Step-by-step derivation of cosmological redshift in stationary space
         Consider homogeneous universe in a form of Einstein's 3-sphere of radius R_s (and therefore of volume 2π²R_s³) [1] filled with dust of density ρ (with a particle of dust representing a galaxy). Let energy conservation holds. Let photons move through this dust interacting with it only gravitationally via dynamical friction [2] [3] [4] [5] [6] losing gradually their energy to this dust. Qualitatively, to the observer at some distance from the light source this energy transfer from photons to dust manifests itself as a change in wavelength, simulating the tired light effect, first observed by Hubble and then worked on by Zwicky. The relativistic interpretation of this result allows the derivation of cosmological redshift, including discovery that Hubble's "constant" depends on the distance between the light emitting place in deep space and the observer [7]. Let's do some math to find out what happens quantitatively. It turns out that the Newtonian math suffices for this purpose.
         Let photons of energy E_o are radiated out from an arbitrarily placed center of coordinate system called "point zero" in the described above homogeneous space. When the radiated out photons leave an empty hole at point zero in otherwise homogeneous space the space becomes inhomogeneous. The Newtonian "gravitational force" shows up and starts pushing the dust away from the empty hole at point zero like an air bubble in a tank of water "pushes away" with its "gravitational force" the surrounding water. The space around point zero gains gravitational energy that given enough time, gets eventually converted into kinetic energy of movement of dust particles. This effect refers to the future though that we don't need to be concerned with since we describe only the present, namely the gravitational energies, The future state of universe can have no influence on the present and its energies.
         Let the gravitational energy of dust contained in the volume of a ball of dust of radius r be E_d(r). At distance r from point zero the gravitational force pushing the dust particles away is equal according to Newton's math, using Einstein's relativistic relation between mass and energy E=mc²

Fparticle = ( G / c2 )[ Eo - Ed(r) ] mparticle / r2

(1)

where m_particle is the mass of a particle of dust universe (typically a galaxy).
         Integrating the mass over all dust particles in a spherical shell of dust of radius r and thickness dr we get mass of this shell of dust at distance r from point zero as

mshell = 4 π ρ r2 dr

(2)

and merging (1) with (2) the total force that is the source of gravitational energy of dust of this shell becomes

Fshell(r) = ( 4πGρ / c2 ) [ Eo - Ed(r) ] dr

(3)

and since F_shell(r) = - dE_shell(r) / dr we have also

- dEshell(r) / dr = ( 4πGρ / c2 ) [ Eo - Ed(r) ] dr

(4)

         Integrating both sides of (4) over all spherical shells between point zero and r to get total gravitational energy of dust, and differentiating both sides with respect to r to get rid of the integral on the right side of this equation, we get

- d2Ed(r) / dr2 = ( 4πGρ / c2 ) [ Eo - Ed(r) ]

(5)

and substitutig E_d(r) = E_o - E_ph(r) where E_ph(r) is energy of photons at distance r from their source and introducing square of radius of stationary universe R_s² = c²/4πGρ we get the final differential equation controlling the phenomenon as

d2Eph(r) / dr2 = Eph(r) / Rs2

(6)

         Solving equation (6) with initial conditions E_ph|_r=0 = E_o and dE_ph/dr|_r=0 = - E_o / R_s meaning selecting a solution that makes physical sense, we get

Eph(r) / Eo = exp( - r / Rs )

(7)

         Since we know that in general relativity there is nothing else but the time dilation and the curvature of space as the media controlling gravitation we now switch from the Newtonian math to the relativistic interpretation of the above result, which is the time running slower at a distance from (any) observer according to relation

dτ/dt = exp( - r / Rs )

(8)

where τ is proper time at point in deep space and t is coordinate time at observer. The effect might be called Hubble time dilation in honor of its discoverer, and as distinguished from the gravitational time dilation discovered by Einstein.
         After differentiating the above equation at r = 0 we get a relation between the Hubble time dilation in deep space (d²τ/dtdr) and the square root of curvature of space (1 / R_s ) as

d2τ/dtdr + 1 / Rs = 0

(9)

that suggests the existence of a tensor named here tentatively H_μν or Hubble tensor, modifying the right side of Einstein's field equation such that H_μν + R_μν = 0 indicating that the spacetime is intrinsically flat as proposed by Narlikar and Arp [8] and required by the law of conservation of energy (allowing also to remove the cosmological constant Λ from Einstein's field equation - a note for mathematicians rather than grannies who might even not know what Einstein's field equation is nor they need to know to understand this derivation).
         It follows from equation (7) or (8) equivalently, that the redshift, produced by Hubble time dilation, is equal to

