Relativity and Cosmology


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 = E0 exp(-Ωat/c), where Ω is the angular velocity of the space (it meets the Hubble constant H0 = 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(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.

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

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[v1] 21 Feb 2010

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