On GR dragging and effective galactic dark matter

In recent years, there has been an increase in the number of papers regarding general-relativistic explanations for the dark matter phenomena in disc galaxies. The main focus of this scientific discussion is whether a previously unexamined relativistic dragging vortex could support flat rotation curves, with various research groups taking different stances on its feasibility. In this paper, we discuss the different points of view by placing the various arguments within a general theoretical context. We explicitly state the conceptual assumptions, and indicate what we believe to be the correct interpretation for the physical quantities of interest. We show how the dragging conjecture fails under certain hypotheses, and discuss the flaws of the most common dragging models: the linearised gravitomagnetic description and the one of Balasin&Grumiller. On the other hand, we illustrate how to avoid failure scenarios for the conjecture, emphasizing the features for a physically reasonable disc galaxy dragging model. In particular, we stress that the non-linearities of the Einstein Equations must play an essential role in generating what we define as ``pseudo-solitonic" solutions -- the only non-trivial physically viable solutions for the class of models considered. Furthermore, the dragging vortex is proven to show important contributions to the gravitational lensing in these models, thus providing an ulterior measure of its relevance. Moreover, by qualitatively exploring these pseudo-solitonic solutions, we find that a dragging speed of just a few kilometers per second would be enough to explain a non-negligible fraction of the galactic dark matter. Finally, we propose and analyse the feasibility of three independent measurements which could be carried out to detect the presence of dragging vortices in disc galaxies.