The myth of black holes
"The essential result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in physical reality. Although the theory given
here treats only clusters whose particles move along circular paths it does not seem to be subject to reasonable doubt that more general cases will have analogous
results. The "Schwarzschild singularity" does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the
constituting particles would reach the velocity of light."
Einstein (1939)
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Einstein says its conviction that the Schwarzschild radius is insuperable
(i.e. a black hole cannot be formed by gravitational collapse).
However this conviction is now a shown result.
Indeed, there are many
proofs owing to the fact that a gravitational collapse of a spherical body
cannot give rise to a black hole within the framework of general
relativity.
Some references:
A. EINSTEIN ; Annal Math. Vol. 40 pp922-936 (1939).
N. STAVROULAKIS : Mathématique et trous noirs; Gazette des mathématiciens, numéro 31 pp 119 -132 (1986).
J.V. NARLIKAR : The Schwarzschild solution : some conceptual difficulties, Found. Phys. 18 (1988) numéro 6 pp.659 - 668.
L. S. ABRAMS : Black holes : the legacy of Hilbert's error; Can. J. Phys. Vol 67 pp. 919-926 (1989).
L. S. ABRAMS : The total space-time of a point-mass when Lambda < 0, and its consequences for the Lake-Roeder black-hole; Physica A 227 (1996)
pp.131-140.
M. MIZONY : Sur le théorème de Birkhoff, dans La relativité générale aujourd'hui; publications de l'université Claude Bernard, Lyon (1993) numéro 12 pp. 23-42.
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Two problems arise: a) Why the demonstrations proving
the formation of black holes, within the framework of general relativity,
are erroneous?
b) Were black holes observed, even indirectly?
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a) There are three principal sources of errors: I pass quickly on
the first which consists in using a nonbijective change of variable,
by forgetting precautions to be taken. The second source of errors is
epistemological significant. Indeed the " radius of Schwarzschild "
has a perimetric significance and not that of a radius. It is, in fact,
a " radius of curvature " (concept which has a precise meaning in
geometry).
For my part I now systematically use in my teaching
the expression perimetric radius of curvature
in the place of
the dangerous denomination, especially in nonEuclidean geometry, of
" radius of curvature ". This " perimetric radius of curvature " is defined
as the quotient of a perimeter per pi and not as the distance to the center,
which, in the case of a curved space, is not the same thing.
The third source of error comes from the global use of the theorem
of Birkhoff which is valid only locally.
Another problem arises: the concept of horizon of a black hole
is not covariant.
Other note: If the photon cannot escape from a black hole, then the
graviton either! What is then the emitted gravitational field?
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b) On the level of the observations, the candidates black holes turn
to be neutron stars. There remain nothing any more but
the massive black hole candidates who would be in the center of
galaxies. But
let us take for example the very famous candidate black hole
(one of the latest to date).
The elliptic galaxy M87 would contain a black hole with two to three
billion solar mass in its center because that would explain
the fast rotation (550km/s) observed 30 away years from
the center. However there are other possible explanations of this fast
rotation without calling upon a black hole.
Here is one which is a simple application of... the theorem shown
by Einstein in its article of 1939.
Let us suppose that the center of M87 is made
of a star cluster with a radius of 30 year and 1 billion solar mass, and
checking the assumptions of the theorem of Einstein.
Then the speed of 550km/s
is explained perfectly (by the use of the formula 23 of the article
of Einstein)!
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The concept of black hole is a purely geometrical concept.
What a beautiful myth!
An anthem with this myth: the special issue of "Pour la Science ",
summer 1997.
The last anthem is appeared in " La Reccherche ", September 98, cf.
the heading "bac to basics".
Fortunately " Sciences et Avenir " in its special issue " Myths and
Legends of the Science " of the summer 1997 denounces this imposture.
Nicolas Witkowski finishes his article while saying:
" And if one wants to admit well that there is no
God behind the Big-bang, how to don't see the devil hides behind
the black holes?"
Let us rehabilitate the concept of quasi black hole
who is an object emitting a very strong field but that
one cannot
identify with the limit object (mathematical) black hole. In
the same manner
that the concept of point mass is a limiting object (physically
unrealistic) but extremely useful in some cases
to study spherical bodies.
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Some new references:
A. MITRA : Non-occurence of trapped surfaces and black holes in spherical gravitational collapse ; Foundations of Physics Letters, Vol 13, p. 543,
(2000).
A. MITRA : On the Final State of Spherical Gravitational Collapse; Found.Phys.Lett. 15 (2002) p.439.
A. LOINGER The black holes are fictive objects; astro-ph/9810167.
Stanley L. Robertson, Darryl J. Leiter :astro-ph/0208333, astro-ph/0310078.
M. Mizony : La relativité générale aujourd'hui, Editions Aléas, Juin 2003.
And what Schwarzschild has already written :
K. Schwarzschild: On the gravitational field of a mass point according to Einstein's theory, (translation and foreword by S.Antoci and A.Loinger),
physics/9905030. !
A new argument :
astro-ph/0503200 :
Title: Dark Energy Stars
Authors: G. Chapline ; Proceedings of the Texas Conference on Relativistic Astrophysics, Stanford, CA, December, 2004
and also
physics/050395 " Questions concerning Schwarzschild's solution of Einstein's equations " de J.Dunning-Davies qui
a également écrit un plus lond texte disponible sur
http://redshift.vif.com/JournalFiles/V12NO3PDF/V12N3DUN.pdf
intitulé "Black Holes, Other Exotic Stars and Conventional Wisdom". !