Matter-ghost
matter astrophysics. 7 :
Confinment
of spheroidal galaxies by surounding ghost matter. (p3)
.
- The gravitational
field in a spherical hole.
We compute it by combination of
two systems. The first is an infinite constant density r medium. The second
is a simple sphere, filled by the same constant density r material. Let us
compute the field created by such a sphere, considered as isolated.Inside
:
(19)
whose solution is :
(20)
Outside :
(21)
This field is attractive . See
figure 12.
Fig. 12
: Gravitational field due to a constant
density sphere whose density
is r > 0
If we soustract this from a constant
mass density medium, we get the same, plus a spherical hole. As the constant
density medium gives a zeo field, this one in unchanged. See figure 13.
Fig. 13 : Gravitational
field in a hole.
If elliptic galaxies
are surrounded by dense ghost matter, spheroidal galaxies must be too.
As a conclusion this ghost matter environment must confine them too, produce
a missing mass effect and strong lensing, due to negative lensing effect.
References.
[1] R.Adler, M.Bazin & M.Schiffer
: Introduction to general relativity, Mac Graw Hill book, 1975, chapter 10,
section 10.5 : Classical limit of gravitational equations, p. 345.
Achnowledgements :
This work is supported by the
french CNRS and by the A. Dreyer Brevets et Développement company.
Déposé sous pli cacheté à l'Académie des
Sciences de Paris, 1998.
Commentaire.
Ce travail fait l'objet de discussions
passionnées avec le mathématicien Jean-Marie Souriau, mon voisin
et ami. Nous ne sommes pas parvenus à un accord et chacun est resté
campé sur ses positions.
Souriau :
- A partir de Newton, tu retrouves
Poisson. Mais à partir de Poisson, tu retrouves Newton.
- Certes, mais d'où
sors-tu l'équation de Poisson, de ton chapeau ?
- Eh bien je préfère
décider que l'univers obéit à l'équation de Poisson,
c'est tout.. C'est comme ça.
