Thunderblog - Guest Contributor Stephen J Crothers
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Big Bang Busted!
(The Black Hole, the Big Bang, and Modern Physics)


There has been a deliberate suppression of important scientific papers by the community of physicists and astronomers concerning the black hole, beginning with the original paper by Karl Schwarzschild of 1916, evidently for vainglory, money and self-aggrandisement. I bring you free access to those papers, and others of relevance, in the hope that this fraud can be exposed and physics restored to a rational search for knowledge. The black hole has no foundation in theory whatsoever. Neither Newton's theory nor Einstein's theory predict it. In fact, both theories preclude it, contrary to what the orthodox relativists claim.

The so-called "Schwarzschild" solution is not due to Karl Schwarzschild at all. The experts have either not read Schwarzschild's 1916 memoir or have otherwise ignored it. Go here to get Schwarzschild's original paper, in English. The so-called "Schwarzschild" solution is due to David Hilbert, itself a corruption of a solution first derived by Johannes Droste in May 1916, whose paper has also been buried or ignored at the convenience of the experts. It appears that the experts have not read Hilbert either. Go here to get a copy of Hilbert's erroneous derivation, in English. Hilbert's mistake spawned the black hole and the community of theoretical physicists continues to elaborate on this falsehood, with a hostile shouting down of any and all voices challenging them. Schwarzschild's solution has no black hole, and neither does Droste's solution. Schwarzschild's paper is a piece of flawless mathematical physics, but Hilbert's is a poor show. And while you're at it you might as well go here to get a copy of Marcel Brillouin's 1923 paper, in English, in which he gives another valid solution and also simply and dramatically demonstrates that the black hole is nonsense. Brillouin's paper has also been ignored.

The experts are always quick to conveniently brand anyone who questions the black hole as a crackpot. Unfortunately for the experts that does not alter the facts. The experts must also include Schwarzschild himself as a crank since his paper invalidates the black hole outright, as does Brillouin's, and Droste's. They must also label Einstein a crackpot, because Einstein always rejected the idea of the black hole, claiming in his research papers and other writings that it is not physical, and that singularities in the field nullify the theory of General Relativity.

It is also commonly held by experts, for example, Hawking and Ellis, Misner, Thorne and Wheeler, S. Chandrasekhar, that the Michell-Laplace dark body is a kind of black hole, or an anticipation of the black hole, and that black holes can be members of binary systems and that black holes can collide. These claims are patently false. Go here for a copy of G. C. McVittie's conclusive arguments which invalidate these ridiculous claims. So if you are a scientific man you will read Schwarzschild's paper, and those of Droste, Hilbert, and Brillouin. You have no legitimate excuse not to, as they are given to you herein. This is not a question of historical priority, as the orthodox relativist is apt to claim when confronted with reality, but one of fundamental science.

It is also claimed by the very same "experts" that General Relativity predicts that the Universe is expanding. This is patently false. The mathematically rigorous proof that these "solutions" are nonsense is given below.

Also listed below are my own research papers in which I derive, on the standard manifold with boundary, the general solution to Einstein's field equations for the static, vacuum field of the point-mass in all its configurations, confirming Schwarzschild's solution, Droste's solution, and Brillouin's solution as particular cases, and that black holes are not consistent with General Relativity, as so well noted by Schwarzschild, Brillouin, and Droste, contrary to common contemporary expert opinion. The point-mass is itself a fictitious object and is to be rightly considered as the centre of mass of an extended body.

Here are some important papers that deal with the Black Hole and the Big Bang. They prove that these theories are not consistent with General Relativity and have no basis in theory whatsoever.

1. On the Gravitational Field of A Sphere of Incompressible Fluid According to Einstein's Theory.
Another masterful 1916 paper by Karl Schwarzschild, also suppressed by the relativistists.

2. The field of a single centre in EINSTEIN'S theory of gravitation, and the motion of a particle in that field.
Droste's 1917 paper in which he derives for the first time the metric obtained later and corrupted by Hilbert, erroneously attributed to Schwarzschild by the experts. There is no black hole.

3. On the Theory of Gravitation.
Hermann Weyl's 1917 paper in which he obtains Droste's solution by another method. I am currently translating this paper into English from the German. Here is an incomplete and rather rough translation, but still with all the facts. I will improve it if and when I get an opportunity.

4. Black Holes: The Legacy of Hilbert's Error.
A brilliant paper by Leonard S. Abrams which demonstrates the invalidity of the Hilbert solution and the black hole.

5. The Total Space-Time for the Point Charge and its Consequences for Black Holes.
Another brillant paper by Abrams demonstrating the invalidity of the Reissner-Nordstrom black hole.

