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

TL;DR

This paper derives a comprehensive formula for comparing clock rates at different spacetime points, applicable to cosmological and solar system contexts, incorporating various relativistic effects.

Contribution

It introduces a general formula for clock rate comparison that unifies multiple relativistic effects in both cosmological and solar system scenarios.

Findings

Includes Hubble redshift, Doppler, gravitational redshift, Rees-Sciama effects

Applies to perturbed Robertson-Walker metric for cosmology

Useful for precise time measurements in space missions

Abstract

In this paper we deduce a quite general formula which allows the relation of clock rates at two different space time 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 space time 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.