The Abraham Zelmanov Journal
The journal for General Relativity, gravitation and cosmology
Non-Linear Cosmological Redshift: The Exact Theory According to General Relativity
A new method of calculation is applied to the frequency of a photon according to the travelled distance. It consists in solving the scalar geodesic equation (equation of energy) of the photon, and manifests gravitation, non-holonomity, and deformation of space as the intrinsic geometric factors affecting the photon's frequency. In the space of Schwarzschild's mass-point metric, the well-known gravitational redshift has been obtained. No frequency shift has been found in the rotating space of Gödel's metric, and in the space of Einstein's metric (a homogeneous distribution of ideal liquid and physical vacuum). The other obtained solutions manifest a cosmological effect: its magnitude increases with distance. The parabolic cosmological blueshift has been found in the space of a sphere of incompressible liquid (Schwarzschild's metric), and in the space of de Sitter's metric, which is a sphere filled with physical vacuum whose density is negative (it is a redshift, if the vacuum density is positive). The exponential cosmological redshift has been found in the expanding space of Friedmann's metric (empty or filled with ideal liquid and physical vacuum). This explains the accelerate expanding Universe. The redshift reaches z = eπ - 1 = 22.14 at the event horizon. These results are obtained in a purely geometric way, without the use of the Doppler effect.
Ref: The Abraham Zelmanov Journal, 2012, volume 5, pages 3-30
Full text: PDF (updated with errata on October 25, 2012)
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The Abraham Zelmanov Journal is an annually issue scientific journal registered with the Royal National Library of Sweden.