Abstract
In this paper, we deduce a quite general formula which allows the relation of clock rates at two different spacetime points to be discussed. In the case of a perturbed Robertson–Walker metric, our analysis leads to an equation for the comparison of clock rates at different cosmic spacetime points, which includes the Hubble redshift, the Doppler effect, the gravitational redshift and the Rees–Sciama effects. In the case of the solar system, when the 2PN metric is substituted into the general formula, the comparison of the clock rates on both the Earth and a space station could be made. It might be useful for the discussion on the precise measurements on future ACES and ASTROD.
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