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Geometries induced by ghost matter.
In the preceeding section we have studied the conjugated
geometries due to the presence of a constant density, positive mass M, located
in fold F. Now let us suppose that a ( constant density r*
0 ) positive mass M*>0 is present in the fold F*. We assume that in this
portion of the universe the conjugated region of Fis empty.
Then T* describe the content of energy-matter of
the non-empty portion of fold F*. The corresponding field equation system
is :
S = - c T*
S* =c T*
The geometries simply commute :
(135)
Looking at figure (135) we see that a mass M*, located
in fold F*, attracts ghost masses, which follow geodesics of this twin fold,
and repel normal masses, following geodesics of fold F.
Looking at figure (135) we see than fold Fwons an induced
geometry, due to the presence of a ghost mass M* in its fold F*.
The interaction laws.
From (128) and (135) we can deduce the interaction laws
:
-
Matter attracts matter
-
Ghost matter attracts ghost matter.
-
Matter and ghost matter repel each other.
See also :
J.P.Petit & P.Midy : Matter ghost-matter astrophysics.
1.The geometrical framework. The matter era and the newtonian approximation.
Geometrical Physics A , 4 , march 1998.
In this paper we show, in addition, that the interaction
forces is newtonian.
We see this is different from the schema proposed by J.M.Souriau,
where two particles of the second species repel each other.
In our schema, we see that all masses m and m* are positive.
But induced geometry phenomenon makes it possible to have local negative curvature,
somewhere, which was forbiden in classical general relativity.
To sum up we can write the field equation system :
(136)
S =c (**T
- T***)
(137)
S* =c (**T*
- T**)
which gives inverse scalar Riemann curvatures :
(138)
R* = - R
If the local curvature is positive in fold F, it means that :
(139)
T > T*
or :
r > r
*
Then the conjugated curvature is negative in the adjacent
portion of F*.
Conversely, if the local curvature is negative in fold
F, it means that
(140)
T < T*
or:
r < r
*
Then it is positive in fold F*.
If the local curvature is zero, in fold F, it means that
the curvature is null too in the adjacent portion of the twin fold F*.
In addition , either
T = T* = 0
or : r
= r * = 0
T = T* ( r
= r *)
About classical general relativity tests.
Matter and ghost matter repel each other. A galaxy is
a concentration of matter. Then the adjacent portion of the twin space F*
is extremely rarefied, for masses m* have been pushed away. In the vicinity
of the Sun the ghost matter density ( r*
or T* ) can be neglected. Then the field equations system reduces to
:
(141)
(141 bis )
(141) is the Einstein equation, from which we build all
the local classical tests of general relativity.
The Einstein equations become the limit case
when the ghost matter density tends to zero.
