Mathematician Claims Black Holes Are the Result of Bad Math!
Much as science hates to have its apple cart upset, mathematician Stephen J. Crothers seems to be spoiling to do just that! He claims that the equations used to justify the existence of "black holes" are themselves either incorrect or inapplicable, thus meaningless and in error...
Needless to say, his assertions rub astronomers and astrophysicists the wrong way. However, if his assertions are accurate, then a large chunk of current astronomy is predicated upon a false concept.
Crothers claims to have mathematically (and rigorously) demonstrated that the math behind black holes has been incorrectly applied and in some cases incorrectly attributed (IE, the wrong scientists given credit for particular valid or invalid mathematical contributions).
To briefly summarize some of Crothers' claims regarding the history of black hole theory:
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
... 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
... 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
... Marcel Brillouin's 1923 paper, in English, in which he gives another valid solution
... also simply and dramatically demonstrates that the black hole is nonsense. Brillouin's paper has also been ignored.
Crothers provides links to the original papers of the various authors he claims got it right (Schwarzchild, Droste & Brillouin) and those he claim got it wrong (Hilbert). He also reserves a few ascerbic observations for many of the so-called "experts."
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.
Crothers speaks in no uncertain terms. His assertions that astronomers / astrophysicists got the math wrong are also relatively to the point, though a bit overly technical...
First, the fundamental black hole (a so-called "Schwarzschild" black hole) is allegedly obtained from a solution for Ric = Rij = 0 (subscripts i,j = 0,1,2,3), which is a spacetime that, by definition, contains no matter. So the alleged black hole can interact with nothing because its associated spacetime is empty by definition - it precludes the presence of any matter by virtue of Ric = 0. So there is no matter outside the black hole by initial hypothesis.
The problem is that the energy-momentum tensor describes the matter causing Einstein's alleged "curvature of spacetime." Setting it to zero basically means removing all matter / mass from the associated spacetime (our spacetime)! In essence Ric=0 (the Ricci curvature tensor set to zero), from which the mathematical notion of black holes were derived, describes an empty universe!
Our universe is NOT empty. This appears to be a fundamental flaw in the mathematical / physical reasoning behind black holes... Assuming Crothers' understanding of the associated math and its physical implications is correct.
Crothers goes on to expose what he considers to be several other fundamental flaws in black hole theory.
... the alleged radius of the event horizon, the [so-called] "Schwarzschild radius", is not a distance in the spacetime manifold, let alone a radial distance. The astrophysical scientists have asserted this in ignorance of even elementary differential geometry!
...it is not the geodesic radial distance from the centre of spherical symmetry of the spatial section.
...it is in fact the inverse square root of the Gaussian curvature of any spherically symmetric geodesic surface in the spatial section of the spacetime manifold ... the radius of Gaussian curvature thereof.
In essence what Crothers highlights is that the "Schwarzchild radius" is not a physical radius of a sphere in 3D space. It is the radius of Gaussian curvature, a completely different mathematical entity than scientists obliviously claim it to be (according to Crothers).
Wikipedia defines "radius of curvature" thus:
Radius of curvature is a term characterizing the measure of how curved, or bent, a given curve or surface is.
This is considerably different from the typical "radius" of a sphere.
In essence, it seems Crothers is implying that astronomers and astrophysicists do not understand differential geometry and have misused one type of radius in place of another, and thus created a more-or-less fictional entity: the black hole.
This issue bears further attention and review by the astrophysical community (as opposed to unscientific summary dismissal of an unpopular idea). Even if the attention is a mathematical disproof of Crothers' work, at least it would be in the realm of good science. Point, counter-point.
If, however, Crothers' work is upheld, and black holes are essentially "mathematical nonsense," astronomers will have a long hard road ahead of them, if their favorite hobby-horse is found to be defunct. What, then must be called upon to explain various observations in space that have heretofore been dressed up to fit the mold of "black holes?" Interesting times ahead!
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