij/k are the components of a gravitational energy tensor. Thus the total energy of Einstein’s gravitational field is always zero; the Gij/k and the Tij must vanish identically (i.e. when Tij = 0 then Gij = 0 and vice-versa); there is no possibility for the localization of gravitational energy (i.e. no Einstein gravitational waves). This also means that Einstein’s gravitational field violates the usual conservation of energy and momentum. Since there is no experimental evidence that the usual conservation of energy and momentum is invalid, Einstein’s General Theory violates the experimental evidence.

I continue my previous post.

It was early pointed out to Einstein that his General Theory violated the usual conservation of energy and momentum. So Einstein, to save his Theory, did something very unscientific: he invented something to get what he wanted. His invention had a two-fold purpose (a) to bring his theory into line with the usual conservation of energy and momentum, (b) to enable him to get gravitational waves that propagate with speed c. In other words, Einstein just made things up. His invention was his pseudo-tensor. First, it is not a tensor, and therefore not in keeping with his theory that all equations be tensorial. Second, he concocted his pseudo-tensor in such a way that it behaves like a tensor in one particular situation, that in which he could get gravitational waves with speed c. Thus, he invented to satisfy his objectives, and because his Theory failed otherwise. But Einstein (and his followers) did not realise that his invention, as well as being simply unscientific augmentation to satisfy a desire, is nonsense, for the following reason: his pseudo-tensor is in fact just a meaningless concoction of mathematical symbols and so describes nothing. The technical reason is this: Einstein’s pseudo-tensor implies the existence of what is called by the pure mathematicians, a 1st-order intrinsic differential invariant which depends only upon the components of the metric tensor and their 1st-derivatives. But the pure mathematicians G. Ricci-Curbastro (after whom Ric = Rij is named) and T. Levi-Civita proved, in 1900, that such invariants do not exist! Thus, Einstein’s pseudo-tensor is just rubbish, and consequently everything built upon it also rubbish. Black holers and big bangers are ignorant of these irrefutable facts, and blunder on in their ignorance, making all manner of fantastic claims that have no foundation in science whatsoever.

This is not all. In order to get a “Newtonian approximation” from his Theory, Einstein made another fatal mistake; a fatal fudge (repeated ad infinitum by his followers). His field equations are highly non-linear, and so he proposed a linearization of his field equations so that he could solve them for a potential function, which he approximated to Newton’s potential function. This is inadmissible actually, on physical grounds, but I will leave this aside for the time being and concentrate on the mathematical issue – linearization. It is always a dangerous thing to linearise a non-linear system of equations because one cannot be certain that the original non-linear system can be approximated by a linear system (mathematicians are well aware of this). But this is precisely Einstein’s blunder, because his field equations cannot be approximated by a linear system, for the following reason: linearization of Einstein’s field equations implies the existence of a tensor which, except for the trivial case of being precisely zero, does not otherwise exist! This was proven by the celebrated applied mathematician Hermann Weyl, in 1944. Once again, the black holers and big bangers blunder on in ignorance of the irrefutable facts.

In a later post I will amplify another mathematical falsehood relied upon by the black holers to get their black hole. It involves Gaussian curvature, and is irrefutable.

Before dealing with Gaussian curvature I will return to the question of the field equations Ric = 0.

In the space of Newton’s theory of gravitation, one can simply put in as many masses as one pleases. Although solving for the gravitational interaction of these masses rapidly becomes beyond our capacity, there is nothing to prevent us inserting masses conceptually. This is essentially the Principle of Superposition. However, one cannot do this in General Relativity, because Einstein’s field equations are non-linear. In GR, each and every configuration of matter must be described by a corresponding energy-momentum tensor and the field equations solved separately for each and every such configuration, because matter and geometry are coupled. Not so in Newton’s theory where geometry is independent of matter.

