  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 nonshearing congruences
of observers which, at infinity, have zero vorticity and acceleration. As
applications, we consider the Friedmann-Lema\^itre-Robertson-Walker (FLRW),
Kerr and Newman-Unti-Tamburino (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.
