君知否，“黑洞”乃是数学没玩好的产物

Mathematician Claims Black Holes Are the Result of Bad Math!

       by mgmirkin

by dkeachie

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Muchas science hates to have its apple cart upset, mathematician Stephen J.Crothers seems to be spoiling to do just that! He claims that theequations used to justify the existence of "black holes" are themselveseither incorrect or inapplicable, thus meaningless and in error...

Needless to say, his assertions rub astronomers and astrophysiciststhe wrong way. However, if his assertions are accurate, then a largechunk of current astronomy is predicated upon a false concept.

Crothers claims to have mathematically (and rigorously) demonstratedthat the math behind black holes has been incorrectly applied and insome cases incorrectly attributed (IE, the wrong scientists givencredit for particular valid or invalid mathematical contributions).

To briefly summarize some of Crothers' claims regarding the history of black hole theory:

Theso-called "Schwarzschild" solution is not due to Karl Schwarzschild atall. The experts have either not read Schwarzschild's 1916 memoir orhave otherwise ignored it
... The so-called "Schwarzschild"solution is due to David Hilbert, itself a corruption of a solutionfirst derived by Johannes Droste in May 1916, whose paper has also beenburied 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 oftheoretical physicists continues to elaborate on this falsehood, with ahostile 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 offlawless 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.

Source: sjcrothers.plasmaresources.com

Crothers provides links to the original papers of the variousauthors he claims got it right (Schwarzchild, Droste & Brillouin)and those he claim got it wrong (Hilbert). He also reserves a fewascerbic 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.

Source: sjcrothers.plasmaresources.com

Crothers speaks in no uncertain terms. His assertions thatastronomers / astrophysicists got the math wrong are also relatively tothe point, though a bit overly technical...

First,the fundamental black hole (a so-called "Schwarzschild" black hole) isallegedly 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. Sothere is no matter outside the black hole by initial hypothesis.

Source: thunderbolts.info

The argument goes that by setting Einstein's energy-momentum tensor to zero it can be shown that the Ricci scalar invarinat is zero and will also set the Ricci curvature tensor to zero.

The problem is that the energy-momentum tensor describes the mattercausing Einstein's alleged "curvature of spacetime." Setting it to zerobasically means removing all matter / mass from the associatedspacetime (our spacetime)! In essence Ric=0 (the Ricci curvature tensorset to zero), from which the mathematical notion of black holes werederived, describes an empty universe!

Our universe is NOT empty. This appears to be a fundamental flaw inthe mathematical / physical reasoning behind black holes... AssumingCrothers' understanding of the associated math and its physicalimplications 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!

Source: thunderbolts.info

...it is not the geodesic radial distance from the centre of spherical symmetry of the spatial section.

Source: thunderbolts.info

...itis in fact the inverse square root of the Gaussian curvature of anyspherically symmetric geodesic surface in the spatial section of thespacetime manifold ... the radius of Gaussian curvature thereof.

Source: thunderbolts.info

In essence what Crothers highlights is that the "Schwarzchildradius" is not a physical radius of a sphere in 3D space. It is theradius of Gaussian curvature, a completely different mathematicalentity than scientists obliviously claim it to be (according toCrothers).

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.

Source: en.wikipedia.org

This is considerably different from the typical "radius" of a sphere.

In essence, it seems Crothers is implying that astronomers andastrophysicists do not understand differential geometry and havemisused one type of radius in place of another, and thus created amore-or-less fictional entity: the black hole.

Crothers has also previously challenged physicists to review his rigorous papers on the history of "black hole" theory and those refuting black holes mathematically.

This issue bears further attention and review by the astrophysical community (as opposed to unscientific summary dismissalof an unpopular idea). Even if the attention is a mathematical disproofof 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 areessentially "mathematical nonsense," astronomers will have a long hardroad ahead of them, if their favorite hobby-horse is found to bedefunct. What, then must be called upon to explain various observationsin space that have heretofore been dressed up to fit the mold of "blackholes?" Interesting times ahead!

数学家说黑洞理论完全不靠谱

matrix 发表于 2008年9月10日 14时00分 星期三
来自连根拔起部门

数学家Stephen J Crothers过去5年一直致力于理解黑洞理论中的数学，声称证明黑洞存在的方程式要么本身有错误，要么是不适用该条件，因此毫无意义。如果他的话是正确的，这显然会产生多米若骨牌效应。Crothers认为，黑洞存在的导出需要把爱因斯坦能动张量设为零。但相对应的数学假设存在问题，因为物质的质量（非零的能动张量）产生了被爱因斯坦称作是时空弯曲的效应。能动张量为零意味着要从相应的时空中移除所有的物质/质量。但实际上，Ric=0(Ricci曲率张量为零）——推导黑洞存在的数学概念——描绘的是一个空的宇宙。毫无疑问我们的宇宙绝对不是空的。

他说，所谓的史瓦西（Schwarzschild）方法（PDF）压根儿与Karl Schwarzschild无关。“专家们”要么没读过Schwarzschild 1916年的回忆录，要么就是忽视了它。所谓的史瓦西方法其实来自大卫希尔伯特（DavidHilbert），1916年5月JohannesDroste首先证明它存在错误，不过他的论文可能丢失了，或者专家故意忽视了。希尔伯特的错误方法产生了黑洞，而理论物理学界却继续沿着错误的道路上行进下去。史瓦西的方法没有黑洞，它是完美的数学。但希尔伯特的方法是有缺陷的，MarcelBrillouin在1923年的论文中提供了另一个正确的方法，简单而引人注目的证明黑洞根本就是胡扯，当然这篇论文专家们又没理睬它。Crothers提供了原始作者的论文，包括Schwarzchild，Droste &Brillouin。MIT的教授、《探索黑洞》的作者Edwin F. Taylor在电子邮件中写道，“如果你是对的，我们所有的书都是毫无意义的，都应该被抛弃”。