Z = exp( r / Rs ) - 1

(10)

simulating the expansion of space, with the Hubble "constant" of this apparent "expansion" at r = 0

Ho = c / Rs

(11)

and after expanding the Hubble "constant", H(t), into Taylor series around t = 0 and neglecting the higher order terms, the "acceleration" of this apparent "expansion" equals

dH / dt = - Ho2 / 2

(12)

which agrees within one standard deviation with 1998 observations by the Supernova Cosmology Project team [9]. The additional gain from all the above is that, "Einstein's biggest blunder of his life" [10], the infamous "cosmological constant" [11], a.k.a. "dark energy", falls out from Einstein's field equation.

Some numerical results
         Assuming H_o = 70 km/s/Mpc, as it is presently observed, and the same lower limit of dynamical friction value for space probes (since in the above derivation there was no dependence on the velocity of photons and so it refered to any velocity, also that of cosmic probes as Pioneers 10 and 11) the deceleration of cosmic probes comes out as 7×10^-10 m/s², the volume of space of our universe is 1.6×10¹² Mpc³ making room for about 10¹² galaxies. The average density of universe is 6×10^-27 kg/m³, and its total mass is 3×10⁵³ kg making the mass of average galaxy equal 3×10⁴¹ kg or 10¹¹ solar masses. The apparent "acceleration" of space dH/dt = - H_o²/2 as predicted in 1985 by Einsteinian gravitation and observed in 1998 [9]. The numerical results have been never allowed to be published though in any scientific journal (not even in a popular science magazine as "Scientific American") so the astronomers for whom it might be an important news couldn't learn that the hypothesis of creation of the universe might be wrong. That this hypothesis not only contradicts Einstein's general relativity (replaced by Wheeler's cerationist version of general relativity based on an axiom of creation) but contradicts also quite unnecessarily the principle of conservation of energy since as it has been shown above, this principle delivers quite reasonable results, not only qualitatively but also quantitatively.

Conclusions
         The analysis of cosmological redshift can be carried out in just dozen simple steps using general relativity and the law of conservation of energy. The observed cosmological redshift can be attributed to the time dilation coupled to the curvature of space in the universe which remains stationary as predicted by Einstein in 1917. In addition to reproducing the measured properties of cosmological redshift, the approach outlined in this paper allows direct calculation of the important parameters of our universe such as the average density of space and the acceleration of its apparent expansion. While the formula for cosmological redshift, equation (10), can be derived directly from equation (7) obtained using Newtonian approximation, it is equation (8), which expresses the essential transition from Newtonian approach in which space and time are distinct, to a general relativistic spacetime.
         The additional gain from the above derivation is realization that redshift of quasars being proportional to the local curvature of space integrated over the whole distance between the quasar and the observer, as equation (9) suggests, doesn't need to reflect anymore the Hubble distance/redshift relation since the local curvatures of space don't need to be the same as the average, and the local curvature might be even many orders of magnitude greater than the agerage that reflects the average cosmological redshift.

Acknowledgments
         The author expresses his gratitude to Dr Halton Arp, Dr Helmut A. Abt, Dr Chris E. Adamson, Prof. John Baez, Prof. Tadeusz Balaban, Prof. Michal Chodorowski, Dr Tom Cohoe, Prof. Marek Demianski, Dr Marijke Van Gans, Prof. Roy J. Glauber, Dr Mike Guillen, Prof. Alan Guth, Dr Martin J. Hardcastle, Dr Franz Haymann, Dr Chris Hillman, Dr Marek Kalinowski, Dr Alan P. Lightman, Prof. Krzysztof Meissner, Prof. Jozef M. Namyslowski, Dr Bjarne G. Nielsen, Prof. Bohdan Paczynski, Janina Pisera, BS, Dr Ramon Prasad, Dr Frank E. Reed, Dr Anrzej Szechter, Prof. Henryk Szymczak, Jerzy Tarasiuk, MS, Dr Michael S. Turner, Dr Slava Turyshev, Prof. Clifford M. Will, Prof. Ned Wright, and anonumous referees from various scientific journals, for the time they have spent discussing with the author the subject of the paper and related issues. The most thanks goes to Prof. Michal Chodorowski of CAMK-PAN (Copernican Astronomical Center of Polish Accademy of Science), without whose friendly critique the ideas expressed in this paper might have never developed to a legible state.

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