General Formula for Comparison of Clock Rates -- Applications to Cosmos and Solar System

摘要

In this paper we deduce a quite general formula which allows the relation ofclock rates at two different space time points to be discussed. In the case ofa perturbed Robertson-Walker metric, our analysis leads to an equation for thecomparison of clock rates at different cosmic space time points, which includesthe Hubble redshift, the Doppler effect, the gravitational redshift and theRees-Sciama effects. In the case of the solar system, when the 2PN metric issubstituted into the general formula, the comparison of the clock rates on boththe earth and a space station could be made. It might be useful for thediscussion on the precise measurements on future ACES and ASTROD.