# The End of Big Bang, Black Holes and the Science of Stephen Hawking?

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Iconic figure in cosmology, Professor Stephen Hawking, has his Singularity Theorem claims challenged in a remarkable new paper by probably the most able scholar in Einsteinian type general relativity, Stephen Crothers, of Queensland, Australia.

Crothers has produced many definitive refutations of the ‘Big Bang,’ black holes and other fallacies spawned from Einsteinian general relativity that have irked the scientific mainstream. In his latest paper, ‘On the Invalidity of the Hawking-Penrose Singularity ‘Theorems’ and Acceleration of the Universe from Negative Cosmological Constant,’ [1]

Crothers argues, “To disprove the Hawking-Penrose Singularity Theorem requires only disproof of one of the conditions the Theorem must satisfy. Nonetheless, all of the required conditions are proven invalid herein.”

As with his previous papers (2005, 2008, 2010, 2012, 2012b) Crothers demonstrates that ‘Big Bang’ scientists “have no valid basis in science bearing in mind that their concepts and arguments are based on the General Theory of Relativity which is easily proven to violate the usual conservation of energy and momentum and to not predict the black hole.”

The abstract is below and a link to the full paper is found here.

**ABSTRACT**

Hawking and Penrose proposed “A new theorem on spacetime singularities …

which largely incorporates and generalizes the previously known results” which

they claimed “implies that space-time singularities are to be expected if either the

universe is spatially closed or there is an ‘object’ undergoing relativistic

gravitational collapse (existence of a trapped surface)” and that their ‘Theorem’

applies if four certain physical conditions are satisfied. Hartle, Hawking and

Hertog have proposed a quantum state with wave function for the Universe which

they assert “raises the possibility that even fundamental theories with a negative

cosmological constant can be consistent with our low-energy observations of a

classical, accelerating universe.” They also relate this concept to string cosmology.

It is however proven in this paper that the Hawking-Penrose Singularity ‘Theorem’

and accelerated expansion of the Universe with negative # are invalid because they

are based upon demonstrably false foundations relating to Einstein’s field

equations, trapped surfaces, and the cosmological constant.

Crothers concludes that with the ‘Big Bang’ Cosmology, lacking any theoretical basis it tells us that the Cosmic Microwave Background is not the afterglow of the birth of the Universe from a Big Bang “creatio ex nihilo or otherwise.”

*******

[1] Crothers, S., J., ‘On the Invalidity of the Hawking-Penrose Singularity ‘Theorems’ and Acceleration of the Universe from Negative Cosmological Constant,’ (Queensland, Australia), http://vixra.org (May 4, 2013)

Tags: Albert Einstein, Big Bang theory, black holes, Cosmology, Stephen Crothers, Stephen Hawking

## Ron Beck

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For starters, Stephen Crothers by his own admission is “neither a mathematician nor a physicist”. In fact, he is just an amateur scientist — yeah, and so is my 7 year old nephew who just got his first toy chemistry set for his birthday.

But there are individuals who have actually made it all the way through graduate school (unlike Crothers) and have studied and understand the mathematics. They have looked at Crothers papers and found them to be “rife with errors”.

Here is just one of the many articles that refute Crothers’ error-ridden claims; it explains exactly why Crothers’ mathematics is flawed. Incidentally, Crothers has known about this article for over three years now, but continues to avoid any discussion of it. Read it and find out why Crothers is flat-out wrong:

“The Mathematics of Black Hole Denialism” – Dr. William D. Clinger (PhD in Mathematics from MIT)

http://www.internationalskeptics.com/forums/showthread.php?p=8092280#post8092280

## Stephen J. Crothers

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http://www.sjcrothers.plasmaresources.com/critics.html

## John OSullivan

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From Paul Rickey Mays via PSI:

Many a physicist has fallen in the trap of viewing a model as reality… “The skeptic will say, ‘It may well be true that this system of equations is reasonable from a logical standpoint, but this does not prove that it corresponds to nature.’ You are right, dear skeptic. Experience alone can decide on truth. ” – Albert Einstein

Mays’s Axiom’s

1) There are no infinities… are but illusion that occurs when mathematical constructs fail due to scale…

2) There are no paradox’s … Are but a mental construct in the absence of all known rules….

3) All observed constants in nature are variable… but on such scales as to be undetectable as varing from the limited scale of observation of the observer…

4) Man knows far less than he knows he knows….

