Presentation
of the article****Questionable
black hole
French translation :
Des doutes
sur l'existence des trous noirs.
Authors :
Jean-Pierre
Petit, Marseille Observatory
| sciences | jp-petit.com |
Pierre Midy,
Orsay CRI.
To
go straight to the scientific paper.
This
work represents the results of ten years of effort. For the last 30 years, astrophysicians
have had only one term on their lips "black holes". The subject fascinates
the public and several books have already been devoted to it. However observational
confirmation is still lacking : black holes "shine by their absence".
And yet the cosmos is vast. Our galaxy alone contains at least 100 to 200 milliard
stars.
The
existence of certain objects has been shown by observation, quasars for example.
We now know of more than four thousand of them. That does not mean that we understand
these objects completely, how they are formed, how they evolve and their lifespan.
In fact we do not know anything about them. They are just catalogued in the
same way as were "nebulae" in the astronomer Messier's time.
Apparently certain quasars live in the centre of formations of the type galaxy.
These galaxies have an "active core", which could mean anything and
nothing at the same time we know nothing of the nature of the activity, what
its energy source is for example.
Contemporary astrophysics seems to satisfy itself with little. To the question
:
- What
is a quasar ?
The
astrophysician replies :
- It
is the core of an active galaxy.
And
to the question :
- What
is an active galaxy ?
He will
reply :
- It
is a galaxy with a quasar at its center...
Recently,
a few years ago, we discovered "gamma flashes", one per day. The cover
of the French magazine Ciel et Espace (Sky and Space) once had the
headline "gamma flashes : a mystery solved at last". Reply, in the
magazine's columns : a small, brilliant spot has just been observed at the position
of a detected gamma flash. Meaning : solving a mystery means knowing that areas
of the sky that emit flashes also emit light....
Isn't that a little .. poor ?
Conversely,
other objects exist whose existence was surmised, often with good precision,
before their observation. The typical example is the supernova, described in
1931 by the American astrophysician (of Swiss origin) Fritz Zwicky during a
famous conference at Caltech, USA. Zwicky explained at the time that sufficiently
massive stars, say with masses above twenty solar masses, should come to a paroxystic
end with an increase in power in the space of a few days, the whole phenomenon
taking place over twenty days or so. It was a remarkable prediction, though
it wasn't taken seriously at the time. However Zwicky, tenacious, discovered
the first supernovae. Nowadays we know of several hundred. The same goes for
neutron stars, identified subsequently with pulsars (rotating neutron stars)
and white dwarves. This species too has several hundred identified individuals.
The
black hole was proposed as an answer to a problem : what becomes of a neutron
star that exceeds a certain "critical mass". These neutron stars,
clearly identified, resemble enormous nuclei of atoms, without protons. Why
are these objects composed exclusively of neutrons?
We consider
neutron stars to be what remains of the iron core of a massive star after it
has exploded. A massive star is a star in which several types of fusion take
place during its lifetime. It ends by producing iron which cannot take part
in any further exo-energetic fusion reaction. This iron, heavy, falls to the
centre of the star therefore, like ash in a fireplace. When the star suddenly
runs out of fuel (as Zwicky understood) it collapses on itself � 80,000 kilometres
per second (give or take a kilometre per second of course). When falling onto
the iron nucleus this gaz is strongly compressed. Not only does it bounce off,
but several fusion reactions are produced and which no longer need to be exo-energetic
as energy comes from the brutal contraction of the star on itself. All sorts
of nuclear species are created, including many radioactive atoms of extremely
variable lifetimes. In 1987 the explosion of the star Sanduleak, in the Magellan
cloud, gave definite confirmation of the existence of such phenomena (only 150,000
light years away).
The
phenomenon crushes the iron core completely by dislocating its atoms. It becomes
so compressed on itself that electrons no longer have sufficient space to move
between nucleons. Trapped, they therefore combine with protons to give neutrons
and neutrinos.
