6 The Shell-Universe - a static Universe

The Shell-Universe and The V-effect - Chapter 6 - 6.3

6 The Shell-Universe - a static Universe.

The Shell-Universe is an idea to test the statement by Friedmann-Lemaitre in 6.1.
Is it possible to "design" a static Universe, with accepted physical laws and with plausible assumptions ?

The Shell-Universe is built of a sphere with stars and galaxies as we can observe. Around it there is a shell, which partly consists of photons and neutrinos. The radius is decided by the Schwarzschild radius, so that photons and neutrinos circulate the Universe.

6.1 Statement by Friedmann-Lemaitre.

In many books the author uses the following statement as an argument for the theory of BigBang :

"Friedmann - Lemaitre have used Einstein's equations and have shown, that a static Universe cannot exist. It would collapse by its own weight."

What they really have shown is that, with the assumptions they have used, a static Universe cannot exist. Other assumptions might change the result.

6.2 The Schwarzschild radius.

The Schwarzschild radius, Rs , is the maximum radius a sphere can have, to prevent light to leave the sphere - or to make the photons circulate the sphere in a planetary movement.

Rs = 2 * G * msphere / c2 [ F7 ]

The gravitation force at the surface of this sphere is

Fgrav = G * m1 * msphere / R2 [ F1 ] or

Fg,sphere = G * msphere/ R2 [ F2 ]

Rs = 2 * Fg,sphere * R2 / c2 but R = Rs

Rs = c2 / 2 / Fg,sphere
For the Shell-Universe

Fg = Fg,tot = Fg,sphere + Fg,shell

and the Schwarzschild radius

Rs = c2 / 2 / ( Fg,sphere + Fg,shell ) [ F6.2 ]

6.3 Calculation of The Shell-Universe.

The calculation is built on

Newton´s Law of Gravitation

F = G * m1 * m2 / D2 [ F1 ]
The Redshift of Gravitation

Fg = G * m2 / L2 / ( H0 / c * L + 1 ) [ F4.3d ]
The Schwarzschild Radius

Rs = 2 * G * msphere / c2 [ F7 ]
The data used are

c speed of light 0.3E9 m / s

G gravitational constant 67E-12 m3 / kg / s2

H0 as in 5.1
Dens as in 5.3

Calculation of gravitation forces.
The first calculations are made with Newton´s Law of Gravitation. [ F1 ]
Then the gravitation is reduced by a redshift . [ F4.3a ]

Calculation with the computer program.
The computer program is called "ShellUni".

When starting the computer program it is possible to chose a calculation of

a sphere,
an empty shell or
a sphere with a shell - The Shell-Universe

The following factors should also be given values

the Hubble parameter H0
the density of the sphere Dens
a preliminary radius Rprel

The calculation can be done

without redshift of gravitation or
with redshift of gravitation

The computer program

divides the sphere into small unit cubes and the shell into small unit squares.
I have used a division into 550 000 units in my calculations.
calculates the gravitation force from each unit on units along the X-axis.
adds the gravitation forces, to get the total influence for each unit along
the X-axis. This gives the curves in the following figures.
compares the influence from the sphere with the influence from the shell, to find which "surface density" for the shell, that compensates the influence from the sphere. This is done at the point, 0.4 * radius from the centre.
calculates the total influence in The Shell-Universe. This gives figure 6.6a .
calculates the radius, at which the radius of The Shell-Universe is equal to the Schwarzschild radius. This gives the curves in figure 6.7 .
calculates the thickness of the shell, assuming a density like the density of our galaxy.

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