5) Physical Laws apply whether or not man has symbolically defined it…..

a) Mathematical symbolism is not the event its describes…

b) All physical aspects will occur in the universe whether we recognize it or model it… or even if we cease to exist…

6) Vines will n

## Stephen J. Crothers

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As for timedilation’s claim that the black hole model universes are not claimed to be literal I refer timedilation and all readers here to my post dated 2013-06-21 11:39. It’s literal!

Stephen J. Crothers

## Stephen J. Crothers

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(7) General Relativity is a nonlinear theory. Therefore the Principle of Superposition is invalid in General Relativity. Consequently no alleged black hole model universe can be blended (superposed) with any alleged big bang model universe, no alleged black hole model universe can be blended (superposed) with any other alleged black hole model universe or with itself, no alleged big bang model universe can be blended with any other big bang model universe or with itself or with any alleged black hole model universe. Let [b][i]X[/i][/b] be some alleged black hole model universe and [b][i]Y[/i][/b] some alleged big bang model universe, and let ‘[i]a[/i]’ and ‘[i]b[/i]’ be scalars. Then the linear combination [i]a[/i][b][i]X[/i][/b] + [i]b[/i][b][i]Y[/i][/b] (superposition) is not a universe, it is not a solution to Einstein’s field equations. Indeed, [b][i]X[/i][/b] and [b][i]Y[/i][/b] pertain to entirely different sets of Einstein field equations and so they have nothing whatsoever to do with one another. Moreover, there are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can be asserted that his field equations contain latent solutions for two or more masses. Superposing alleged black hole model universes with themselves and with alleged big bang model universes and superposing alleged big bang model universes with themselves and with alleged black hole model universes contradicts the invalidity of the Principle of Superposition in General Relativity.

(8) General Relativity violates the usual conservation of energy and momentum and is therefore in conflict with experiment on the deepest of levels. Einstein’s attempt to circumvent this catastrophe by means of his so-called ‘pseudotensor’ is fallacious because his pseudotensor is not only not a tensor, it also implies the existence of a ‘first-order intrinsic differential invariant’. But the pure mathematicians proved in 1900 that such invariants do not exist! Thus, assuming the validity of Einstein’s pseudotensor produces an absurdity, and so the initial premise is false (by [i]reductio ad absurdum[/i]). The Landau-Lifshitz pseudotensor suffers from precisely the same fatal defect. These pseudotensors contradict pure mathematics. This is far removed from timedilator’s allegation that I have “[i]a childish misunderstanding of how mathematical physics works[/i].”

(9) What Hawking and Penrose and all proponents of the black hole call the ‘radius’ in one way or another, of their ‘trapped surfaces’, is easily proven to be neither a radius nor a distance. Yet they always treat it as the ‘radius’. That contradicts mathematics.

I note that timedilator hides behind a non de plume, having no courage to reveal his true identity. He complains that I write to physicists and calls me aggressive. Poor physicists, they are allowed to write as much rubbish as they please, but it is not nice for me to have them account for their gibberish.

Stephen J. Crothers

## Stephen J. Crothers

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(4) All alleged black hole model universes actually contain no matter because although they are alleged to contain only one mass, that of the black hole itself, no such mass appears in any related Einstein field equations. Consider the so-called ‘Schwarzschild solution’ for the field equations Ric = 0. In Ric = 0 the (energy-momentum tensor) = zero, and hence, by mathematical construction Ric = 0 contains no material sources. However, Einstein and his followers assert that a material source is nonetheless present, namely a star, which, according to Einstein’s followers can ‘collapse’ to form a black hole. This star is the alleged source of the gravitational field for Ric = 0. However, for de Sitter’s empty universe, described by Ric = lambda (g_ij) the (energy-momentum tensor) = 0, and for this very reason de Sitter’s universe is empty. Thus it is claimed by the proponents of black holes and big bangs that (energy-momentum tensor = 0) both includes and precludes material sources. This is impossible. Thus they are mutually exclusive by their contradiction. The fact is, (energy-momentum tensor = 0) = (no gravitational field) = (no model universe).

(5) All alleged black holes are alleged to have an escape velocity and no escape velocity simultaneously. This is impossible, because it is a contradiction.

(6) All alleged solutions to various sets of Einstein field equations for black hole model universes obtain their sole respective mass by an arbitrary insertion of Newton’s expression for escape velocity, an implicit two-body relation thus inserted into what is allegedly a solution for a one-mass universe, but which is in fact mass-less universe. (See point (5) above). Inclusion of Newton’s implicit two-body relation contradicts the definition of the problem set to be solved.