Normally, when we compress a gas, the phenomenon known as pressure counteracts
the compression. This is also true for a liquid or a solid (everything is compressible).
This is what happens when a young star is born. The proto-star is a mass of
gas which settles on itself. But in doing so it heats up and the force of pressure
limits contraction. It is a poor radiator but must lose energy by radiation
(infrared) before it can contract enough to become a real star. However if its
mass is insufficient it will become a "big Jupiter" (this giant planet
continues to radiate more energy than it receives from the Sun but will never
become a star).
When the explosion of a supernova compresses the iron nucleus, the latter evacuates
its energy by emitting a fantastic quantity of...neutrinos. Here the scenario
changes completely : radiative cooling is instantaneous because the neutrinos
can escape without difficulty. No counter-pressure therefore. The lump of iron
is crushed lamentably. Just a pile of neutrons remains, pressed up against each
other like Japanese in the subway during rush-hour.
Why a critical mass? Because the neutrons cannot take a pressure greater than
a maximum value. Like electric lightbulbs piled up in a mineshaft. After a certain
level of bulbs the glass will break and a pile of broken glass will fall to
the bottom of the shaft.
When a neutron star has a mass a little greater than twice the mass of the Sun,
pressure in its core becomes too great. The neutrons can no longer support it.
It is then supposed to collapse on itself and no known physical phenomenon is
able to go against this "gravitational collapse". A distressing perspective
for an astrophysician.
Even before it explodes a neutron star is a "relativist", as opposed
to a "newtonian" object. This is shown by the aspect of the trajectories
of the "reference-particles" near a mass m (an atom, for example).
We know that the space-time curve phenomenon brings about a precession of the
elliptical orbit of Mercury. But the precession is minute. However, the following
figure, developed from computer calculations, shows the important precession
of a quasi-elliptic trajectory around a neutron star.
So,
there is no question of describing a neutron star with "newtonian material".
The
calculation programme is relatively simple and one day, when Ihave the time,
I'll put it on the site so that you can play with it, and show the gravitational
lens phenomenon (very exaggerated in the following) :
So,
as it is a question of describing the destiny of a neutron star reaching criticity,
a "field equation" needs to be used, that of Einstein.
S
= c
T
T
is a "tensor" which describes the local content in "matter energy".
The tensor is nil on the exterior and non nil on the interior. The geometric
solution must therefore be deduced from two equations.
For the interior :
S
= c
T
for the interior
S
= 0
Solutions
for this type of equation are called "metrics". However it doesn't
matter what form the objects take. As well as that they are "tensors",
and to understand what a tensor is, good luck ... It took me quite a while.
The
Sun is associated with a local "geometry", which is the solution for
the two equations. The first describes the interior of the Sun and the second
the void around it. However we can only describe a sort of "ideal sun"
which consists of a sphere filled with matter of constant density. But that's
better than nothing. These solutions have mathematical expressions which we
won't go into here. They will not mean anything to you. Each has its own "personal
pathology". Let us call rn the star's radius, of constant density r. From
this density r, and the value c of the speed of light, we can calculate a first
characteristic radius, "R circumflex" :
The
interior geometric solution is "non-pathological" if, and only if,
the value of radius rn is inferior to this critical value.
With
the same data we can calculate the second characteristic radius :
which we call the "Schwarzschild
radius" Rs. The exterior solution, which makes reference to the "void"
surrounding our star of constant density r and constant radius will be non-pathological
if, and only if, the value of the star's radius rn is superior to this characteristic
length.When grouping both it is necessary that :
The
quantity to the right depends on the star's density (between
1015 and 1016 grammes
per cubic centimetre). At constant density the quantity to the left increases
as the cube of the radius Rn of
the star.
This
is valid for the sun, considered to be a star of constant density at first approximation.
