f31003 Matter-ghost matter astrophysics. 7 : Confinment of spheroidal galaxies by surounding ghost matter. (p3) .
3) 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. *
