## Hubble Redshift due to the Global Non-Holonomity of Space

**Authors:** Dmitri Rabounski

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 = E_{0} exp(-Ωat/c), where Ω is the angular velocity of the
space (it meets the Hubble constant H_{0} = c/a = 2.3x10^{-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(H_{0} r/c)-1 ≈ H_{0} r/c. This solution
explains both the redshift z = H_{0} 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.

**Comments:** 18 pages, Published in "The Abraham Zelmanov Journal", vol.2, pp. 11-28 (2009).

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### Submission history

[v1] 21 Feb 2010

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