6. The Total Space-Time of a Point-Mass when λ ≠ 0, and its Consequences for the Lake-Roeder Black Hole.
Yet another interesting paper by Abrams in which he also demonstrates the invalidity of the aforesaid black hole (but his arguments are incomplete).

7. On a paper by J. Smoller and B. Temple.
A first-class demonstration by Nikias Stavroulakis (2002) that the black hole is universally inconsistent with General Relativity. The paper by Smoller and Temple shows that black holes never form in solutions of the Oppenheimer-Volkoff equations, but they do not treat of the black hole concept in general. Stavroulakis does.

8. On the Principles of General Relativity and the SΘ(4)-invariant Metrics.
A very well argued paper showing that the standard manifold with boundary is inadmissible and that a gravitating body cannot collapse to a material point. Stavroulakis also discusses in detail the invalidity of the implicit transformations routinely employed by the orthodox relativists.

9. A Statical Smooth Extension of Schwarzschild's Metric.
This is an early paper by Stavroulakis (1974) in which he disproves the black hole in general, by eliminating the manifold with boundary from all consideration, and obtains the metric for an extended spherically symmetric body.

10. Non-Euclidean Geometry and Gravitation.
Another cogent paper by Stavroulakis. This paper was published in Progress in Physics.

Here are some important papers dealing with the localisation of gravitational energy.

11. Mechanics. - On the Analytical Expression that must be given to the Gravitational Tensor in Einstein's Theory.
A very nice paper by T. Levi-Civita in 1917, one of the inventors of Tensor Calculus, showing that Einstein's pseudo-tensor is nonsense because it leads to the requirement for a first-order, intrinsic, differential invariant, which, as is well known to the pure mathematicians, does not exist! This too has been ignored by the relativists.

12. How far can one get with a Linear Field Theory of Gravitation in Flat Space-Time?.
An interesting treatment by Hermann Weyl (1944) demonstrating that the standard linearization of Einstein's equations is inadmissible because it leads to the requirement of a tensor, which, except for the trivial case of being zero, does not otherwise exist! It is in English. Another important paper ignored by the orthodox physicists.

My papers.

1. On the General Solution to Einstein's Vacuum Field and its Implications for Relativistic Degeneracy.
A derivation of the general solution for the simple 'point-mass'. It also demonstrates that the Hilbert solution (invariably and incorrectly called the "Schwarzschild solution" in the textbooks and the bulk of the research literature) does not admit a black hole, and that black holes are nonsense. It is impossible for a black hole to be derived from Schwarzschild's true solution without violating the geometry of his solution (which is precisely what the orthodox relativists have always done to get their black holes and big bangs). This paper was published in Progress in Physics. Karl Schwarzschild's original paper (in English) can be obtained here.

2. On the Ramifications of the Schwarzschild Space-Time Metric.
A derivation of the general solution for the point-charge, the rotating point-mass, and the rotating point-charge. It also demonstrates that the Reissner-Nordström solution, the Kerr solution, and the Kerr-Newman solution, do not admit black holes, and that black holes are nonsense. This paper was published in Progress in Physics.

3. On the Geometry of the General Solution for the Vacuum Field.
A detailed discussion of the significance of the coordinate radius r in the metric for the vacuum field. I show that r in general is neither a radius nor a coordinate in the gravitational field and is in fact only a real-valued parameter, and that the proper radius and the radius of curvature, both functions of r, and which are not the same in Einstein's gravitational field, are the relevant radial quantities in Einstein's gravitational field. The assumption by Hilbert and the conventional relativists that r is 'the' radius in the gravitational field is a grave error, as is the assumption that 0 < r < 2m and 2m < r < are valid ranges for r, and the assumption that a singularity can only occur in the gravitational field where the Riemann tensor scalar curvature invariant (the Kretschmann scalar), f = RαβσρRαβσρ, is unbounded. One cannot talk of r as a radius or of its range by mere assumption. Mathematical rigour must determine the nature and range of r appearing in the metric for the gravitational field, and the nature of a singularity in the field. The orthodox analysis has completely failed to appreciate that the structure of the manifold is contained in the intrinsic and invariant geometry of the metric. I rigorously prove that the orthodox assumptions are invalid. This paper was published in Progress in Physics. Errata: An incorrect statement in this paper, relating to great circles, has been corrected in this paper On Line Elements: A Correction, also published in Progress in Physics.

4. On the Generalisation of Kepler's 3rd Law for the Vacuum Field of the Point-Mass.
I generalise Kepler's 3rd Law to the rotating point-charge, from which the expressions for Kepler's 3rd Law for all other configurations of the material point can be easily recovered. Contrary to the allegations of the relativists, Kepler's Law is modified significantly by General Relativity. This paper was published in Progress in Physics.

