Coordinate transformations and gauges in the relativistic astronomical reference systems

This paper applies a fully post-Newtonian theory (Damour et al. 1991, 1992, 1993, 1994) to the problem of gauge in relativistic reference systems. Gauge fixing is necessary when the precision of time measurement and application reaches 10−16 or better. We give a general procedure for fixing the gauges of gravitational potentials in both the global and local coordinate systems, and for determining the gauge functions in all the coordinate transformations. We demonstrate that gauge fixing in a gravitational N -body problem can be solved by fixing the gauge of the self-gravitational potential of each body and the gauge function in the coordinate transformation between the global and local coordinate systems. We also show that these gauge functions can be chosen to make all the coordinate systems harmonic or any as required, no matter what gauge is chosen for the self-gravitational potential of each body.