## 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).

**Download:** **PDF**

### Submission history

[v1] 21 Feb 2010

**Unique-IP document downloads:** 73 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*