5.-DARK MATTER. CONFORMAL GRAVITY

The astrophisicists using the formulas of the General Theory of Relativity have tried to explain the anomalous movement of rotation of the biconvex galaxies. This movement is quite greater than the one than could be expected at sight of the detected visible matter. It is for that reason that introduces the concept of Dark Matter. There are several exotic hypotheses on what it would form the dark matter, particles, stars extinguished, etc. No of those hypotheses has been confirmed by the observation. In fact there are physicists who postulate the nonexistence of such dark matter and the necessity to find a new formulation of the gravitation. In this chapter I show how the quantum expression of previous chapter is compatible with the GTR and in addition allows to predict the rotation speeds of the spiral and biconvex galaxies with no need to resort to the introduction of the concept of dark matter.

In chapter 2 (quantum gravity) we obtained the following expression (2.6) for the gravitational field:

V(m) = - [ (1/2) m c² ρ(r) r² / ρ(R_h) R_h² - (1/2) m c² r² / R_h² ]    (5.1)

If in this expression we replaced the value of the average density of the universe ( ρ(R_h) ) by its value (3 c² / 8 π G R_h²), we obtain the following thing:

V(m) = - [ (4/3) π G m ρ(r) r² - (1/2) m c² r² / R_h² ]

If the second adding of the previous expression we multiplied and we divided by the factor [(4/3) π G] and next we extract it as common factor we obtain:

V(m) = - (4/3) π G [ ρ(r) r² - 3 c² r² / 8 π G R_h²]

And if finally we called ρ_v(R_h) to 3 c² / 16 π G R_h², we obtain:

V(m) = - (4/3) π G r²[ ρ(r) - 2 ρ_v(R_h) ]    (5.2)

In 5.2 it is easy to recognize the simplified expression of the GTR.

A peculiarity of (5.1) is that in the edge of any other geometric distribution of energy generated by a particle system only cohesive by the gravitational field of the system itself, the result can be different from which would be obtained with the law of Newton gravitation. En particular with a distribution, for example, biconvex like which usually they have the spiral galaxies. In this case so that V(m) was constant, it would be enough to consider constant r supposed a constant density, that is to say, we could apply it to the circumference that forms two opposite cones united by their base with radio r and height h each one. This situation enough is approximated to which really it occurs in the observed galaxies. The volume of the biconvex geometric figure would be (2/3) π r² h. Calling k to the relation between r and h, k = r/h. We obtain for g the following expression:

g = - 2 k G M / r²

We observed that is 2k times superior to which the law of Newton predicts. This result would justify the speeds of rotation observed in these galaxies with no need to introduce the concept dark matter.

_{© Jorge Ales, 2002. http://www.livinguniverseweb.com}