A Stationary Universe and the Basics of Relativity Theory
  A stationary line element of general relativity seems to be compatible to essential cosmological facts (though only as far as one can expect solving the nonlinear Einstein equations neglecting local cosmic evolution and all spatial inhomogeneities as well).   There is a preferred spatially Euclidean cosmic reference frame where the extra-galactic speed of light is constant c* = c, and the galaxies are statistically at rest. Spectral rods and atomic clocks, however, do not indicate this cosmic space and this cosmic time.   The solutions put up here for discussion are suitable to avoid serious difficulties in physics such as a beginning of the universe as a whole or the necessity of continuous creation of matter or an empty universe with a cosmological constant but no matter at all.   Especially from the stationary line element, it follows a negative cosmic gravitational pressure of one third the critical energy density. In addition, there is an average baryonic radiation density equivalent to a black body radiation of approximately 3 K.   The resulting increase of the time rate of natural clocks in comparison with cosmic time is a simple explanation for the redshift of starlight. This redshift turns out to be independent of time, thus indicating a stationary universe. 
Peter Ostermann