## Stephen J. Crothers

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timedilator alleges that my “[i]premise is completely wrong[/i].” What premise is that? My premises were not devised by me; they are extracted directly from the claims of the astrophysical scientists, and I have proved them false.

That the black hole universes and the big bang universes are contradictory means that they cannot coexist, by their very definitions, by their very mathematical constructions, contrary to the practice of the astrophysical scientists and the claims of timedilator. Since they are contradictory they are indeed mutually exclusive.

The only thing timedilator comprehends is that black hole universes and big bang universes are ‘models’. Let’s therefore reiterate once again for timedilator, who is evidently incapable of perceiving contradictions in these models. Models that are inherently inconsistent are incompatible, and so they cannot be blended or superposed, despite the standard practice of the astrophysical scientists. Superposition of such models produces nonsense from nonsense.

[b]A FEW SIMPLE CONTRADICTIONS[/b]

(1) All the 4 alleged types of black hole model universes are spatially infinite and so they cannot be blended with (superposed) or inserted into a big bang spatially finite model universe (constant positive curvature), nor can they blended with (superposed) or inserted into big bang model universes that possesses constant zero or constant negative curvature because no alleged black hole model universe possesses such constant curvatures as the three types of alleged big bang model universes. Thus they are mutually exclusive.

(2) The 4 alleged types of black hole model universes are eternal or not non-static (i.e. they are static or stationary) so they cannot be blended with or put inside any big bang model universe because all three alleged big bang model universes are of finite age (they are non-static). Thus they are mutually exclusive by their contradiction.

(3) The 4-alleged black hole model universes are either asymptotically flat or asymptotically curved and so they cannot be blended with or inserted into any of the three alleged big bang model universes because all big bang model universes are not asymptotically anything. Thus they are mutually exclusive by their contradiction.

## Stephen J. Crothers

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timedilator reiterates the same “[i]dreary[/i]” unscientific evasions, as usual. The fact is, as I have proven in the paper cited above, trapped surfaces do not form in General Relativity; they are entirely figments of imagination and invalid mathematics. The Hawking-Penrose Singularity Theorems are demonstrable nonsense, as my paper proves. Without trapped surfaces there are no black holes. That I often repeat my arguments this way or that in different papers merely exposes the black hole nonsense from different standpoints. The proponents of black holes and big bangs repeat their claims every single day now in reports in journals, magazines and internet communications. Repetition is a method the proponents of this nonsense use to try to solidify their dogmatic falsehoods. I’m castigated by timedilator for using the very same method of repetition used by his astrophysical scientists, except that in my case the repetition is of truth whereas in the case of proponents of black holes and big bangs it is repetition of demonstrable claptrap.

Furthermore, I have always had more than one thing to say, so timedilator’s allegation of me that “[i]he has only one thing to say[/i]” is a really big fib, a method so often resorted to by scoundrels.

timedilator says “[i]Crothers appears incapable of grasping that a model is just that: a model. If the assumptions made by two models are not identical, it does invalidate either or both of them[/i].” These are remarks that have nothing at all to do with what I have adduced. First, all mathematical models are models by their very nature, their very definitions. I have never confused models with reality, contrary to the standard practice of the astrophysical scientists. It is therefore a blatant lie that I am “[i]incapable of grasping that a model is just that: a model[/i].” Second, assumptions made for two models that contradict one another necessarily means that that are incompatible and thus mutually exclusive. Third, assumptions made for a given model that contract other assumptions in the very same model invalidate the model. Blending two models that are contradictory between themselves produces an invalid model, and blending two models that contain contradictions within themselves and then combining them with one another compounds the contradictions, rendering them invalid too. Black holes and big bangs are inherently contradictory and also mutually contradictory, and so they are contradictory absolutely, and therefore invalid. A mathematical model that is logically inconsistent is not a model of anything, period.

## timedilator

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Apologies: there was an important ‘not’ missing from one sentence. Corrected version:

If the assumptions made by two models are not identical, it does NOT invalidate either or both of them

## timedilator

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Stephen Crothers has been laboring the same point for years now; every paper is drearily predictable, because he has only one thing to say.

