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. We discuss the extension of the
International Astronomical Union (IAU) reference system to the exact theory. It
is 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 applications, we consider the FLRW, Kerr and NUT spacetimes,
the van Stockum rotating dust cylinder, spinning cosmic strings and, finally,
we debunk the so-called Balasin-Grumiller (BG) model, and the claims that the
galaxies' rotation curves can be explained through gravitomagnetic effects
without the need for Dark Matter. The BG spacetime is shown to be completely
inappropriate as a galactic model: 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 frame -- the congruence of zero angular momentum
observers, which are being dragged by the singularities.Comment: 29 pages, 10 figures. Slightly improved version, typos corrected,
references added. Supplemental material is provided in the ancillary
Mathematica files "NUTmetrics.nb" and "BGmetric.nb". Version to be submitte