Reference frames in General Relativity and the galactic rotation curves

The physical interpretation of the exact solutions of the Einstein field equations is, in general, a challenging task, part of the difficulties lying in the significance of the coordinate system. I will discuss the extension of the International Astronomical Union (IAU) reference system to the exact theory. It will be seen that such an extension, retaining some of its crucial properties, can be achieved in a special class of spacetimes, admitting non-shearing congruences of observers which, at infinity, have zero vorticity and acceleration. As an application, we debunk the so-called Balasin-Grumiller model, and the recent claims that the galaxies' rotation curves can be explained through gravitomagnetic effects without the need for Dark Matter. It is seen to be completely inappropriate as a galactic model, exemplifying the grave consequences of failing to set up an appropriate reference frame: its dust is actually static with respect to the asymptotic inertial frame, its gravitomagnetic effects arise from unphysical singularities along the axis (a pair of NUT rods, combined with a spinning cosmic string), and the rotation curves obtained are merely down to an invalid choice of reference observers -- the congruence of zero angular momentum observers, which are being dragged by the singularities. Flaws of the same type affect other akin gravitomagnetic "galactic models" in the literature. Other applications considered include the FLRW, Kerr and NUT spacetimes, the van Stockum rotating dust cylinder, and spinning cosmic strings.