What do we mean by "pathologies"? Everything : quantities below radicals
that become negative, denominators that become nil. We can see therefore that
a star of constant density cannot be described by the following type of stationary
solution :
The "Schwarzschild radius" of the sun is 3,7 km : well inside (rn
). You can enjoy yourselves calculating it, given that its radius is 695,000
km, the value of the second critical radius "R circumflex" is higher.
If it
was a question of the sun, on the scale of the figure the Schwarzschild radius
(3,7 km) would be just a point and radius "R circumflex" would go
way off the sheet. The above figure refers more to a "subcritical neutron
star".
How does the
"climb to criticity" take place? It suffices to add layers of neutrons,
increasing in constant density (we liken the neutron star to, if not a solid,
at least a drop of practically incompressible fluid).
We obtain
the above curves simply by using the formula shown. The star's radius increases
but the "Schwarzschild radius" catches it up. And the two meet when
rn
reaches the value "R circumflex". Then, on the star's surface, the
quantity of sub-radicals becomes negative, denominators become nil etc. This
if the mathematical, geometrical translation of criticity. Which simply means
that it is impossible to describe the star using either or both the combined
geometrical solutions obtained from the Einstein equation with the second member
non nil (interior) or nil (exterior). The characteristic maximum value of this
radius is about 20 kilometres. The neutron star's density can be calculated
from this.
But
there is something that is little known, including among "cosmic men",
even though it comes from work done during the 40's : there is another criticity,
of physical nature this time, which appears just before the star's radius reaches
this value. It is an extremely close value being inferior by just 5%. But when
the star's radius reaches it or, which comes down to the same thing, the mass
reaches a value double that of the sun's mass, pressure at the centre of
the star becomes infinite , by virtue of a "TOV"model developed
in the 40's by Tolman, Oppenheimer et Volkov (the Oppenheimer of the bomb).
Pressure
inside a neutron star according to the distance from the centre for different
values of object mass.
This
is fundamental piece of data for us.
Hereafter
the evolution of the presure, inside the neutron stard, versus the distanceto
its center, for different masses :
...Maybe
scientists, like others, do not ask themselves questions to which they think
they cannot give a reply. How does one reply to the question :
- What
happens in a milieu where, at a certain point, pressure suddenly becomes infinite?
But
nobody asked the question, at least not in that way. Apparently it caught nobody's
eye. Many cosmology specialists with whom Ihave spoken were unaware of this
aspect.
Let
us return to "the story of the black hole". We could say : The implosion
phenomenon of a destabilised neutron star is an unstationary phenomenon. Let
us build therefore an unstationary solution for the ensemble of the two equations
above. However we do not know how to, in a credible manner. So theoreticians
turned towards the "exterior solution" (that which describes, for
example, the geometry at the exterior of the sun and which becomes "pathological"
at the Schwarzschild radius of 3.7 km).
-
In
other words "take away the sun" and let us explore the properties
of this geometry. Like that... -
But
it's a solution that refers to an empty universe ?! -
Take no notice, let's see what we get ...
Study
began on the radial trajectories of objects in free fall towards what would
be, under these conditions, "a black hole of solar mass" of 3.7 km
diameter. The variable t was retained, it was meant to refer to the time experienced
by an "exterior observer", a good earthling looking at the sun they
had just conjured away. It was discovered that the time of freefall of each
test particle, measured according to this time, became infinite. However if
we attached a clock to the said particle, it would arrive at the geometric centre
of the object in a finite time period.
Theoreticians
therefore proposed the following vision :
- This stationary, exterior
solution finds a new, providential employment. In effect, gravitational collapse
does take place in a very brief period (about one ten thousandth of a second
for a destabilised neutron star). However as the phenomenon seems to last for
an infinite time to an "exterior observer", a stationary solution
can be used to describe an eminently unstationary phenomenon.
If there
are no Thrushes, we'll eat Blackbirds....
Starting
from this idea, theoreticians began to ask themselves what would happen to matter
when it crossed the Schwarzschild surface. And there they found all the horrors
mentioned earlier. The particle's time became... pure imagination. The particle's
speed exceeded the speed of light. It becomes a tachyon, whose mass is ... imaginary
etc., etc.