5. On the Vacuum Field of a Sphere of Incompressible Fluid.
In this paper I generalise Schwarzschild's solution for the gravitational field of a sphere of incompressible fluid. I also obtain an expression for Kepler's 3rd Law for this sphere. There are no singularities anywhere the gravitational field of this case. The 'point-mass' is shown to be rightly the centre of mass of an extended body. This paper was published in Progress in Physics.

6. On the General Solution to Einstein's Vacuum Field for the Point-Mass when λ ≠ 0 and its Implications for Relativistic Cosmology.
This paper proves that Einstein's General Relativity does not predict an expanding Universe, contrary to the claims of the orthodox relativists. The Friedmann solution, the Einstein-de Sitter solution, and all the general relativistic 'solutions' purporting an expanding Universe are invalid. There is no theoretical substantiation of the Big Bang hypothesis. The conventional interpretations of the Hubble relation and the Cosmic Microwave Background are inconsistent with General Relativity. This paper has been published in Progress in Physics.
Errata: In the paragraph immediately before equation (13), replace the words "... cannot be solved exactly..." with the words "... cannot be easily solved exactly ...".

7. Introducing Distance and Measurement in General Relativity: Changes for the Standard Tests and the Cosmological Large Scale.
I treat the four standard tests of General Relativity in terms of the correct general solution for the field equations, on the standard manifold with boundary, and show that there are serious practical limitations to the application of General Relativity in that only the circumference of a great circle is a measurable distance in the gravitational field. There are no practical means by which this circumference can be measured. This paper was published Progress in Physics.

8. A Short Discussion of Relativistic Geometry.
This paper was published in the Bulletin of Pure and Applied Science E (Mathematics). It gives a simple explanation of the geometrical structure of the line element and the geometrical form of spacetime, and indicates the fatal consequences for black holes and cosmology.

9. A Brief History of Black Holes.
This paper gives, in non-technical terms, a true and accurate account of the historical development of the idea of the black hole, verifiable by the literature, and shows how General Relativity has been incorrectly used to obtain it, exposing how an error in analysis has grown into a fully fledged scientific fraud. This paper was published in Progress in Physics.

10. On Isotropic Coordinates and Einstein's Gravitational Field.
In this paper I prove that (dx2 + dy2 + dz2)½ is not a co-ordinate distance in the gravitational field, contrary to the claims of the orthodox relativists concerning the standard line-element in isotropic co-ordinates. This paper was published in Progress in Physics.

11. On the Regge-Wheeler Tortoise and the Kruskal-Szekeres Coordinates.
In this paper I prove that the Regge-Wheeler (Tortoise) coordinates are inadmissible and highlight the fact that the Kruskal-Szekeres extension does not extend the Droste/Weyl/(Hibert) solution into a trapped surface but is in fact a completely separate pseudo-Riemannian manifold that has nothing to do with the gravitational field and is therefore meaningless. This paper was published in Progress in Physics.

12. Planck Partilces and Quantum Gravity.
In this paper Jeremy Dunning-Davies and I show that the so-called 'Planck particles' are not particles at all. It is proved that the claim that Planck particles are black holes is entirely false. This paper was published in Progress in Physics.

13. Relativistic Geometry and its Implications for Black Holes and Cosmology.
This paper is my presentation at the IXth International Conference, SPACE, TIME & GRAVITATION, St. Petersburg, Russia, August 7-11 2006. It expounds the fundamental geometry of Einstein's gravitational field and indicates the fatal consequences thereof for the theories of black holes and big bangs.

14. Concerning the Mistakes Committed by F. W. Hehl, C. Kiefer, et al. on Black Holes, Expansion of the Universe, and Big Bangs.
Prof. Dr. F. W. Hehl is a senior member of the Gravitation and Relativity Group of the University of Cologne. This paper is a thorough refutation of the work of Hehl, Prof. Dr. C. Kiefer, and their Group, on black holes and cosmology. Neither Hehl nor any member of his Group has responded to this refutation, despite request to do so before an international forum of scientists which also has a copy of the document and which has acknowledged it to be correct. Hehl received a copy of this document on or about 4th December 2006 and all the other members of the Cologne Group received a copy of this document on or about 6th December 2006. It is evident that Hehl, who is an editor of the journal Annalen Der Physik, and the members of his Cologne Group, think that ignoring facts and arguments which completely invalidate their work is scientific method. That is in fact scientific fraud. The international forum of scientists has also posted this document to the website of the Alpha Institute for Advanced Study.

