I have a generic question on solution procedure. Suppose I consider a system of several point-like bodies interacting only via gravitation. I formulate PDE+ODE system, containing EFE and geodesic motion of the bodies. Since EFE do not define metric uniquely, I need to impose a particular coordinate condition on metric, say synchronous coordinates. I set initial data for positions and velocities of the bodies and solve the system numerically, e.g. with post-Newtonian expansion or as PDE on the grid. As a result I have the metric and geodesic lines. It's clear that the answer is given upto general coordinate transformations. Solving it in another gauge (say harmonic coordinates), I will have a different answer. In the sense that it is the same Lorentz manifold but in different parametrization. In other way, I take a solution in synchronous coordinates, apply arbitrary coordinate transformations to it, and have a general answer. My question is about comparison of this result with experimental measurements. Suppose, the motion of the bodies is measured by observation from a distant point. E.g. by measuring directions with a telescope and distances with a radar, or by other means. Suppose the motion of the bodies is reconstructed from these data and recorded as vector functions xi(t). Suppose also that this reconstruction was not based on GR, space-time has been considered as flat, i.e. the light was assumed to propagate at a constant speed along straight lines. Now I want to superimpose the answer from GR computations and measure a difference from the experiment, due to GR effects. What to do with general coordinate transformations present in the answer? One idea is to reconstruct the light rays used in telescope and radar measurements, now as light-like geodesic lines in the metric I have computed. In this way I can predict, what the observer will see, assuming the bodies move along their GR solutions, and compare this with the measured data. The picture, which the observer will see, will not depend on general coordinate transformations in other points and will not depend on the gauge conditions used in the computations. However, it would be better to do comparison not on the level of raw measurements, but on the level of reconstructed vector functions xi(t). Is there any standard procedure for comparing the results of GR computations of multibody system with the measurements? Some preferred gauge to solve the eqs? Some preferred coordinate system to transform a solution?