Unfortunately, his premise is completely wrong. His argument (which he has repeated ad nauseam, in every paper, internet comment and unnecessarily aggressive email to a physicist) is the one he parrots in the comments above, for about the ten millionth time:

“All alleged solutions to Einstein’s field equations for the black hole relate to a universe that is spatially infinite, is eternal, contains only one mass, is not expanding, and is asymptotically flat. Big bang models pertain to a universe that is said to be spatially finite (one case – positive curvature) or spatially infinite (two cases – one flat the other negative curvature), of finite age, contains radiation and many masses (including multiple black holes, some of which are said to be ‘primordial’), is expanding, and is not asymptotically flat. Thus the black hole and big bang are mutually exclusive.”

The logic is impeccable until you consider that a mathematical description of the universe is not literal; it is a model. A model makes simplifications because if every variable were to be included it would become impossible to compute a solution. Kepler’s model of planetary orbits makes several untrue assumptions, including that planetary bodies are perfect spheres. However, it agrees closely with observation, because these unaccounted-for variables have a negligible effect. Crothers appears incapable of grasping that a model is just that: a model. If the assumptions made by two models are not identical, it does invalidate either or both of them. His great ‘proof’ is in fact a childish misunderstanding of how mathematical physics works – and one that overlooks the inconvenient fact that experimental observation shows a close agreement with theory, just as Kepler’s imperfect model agrees closely with observation.

## Latour

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Since as x approaches zero, lim 1/x = infinity, by mathematical definition, and it may not exist in a finite universe, one can easily say 1/0 is undefined. There is no problem here, just a semantics style difference reconciled with “infinity” and

“undefined” are synonyms.

I was certainly not moved to dismiss GR or the existence of black holes. Need to study the rebuttals before doing that, in fairness.

## Quantummist

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[quote name=”Latour”]Since as x approaches zero, lim 1/x = infinity, by mathematical definition, and it may not exist in a finite universe, one can easily say 1/0 is undefined. There is no problem here, just a semantics style difference reconciled with “infinity” and

“undefined” are synonyms.

I was certainly not moved to dismiss GR or the existence of black holes. Need to study the rebuttals before doing that, in fairness.[/quote]

The skeptic will say, ‘It may well be true that this system of equations is reasonable from a logical standpoint, but this does not prove that it corresponds to nature.’ You are right, dear skeptic. Experience alone can decide on truth. ” – Albert Einstein

Mays’s Axiom’s 1) There are no infinities… are but illusion that occurs when mathematical constructs fail due to scale…

## Quantummist

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Mays’s Axiom’s 5) Physical Laws apply whether or not man has symbolically defined it….. a) Mathematical symbolism is not the event its describes… b) All physical aspects will occur in the universe whether we recognize it or model it… or even if we cease to exist…

## Stephen J. Crothers

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[quote name=”Latour”]Since as x approaches zero, lim 1/x = infinity, by mathematical definition, and it may not exist in a finite universe, one can easily say 1/0 is undefined. There is no problem here, just a semantics style difference reconciled with “infinity” and

“undefined” are synonyms.

I was certainly not moved to dismiss GR or the existence of black holes. Need to study the rebuttals before doing that, in fairness.[/quote]

This is not semantics at all. Limits are not involved. Precise values producing division by zero occur: “Once a body of matter, of any mass m, lies inside its Schwarzschild radius 2m it undergoes gravitational collapse . . . and the singularity becomes physical, not a limiting fiction.” (Dodson & Poston, Tensor Geometry, Springer–Verlag, 1991); “The black hole’s singularity is a real physical entity. It is not a mathematical artifact” (Carroll and Ostlie, An Introduction to Modern Astrophysics, Addison–Wesley, 1996). Dirac falsely asserts that in Hilbert’s metric, at r = 2m, g_(oo) = 0 and that also then g_(11) = -1/g_(00) = – infinity (Dirac, General Theory of Relativity, Princeton University Press, 1996). But division by zero is undefined in mathematics. Undefined is not infinity. Division by zero is not infinity.

## Stephen J. Crothers

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[quote name=”Latour”]I was certainly not moved to dismiss GR or the existence of black holes. Need to study the rebuttals before doing that, in fairness.[/quote]

All alleged solutions to Einstein’s field equations for the black hole relate to a universe that is spatially infinite, is eternal, contains only one mass, is not expanding, and is asymptotically flat. Big bang models pertain to a universe that is said to be spatially finite (one case – positive curvature) or spatially infinite (two cases – one flat the other negative curvature), of finite age, contains radiation and many masses (including multiple black holes, some of which are said to be ‘primordial’), is expanding, and is not asymptotically flat. Thus the black hole and big bang are mutually exclusive.

