A topological model which relates displacement and rotation leads to diverging geodesics.
The model relates an orientation O=(x/R, y/R, z/R) to a point P=(x,y,z) and also relates a rotation vector V=(dx/R,dy/R,dz/R) to a displacement D=(dx,dy,dz).The axes of the rotation operation is perpendicular to the orientation O and the rotation vector V. R is in the range of 14 billion light years.
This topological model replaces the Euclidian part of the Minkowski space and generates a finite, homogenous, and isotropic model for the geometry of the universe.
The coupling properties of the three axis rotation operations cause the divergence of the geodetic lines.
The question is now, has the topologic divergence of geodesics the same quality as the divergence, we get for geodesics by space dilatation in time?
Is the expansion of a volume transported along geodesics with the speed of light equivalent to a volume expansion due to space dilatation?
Dear Konle,
The topic is deep, and one should be expert in both differential geometry and the relativity (Physics). No doubt, according to your assumptions the two volume expansions are homotopically equivalent in the sense of qualitative geometry. That is the universe the same everywhere, and there is no preferred direction.
Regards
Dear Issam Kaddoura,
Thank you for your answer, which shows that you also see the disruptive potential of a geometrical explanation of astronomic observations without the hypothesis of an expanding universe.
Regards