The Abraham Zelmanov Journal
The journal for General Relativity, gravitation and cosmology
Hubble Redshift due to the Global Non-Holonomity of Space
In General Relativity, the change in energy of a freely moving photon is given by the scalar equation of the isotropic geodesic equations, which manifests the work produced on a photon being moved along a path. I solved the equation in terms of physical observables (Zelmanov A.L., Soviet Physics Doklady, 1956, vol.1, 227-230) and in the large scale approximation, i.e. with gravitation and deformation neglected, while supposing the isotropic space to be globally non-holonomic (the time lines are non-orthogonal to the spatial section, a condition manifested by the rotation of the space). The solution is E = E0 exp (-Ω2 at/c), where Ω is the angular velocity of the space (it meets the Hubble constant H0 = c/a = 2.3×10-18 sec-1), a is the radius of the Universe, t = r/c is the time of the photon's travel. Thus, a photon loses energy with distance due to the work against the field of the space non-holonomity. According to the solution, the redshift should be z = exp (H0 r/c) - 1 ≈ H0 r/c. This solution explains both the redshift z = H0 r/c observed at small distances and the non-linearity of the empirical Hubble law due to the exponent (at large r). The ultimate redshift in a non-expanding universe, according to the theory, should be z = exp (π) - 1 = 22.14.
Ref: The Abraham Zelmanov Journal, 2009, volume 2, pages 11-28
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The Abraham Zelmanov Journal is an annually issue scientific journal registered with the Royal National Library of Sweden.