7
In the paper: J.P. Petit and P. Midy: Matter-ghost matter astrophysics. 7: Confinement of spheroidal galaxies by surrounding ghost matter. [On this site: Geometrical Physics A, 10, 1998.] we re-examined the question of Gauss's theorem, the screening effect, and the Poisson equation. We show that when considering a uniform distribution of matter, possibly unlimited, the Poisson equation ceases to exist simply because it becomes impossible to define a gravitational potential within such a medium. Indeed, Newton's law and the Poisson equation derive from the formalism of General Relativity only when a zero-order stationary solution can be found, which can then be perturbed. However, such a solution cannot exist when the universe is non-empty. In General Relativity, one then obtains the Friedmann solutions, which are fundamentally non-stationary.
The field inside a cavity carved within a uniform distribution is then obtained simply. A distribution of ghost matter (which behaves like a set of negative masses relative to our own matter) containing a spherical hole is equivalent to the superposition of the field produced by a uniform distribution (zero) plus that produced by a sphere filled with ordinary matter of constant density:
The field generated by the solid sphere increases with distance from the center, then decreases. Therefore, a spherical cavity is "confining." The same applies to an ellipsoidal cavity. If the boundary is abrupt, the confining field would be equivalent to that produced by a flattened ellipsoid filled with ordinary matter at uniform density.
But the boundary cannot be abrupt. The hole in the ghost matter is blurred, and this variation in density is accompanied by a pressure gradient. It is precisely this pressure gradient that would cause the ghost matter to fill the cavity if the galaxy were to disappear. In the paper [Geometrical Physics A, 2], section 2, calculations were performed using more sophisticated distributions of matter and ghost matter. The analytical method of calculation was also indicated. It should be noted that the resulting rotation curve is very similar to those observed. See: J.P. Petit and P. Midy: Repulsive dark matter. [On this site: Geometrical Physics A, 3, 1998. Figure 4.]
Thus, we have an alternative theory to dark matter. Personally, I believe a purely theoretical galaxy model could emerge from this, involving two coupled Vlasov equations plus the Poisson equation. See, in this context: J.P. Petit: Twin Universe Cosmology: Astronomy and Space Science 226: 273–307, 1995 and [On this site: Geometrical Physics A, 2, section 4.]
DY = 4πG (ρ − ρ*)
where (ρ* > 0) refers to the ghost matter density. The minus sign arises from the structure of the field equation.
Negative lensing effect.
The "irrefutable" proof of dark matter presence in galaxies, according to astrophysicists, relies on the strong gravitational lensing effects observed. Galaxies produce multiple images, as do galaxy clusters. As usual, when something truly belongs to the cosmic menagerie, after one or two cases, dozens, then hundreds of observations pour in. Indeed, images are accumulating.
The strong effects observed do not match the estimated masses of galaxies or galaxy clusters. There is a significant "missing mass" effect.
But an inhomogeneous environment of ghost matter would produce identical results.
In our sheet of the universe, ghost matter produces a negative gravitational lensing effect.
In the model, and within our sheet of spacetime, conglomerates of ghost matter (or "twin matter"), present in the adjacent portion F* of our sheet F, create a negative "induced curvature" within it. This is what we attempted to illustrate didactically earlier, using the model of a "blunted negacone," whose central part is saddle-shaped (a surface with constant negative curvature). If we consider the figure above, we have suggested the presence of a conglomerate of twin matter, or ghost matter, by a dashed line. This is not optically observable from our spacetime (since, geometrically, photons cannot pass from one sheet to another). However, as suggested in the figure, these conglomerates produce a negative gravitational lensing effect (negative lensing effect).
Photon trajectories within sheet F are schematically represented. But these photons cannot interact with the atoms of ghost matter that constitute the conglomerate present in the adjacent portion of sheet F (whose boundary is shown by dashed lines). Thus, the photons "pass freely through the conglomerate."
As already mentioned, it is the density gradient that produces the effect. A homogeneous distribution of matter or ghost matter would not deflect light rays.
Everything behaves, for ordinary matter, as if matter attracts photons, and for ghost matter, as if it repels photons. A cavity carved within ghost matter would therefore have a focusing effect, as discussed below:
The indication is only schematic, but rest assured: no one knows how to calculate the path of a light ray through an inhomogeneous distribution of matter (or ghost matter).
To this focusing effect would be added the effect due to the presence of the galaxy. Neglecting the surrounding ghost matter environment would make it impossible to account for the phenomenon using only the galaxy's (or cluster's) mass.
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