In the case of general relativity the change in coordinate can give rise to fictitious perturbations, for which we can use gauge invariant variables or we can also choose a specific gauge. My question is how to decide which gauge is suitable for a particular problem?
Pioneering work:
Bardeen J.M. Gauge-invariant cosmological perturbations / Bardeen J.M. //
Phys. Rev.D. –1980. –Vol.22. –P.1882–1905.
Extension to the case of multi-component Universe was firstly implemented in
Kodama H. Cosmological perturbation theory / Kodama H., Sasaki M.
//Prog.Theor.Phys.Suppl. –1984. –Vol.78. –P.1–166.
You chose a gauge to simplify some aspect of your problem, or, in some cases, because most work on a problem uses that gauge and choosing it makes comparing results simpler. Two notable choices (one in each category) are the transverse traceless gauge, which makes gravitational radiation look much like electromagnetism, and the harmonic gauge, the near universal choice for Solar System dynamics work. The first makes the equations simpler, as long as you do not have to worry about the effects of the gravitational waves on orbital dynamics, the second is recommended in the "IAU 2000 resolutions for astrometry, celestial mechanics and metrology in the relativistic framework," which state that "One argument in favor of the harmonic gauge is that tremendous work on General Relativity has been done with the harmonic gauge that was found to be a useful and simplifying gauge for many kinds of applications."
I can say that the mixing of gauges is the cause of a lot of mistakes in work on General Relativity, so you need to be careful to make sure you are always comparing coordinates in the same gauge, or that you know how to convert between them and do so completely and rigorously.
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