Some
even suggested (and you can find it in many books) that on the interior of the
sphere, the variable r transformed itself into time and the variable t into...
radial distance.
As Jean Heidmann, cosmologist
at Meudon, now retired, used to say :
- When
the talk turns to black holes, you have to leave your common sense in the cloakroom...
Under
these conditions, if we decide to forget common sense, where is the limit to
unreasonableness? How do we decide to build a "physics of the unobservable".
This is the case for "dark matter" about which anything and everything
is said and written, often at the rate of several dozen papers a day. Nobody
seems to have looked into the gemellary model, abundantly developed on my site.
However some foreign researchers (China, Japan) seem to have picked up on it
well.
There
is news in this area. In 88-89 Ipublished three articles in Modern Physics
Letters A (reproduced on the site) which launched the idea, unprecedented, of
a cosmology in which physical constants could vary, including the sacrosanct
speed of light c. The idea was "rediscovered" in 1993. Numerous papers
have been published since in very selective reviews such as Physical Review,
Classical and Quantum Gravity. There is already quite a large group of "constant
variers". Some of them have discovered my work on the Internet site. Many
of them were stupefied, even more so by the fact that the work emanated from
France, a country which has never got itself noticed through an important innovation
in cosmology, or even in astrophysics (fields that are typically German, Russian,
American or British). Contact was established in a very cordial manner. The
Chinese, not without humour, said that he had to get down his atlas to find
the whereabouts of Marseille and had "the impression of discovering an
unknown region of the globe".
Why
this digression ? Because, in our opinion, the vertiginous pressure increase
in the neutron star's core should alter the constants of physics and create
a "hypertoric bridge" between the universe and its twin. It is an
idea that needs further study. This being said, if help is required in this
entreprise, it will most likely come from the "constant variers" who
have already crossed the line. For the time being we are the only "gemellarists"
but things might not always remain that way.
In our
opinion therefore, the gemellary context should completely change the scenario
for a destabilised neutron star. However before we are able to propose a challenger
model, we must study the classic model of the black hole. That is what is being
done in this long paper. Things are not treated "in order". In one
section we carefully looked at Kruskal's work, showing the faults in his approach.
Everything
is motivated. In 1960 Kruskal had noticed that in the initial model (the "Schwarzschild
metric") the speed of light was nil on the sphere in question, the "horizon
sphere", alias the Schwarzschild Sphere, and set about curing this "illness".
But
how do you work on geometric solutions ? Can others be invented ? The answer
is no. Ibelieve that the article shows clearly the arbitrary character of the
choice of coordinates. By its essence, a geometric solution is of "invariant
coordinates", it does not depend on the coordinates chosen. Imagine a soap
bubble. It is a surface. In one sense it is a solution to a field equation which
corresponds to the fact that the energy used in tension, to counterbalance a
constant pressure inside the bubble, is constant on all its surface. To the
question :
- What
is the surface that reacts mechanically in way that can support internal overpressure
?
The
reply is :
- It's
a sphere.
But
this sphere, a geometric object, exists independantly of the coordinate
system used to identify its points. Now we know that when using a system of
meridians and parallels we create polar singularities, apparently singular
points whereas in fact they are not. They are singularities induced by the choice
of coordinates. In the case of the sphere, by the way, these singularities are
inevitable. The figure below shows a sphere and its marking system of latitude
and longitude coordinates.
Remark
: We can map a sphere, give it a marking system with two parameters using just
one pole. See the following figures :
First
mark, first family of curves to a parameter a obtained by cutting the
sphere in planes through a straight line tangent to one of its points.
This
is combined with the second family of curves obtained by****cutting
the same sphere along another straight line tangent to the sphere at the same
point, for example, orthagonal to the first.
The sphere,
thus mapped, seen from another angle which hides its unique singularity.
