I have not read the article in detail (we are not peer review), but you should read it with extreme skepticism. There is a long history of works wrongly claiming that general relativity can explain flat galactic rotation curves where Newtonian gravity cannot. From the conclusion of an earlier article, Costa et al. (2023):
In a growing number of works, based both on linearized theory [127, 131] and exact models [13–15, 129, 130], it has been asserted that gravitomagnetic effects can have a significant impact [13, 15, 127, 131], or even totally account for the galactic flat rotation curves [14, 129, 130]. In the framework of a weak field slow motion approximation, this has been shown to be impossible, and such claims addressed, in [125, 128, 132]. It has however been argued [13, 15, 129, 130] that in the exact theory this is possible, due to nonlinear effects not captured in linearized theory (and not manifest “locally” [13, 129, 130]), basing such claims on the BG model, or variants of it. Our exact analysis shows such claims to be also unfounded, the conclusion extending to the akin models in [15, 129, 130] (where the same misguided choice of reference
observers is made). The exact approach proves also useful in determining the nature of the sources: we were able to easily identify a pair of oppositely charged rods of gravitomagnetic monopoles as the source of the gravitomagnetic field $\vec H$; in the far field region, however, this field is, to leading (i.e., dipole) order, indistinguishable from that of a spinning source.
In my view, these works are all fundamentally misguided because galaxies are deep in the Newtonian limit, having potential depths of order $10^{-6}c^2$ and velocities of order $10^{-3}c$. We know that general relativity reduces to Newtonian gravity in this limit. There is no reason for general relativity to make different predictions from Newtonian gravity in this context.
As an aside, I enjoyed the following passage from Costa et al. (2023):
As it replaced Newtonian mechanics as the state of the art theory of gravitation, general relativity brought along equations allowing for a more precise description of gravitational phenomena, at the cost, however, of a mathematical complexity effectively preventing their full use in actual astrophysical scenarios. Since then, two fields have evolved parallelly in a largely separate way: one, finding and mathematically characterizing exact solutions of the Einstein field equations [1–3], which in most cases do not correspond to realistic physical systems (or whose physical significance is not totally clear); and the other, approximate methods such as post-Newtonian theory, for actual astrophysics.
It is a useful point to make here because laypeople and students tend to focus on the exact solutions to a much greater degree than researchers do. The focus of astrophysics research is to understand the systems that actually arise in the Universe, using approximation methods and numerical calculations. This is largely disjoint from the effort of coming up with exact solutions to the Einstein field equations, which are almost never of astrophysical relevance.
