The missing mass problem (p7)
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Post technical comment.
Section 3: In General Relativity, a link is established between the field equation and Poisson's equation by performing a series expansion (11) of the metric around a Lorentzian metric, this background metric, like the perturbation term, being time-independent. The same procedure is repeated, this time with two populations of densities ρ and ρ*. These issues are treated with greater precision in the article:
J.P. Petit and P. Midy: Matter ghost matter astrophysics. 1: The geometrical framework. The matter era and Newtonian approximation.
[On this site: Geometrical Physics A, 4, 1998, section 4.]
Section 4: Eddington's solution emerges from techniques borrowed from kinetic theory of gases (Vlasov equation). Although the detailed calculations are not provided, the method involving two "joint" stationary solutions is the same.
Section 5: When Pierre Midy performed these first computer simulations, he addressed the boundary conditions problem in a classical manner. This issue will be revisited in the paper:
J.P. Petit, P. Midy and F. Landsheat: Matter ghost matter astrophysics. 5: Results of numerical 2d simulations. VLS. About a possible schema for galaxies' formation.
[On this site: Geometrical Physics A, 8, 1998, figure 15.]
Here he used a "slow" program, without velocity truncations or Monte Carlo-style sampling. Therefore, all n² interactions were calculated laboriously, but the result is reliable. In practice, the program stopped whenever an interaction between two point masses caused a trajectory curvature too pronounced. The time step was then reduced accordingly, until the issue was resolved. Then the calculation resumed at normal pace. Figure 8 shows the first "emulsions" obtained with these two populations repelling each other.
Section 7: The problem of invisibility of "twin structures" was then raised. In this article, we took it as an axiom. In classical General Relativity, material objects are assumed to be visible. But in the field equation, no particle appears—this is a macroscopic description of the medium. The astronomer can then claim: "The hypothesis is valid. The proof is that I can observe these objects optically." At this stage, we were content to say, in a way, that the invisibility of twin structures could also be taken as an assumption, neither more nor less valid, adding: "If these structures exist, the 'proof' that this hypothesis works is precisely that we don't see them!"
However, subsequently, a better geometric description of the problem (a two-sheeted covering of a manifold) transformed this "physical hypothesis" into a "geometrical hypothesis." Since photons are assumed to travel along null geodesics of each sheet, and since the sheets are disjoint, photons cannot pass from one sheet to the other. See paper:
J.P. Petit and P. Midy: Matter ghost matter astrophysics. 1: The geometrical framework. The matter era and Newtonian approximation.
[On this site: Geometrical Physics A, 4, 1998, Section 3.]
Critique of this work.
According to this first model, the universe is supposed to be closed. Spatially speaking, it would then be a 3-sphere S³. The drawings in figures 12 and 13 suggest that matter could, at great distances, alternately form clumps and a "lacy network," with transition zones. Immediate objection from an observer:
- Under these conditions, observation at very large distances should reveal such a structure. If galaxies form, in a vast region, a lacy network (Very Large Structure), this tendency should reverse at high redshifts, where galaxies should instead form large clusters—something not observed.
Retained objection.