Now it is routinely claimed by proponents of black holes that black holes can exist in binary systems as two holes or a hole and a star, can merge or collide, or interact with other matter. But Ric = 0, from which the black hole was originally conjured, defines a spacetime (a Universe) that contains no matter. One cannot apply the Principle of Superposition so that a black hole (obtained from Ric = 0) can persist in the spacetime of a given black hole (obtained separately from Ric = 0) so that the two alleged black holes can persist in and mutually interact in a mutual spacetime that by definition contains no matter. Multiple black holes and their interactions with matter cannot by asserted by an analogy with Newton’s theory via the Principle of Superposition, because the latter does not apply in GR. Not only that, there are no known solutions to Einstein’s field equations for the interaction of two or more bodies and no existence theorem has been proven by which it can even be claimed that his field equations contain latent solutions for such configurations of matter, so all claims for black hole interactions are patently false. Indeed, GR cannot account for the simple experimental fact that two fixed bodies will attract one another upon release. But since Einstein’s gravitational field violates the usual conservation of energy and momentum anyway, black holes and big bangs are meaningless from that deeper level.

I now address the matter of Gaussian curvature.

The solution for Ric = 0 is called “Schwarzschild’s solution”. We have already seen that the so-called “Schwarzschild solution” is not Schwarzschild’s solution at all, and that Schwarzschild’s true solution forbids black holes

www.sjcrothers.plasmaresources.com/schwarzschild.pdf

This is a great embarrassment to the black holers, now that it is known more widely, despite their efforts to suppress the fact. Schwarzschild’s actual solution is also for
Ric = 0.

Now in the “Schwarzschild solution” for black holes, there is a quantity designated by the pronumeral ‘r’. In the treatment of black holes it is claimed that a particular value of ‘r’ gives the “Schwarzschild radius” or “gravitational radius”, the radius of the event horizon. It is also claimed that at r = 0 there is an infinitely dense point-mass singularity (in violate of the Theory of Relativity, as we have previously noted). The black holers have never properly identified what their ‘r’ denotes, but in all cases they effectively treat their ‘r’ as not only a distance in the associated spacetime but as a radial distance in the spacetime (recall “Schwarzschild radius”). They claim that at the “Schwarzschild radius” there is a “removable” mathematical singularity and at r = 0 there is the “physical” singularity of the black hole. However, they have never given a proof that their ‘r’ can go down to zero in their expression. They just say it is so and then concoct a method to make it so, the Kruskal-Szekeres coordinates.

But their arguments are fallacious for the following reason: their quantity ‘r’ is not even a distance in the associated spacetime, let alone a radial distance, because it is easily proven that their ‘r’ actually denotes the inverse square root of the Gaussian curvature of a spherically symmetric surface embedded in the space, and this has nothing to do with radial distance in the spacetime. In other words, the black holers don’t even use a distance in the spacetime, but they think they do, and in consequence thereof they make all sorts of calculations and claims in ignorance of elementary differential geometry, and in fact violate the rules of differential geometry. Thus, all their claims are demonstrably false. I have given the proof of Gaussian curvature in my published papers (cited earlier on this forum). It is irrefutable because it is nothing but elementary differential geometry from the pure mathematicians.

Excellent elucidations Mr. Crothers.

Thank you for taking the time to write out those responses, it was a very good read. For someone like myself who has taken courses in the subject, but always intuitively felt like assumptions were being made incorrectly, what you say hits the spot. It was always quite clear to me that black holes are simply a highly popularized mathematical construct, with little basis in reality. Seeing someone with a much better mathematical expertise show the errors quite clearly, is refreshing.

The observed effects which are so often attributed to black holes (for instance the process at the center of galaxies) can just as easily be attributed to processes within plasma physics, a paradigm which has a much more empirical and experimental foundation to work from.

We have mathematicians proving black holes are an erroneous construct. We have plasma cosmologists showing alternate interpretations of phenomena and embracing a view that unifies the process of the universe. We have a general public that is beginning to show more interest in alternate theory than the academic institutions would ever want to admit.

Yet the big bang gets the funding and the publicity, with academia forming an army of followers that conform to authority and have an almost cult-like devotion to a world view that is fragmentary and nihilistic. The system of control runs quite deep.