15. Concerning the Mistakes Committed by the Relativists on Black Holes, Expansion of the Universe, and Big Bangs.
( On the Occasion of the XXIII Texas Symposium on Gravitation and Relativity, Melbourne, Australia, December 2006.)
On or about the 13th December 2006, in formal protest against the proposed funding in the sum of $20m for stage II of the Australian International Gravitational Observatory at Gingin in Western Australia, this variant of the Hehl refutation paper, in company with four other papers by different authors, was sent to the Federal Minister for Education, Science and Training, Julie Bishop MP; the Leader of the Federal Opposition, Mr. Kevin Rudd; the Minister for Science and Innovation Western Australia, Mr. Francis Logan; the Shadow Minister for Science and Innovation Western Australia, Mr. Barry House; the Director of the Australian International Gravitational Research Centre, Prof. David Blair, at the University of Western Australia; the Chariman of the ACIGA, Prof. David E. McClellend at the Australian National University; the editors of the following newspapers - The Australian, The Sydney Morning Herald, The West Australian, The Courier Mail, The Age, The Advertiser; the Executive Director of 'A Current Affair', TCN Channel 9 Sydney; and Mr. Robyn Williams, The Science Show, ABC Radio National. Go here for full details about the protest before the Australian Federal Government and the State Government of Western Australia.

This paper was also sent to all persons who presented papers dealing with aspects of black holes or big bang cosmology before the biannual Congress of the Australian Institute of Physics held in Brisbane 3 Dec. to 8 Dec. 2006, to all website lisited officials of the Australian Institute of Physics, and to all persons who presented papers dealing with aspects of black holes of big bang cosmology before the XIII Texas Symposium on Gravitational, Relativity and Cosmology held at the University of Melbourne during the week commencing Monday 11 Dec. 2006. None of the Australian Institute of Physics scientists responded, none of the contacted participants of the AIP Congress or the XXIII Texas Symposium responded.

Prof. Regind T. Cahill of Flinders University in South Australia presented an important address at the AIP Congress in Brisbane. However, I received a report that the AIP would deliberately omit professor Cahill's paper from the published Proceedings of the Congress, evidently because of its implications for the currently accepted theories and current research projects in gravitation. I sent an email inquiry to the President of the AIP requesting an explanation. Copies were sent to all AIP officials as listed on its website. The AIP ignored the inquiry. Here is the letter of inquiry. It is plain that the AIP actively engages in the suppression of science to further its own ends and those of its colleagues.

In addition these letters of protest were sent to Government and Shadow Ministers, AIGRC Director and ACIGA Chairman, with copies to the aforementioned media concerning the misdirected funding of the AIGO and related organisations.

16. Relativistic Cosmology Revisited.

This paper extends my arguments contained in paper (6) above, and puts the last nails in the coffin of the Big Bang phantasmagoria. The only cosmological solutions permitted by General Relativity are spatially infinite for all values of time. This paper is published in Progress in Physics.

17. Anomalous Spacetimes.
This short and simple paper deals concisely with the invalid assumptions made by the relativists in their claims for derivation of black holes from General Relativity. The invalidity of the standard assumptions renders the black hole concept completely spurious.

18. Gravitation On a Spherically Symmetric Metric Manifold.
The unpublished paper "Anamolous Spacetimes" is incorporated into this paper as an example of the fundamental geometrical features of a spherically symmetric metric manifold. Spherically symmetry on a metric manifold is first explained, and then applied to the case of the so-called "Schwarzschild solution", clearly demonstrating thereby that black holes (and also big bangs) are inconsistent with elementary differential geometry and are therefore nonsense. This paper is published in Progress in Physics.

19. On Certain Conceptual Anomalies in Einstein's Theory of Relativity
This paper shows that Rμν = 0 violates Einstein's Principle of Equivalence, and is therefore invalid. This invalidates the black hole from a different perspective, since the black hole is allegedly derived from a solution for Rμν = 0. It also shows that point-masses are inconsistent with the Theory of Relativity and elaborates on the nature and importance of Gaussian curvature for spherically symmetric Type I Einstein spaces. The consequences of the invalidity of Rμν = 0 for conservation and localisation of energy are also discussed. Einstein's conceptions of the conservation of gravitational energy and the localisation of energy for the gravitational field are erroneous. This paper will be published in Volume 1, 2008, of Progress in Physics, and is currently available online at the Journal's website. However, this paper was modified for publication at the request of the Editorial Board because the original contained a few comments about certain proponents of the Standard Model which we considered a bit too revealing. The original form of the paper (my preferred form) can be read here and also here. This paper is not liked by the Standard Model relativists. Go here for an example of their response.

The E-Print version of the hard-copy journal Progress in Physics can be perused online here. All papers published by this journal can be downloaded free of charge.

A formal protest submitted to Government concerning funding of the misguided Australian International Gravitational Observatory is here.

My own experiences in academia for challenging "conventional wisdom" can be perused here. I was expelled from PhD candidature by the University of New South Wales.

Stephen J. Crothers.


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Black Hole - Artist's impression
Artist's impression (cartoon) of a black hole. CREDIT: Dave Smith and

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