[cygx]

That's the wrong paragraph to cite. The parts relevant to Cooperstock's (and similar) work is this:

> Although filled with controversy, the studies of the galactic rotation via general relativity [16,17,18] reach the same basic conclusion of the present paper. Namely, the dragging effect of a gravitomagnetic component (time-space component of the metric) explains the flat rotation curve at large distances, without the recourse to dark matter. The main problem with the general relativistic models is the very limited number of exact solutions of the Einstein field equations [...]

> The calculated motion in the general relativistic approach corresponds to the free-fall of test particles in the assumed metric, without consistently considering the effect of the large galactic mass density distribution on the metric. Actually, this is the same objection that can be made to the classical approach [...]

> Fluid models, as used in the present paper, consider the mean motion of particles in the Vlasov-like collective gravitational field. The gravitoelectromagnetic weak field approximation to general relativity, used in the present paper, leads to a tractable self-consistent solution of the galactic rotation problem.

Citation [16] in particular is a reference to https://arxiv.org/abs/astro-ph/0610370