## Stephen J. Crothers

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[quote name=”Latour”]I was certainly not moved to dismiss GR or the existence of black holes.[/quote]

Suppose now just two black holes (from what field equations do they come from?); each black hole disrupts the asymptotic flatness of the other black hole so that the spacetime between them is not asymptotically flat. In addition, each black hole encounters an alleged ‘infinite curvature’ at the singularity of the other black hole.

## Stephen J. Crothers

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[quote name=”Latour”]I was certainly not moved to dismiss GR or the existence of black holes.[/quote]

Now consider the 2.5 million ‘supermassive’ black holes that NASA scientists have claimed to have found (NASA’s WISE Survey). None of the alleged black holes are in a spacetime that is asymptotically flat owing to the presence of the other black holes, and each of them encounters 2,499,999 ‘infinite’ curvatures due to the other 2,499,999 alleged black holes. But all alleged black hole solutions to Einstein’s field equations are defined by mathematical construction to have a spacetime that is asymptotically flat, in a universe that is spatially infinite, eternal, and not expanding. Multiple black holes and black hole binaries violate the very definition of the black hole.

## Stephen J. Crothers

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[quote name=”Latour”]Since as x approaches zero, lim 1/x = infinity, by mathematical definition, and it may not exist in a finite universe, one can easily say 1/0 is undefined. There is no problem here, just a semantics style difference reconciled with “infinity” and

“undefined” are synonyms.

I was certainly not moved to dismiss GR or the existence of black holes. Need to study the rebuttals before doing that, in fairness.[/quote]

My paper on the invalidity of the Hawking-Penrose Singularity Theorem proves their ‘trapped surface’ is invalid. That eliminates the black hole completely. A full discussion with almost no mathematics, save for some high school arithmetic and elementary algebra in just a few places, is here:

[url]http://viXra.org/abs/1306.0024 [/url]

The non-mathematical reader is no longer disadvantaged. The fallacies are laid bare for all to see.

## Quantummist

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http://www.4shared.com/office/uYtj2iCx/Postulate_Updated.html

## Sunsettommy

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I have long been a skeptic of the “big bang” conjecture because of the way it was conceived and died several times before it gained favor with those who are deep into the deductive method in the 1950’s.

Eric J. Lerner wrote and published a science paper on the big bang and microwave background nonsense way back in 1988 and wrote a book I have in my library The Big Bang Never Happened.

http://www.photonmatrix.com/pdf/Plasma%20Model%20an%20Alternative%20To%20The%20Big%20Bang.pdf%5B/url%5D

and the book,

http://www.bigbangneverhappened.org/

## Quantummist

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[quote name=”Sunsettommy”]I have long been a skeptic of the “big bang” conjecture because of the way it was conceived and died several times before it gained favor with those who are deep into the deductive method in the 1950’s.

Eric J. Lerner wrote and published a science paper on the big bang and microwave background nonsense way back in 1988 and wrote a book I have in my library The Big Bang Never Happened.

http://www.photonmatrix.com/pdf/Plasma%20Model%20an%20Alternative%20To%20The%20Big%20Bang.pdf%5B/url%5D

and the book,

http://www.bigbangneverhappened.org/%5B/quote%5D

The skeptic will say, ‘It may well be true that this system of equations is reasonable from a logical standpoint, but this does not prove that it corresponds to nature.’ You are right, dear skeptic. Experience alone can decide on truth. ” – Albert Einstein

## ewiljan

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[quote name=”Quantummist”][quote name=”Sunsettommy”]I have long been a skeptic of the “big bang” conjecture because of the way it was conceived and died several times before it gained favor with those who are deep into the deductive method in the 1950’s.

Eric J. Lerner wrote and published a science paper on the big bang and microwave background nonsense way back in 1988 and wrote a book I have in my library The Big Bang Never Happened.

http://www.photonmatrix.com/pdf/Plasma%20Model%20an%20Alternative%20To%20The%20Big%20Bang.pdf%5B/url%5D

and the book,

http://www.bigbangneverhappened.org/%5B/quote%5D

The skeptic will say, ‘It may well be true that this system of equations is reasonable from a logical standpoint, but this does not prove that it corresponds to nature.’ You are right, dear skeptic. Experience alone can decide on truth. ” – Albert Einstein[/quote]

I have never looked this far down the teorietical sewer> why would I wish to?

Albert’s SR ande GR are weird enough but did provide a useful POV while trying to figure what “is”, and did predict correctly..

How do the BB theory or Black-Hole theory

provide insight to what “is”? To me either only form the basis for a new Religion.