In the study of galactic rotation curves, the Newtonian potential
[math:0]∇Φ(r)=G∫3ρ(r')(r-r')/〖∣r-r'∣〗^3 d3r'[/math:0],
derived from the visible mass distribution—stars, gas, and bulge—explains the inner regions of galaxies, where orbital velocities rise and may form a partial plateau. However, in the outer regions, the visible mass alone cannot account for the observed flat rotation curves, motivating the introduction of dark matter.
The gravitomagnetic approach suggests that mass currents in a rotating fluid disk could generate a gravitomagnetic field sufficient to reproduce rotation curves without dark matter. Nevertheless, the scientific consensus highlights significant limitations: gravitomagnetic effects in realistic galactic conditions are far too weak, and the model relies on idealized assumptions not representative of actual galaxies. While conceptually interesting, this approach cannot replace dark matter as an explanation for observed rotation curves.
In this context, it is important to note that the gravitomagnetic treatment used in such analyses is based on the linear, weak-field approximation of General Relativity. This formalism assumes a nearly static mass distribution, low velocities, and weak spacetime curvature, conditions that are appropriate for planetary systems but not for extended, rotating galactic disks. A real galaxy is a large-scale, differentially rotating structure with substantial total angular momentum, where the gravitational field cannot be fully approximated as static. The common conclusion that frame-dragging effects are “negligible” follows from the limitations of this perturbative framework rather than from a complete relativistic treatment, which has never been solved exactly for a rotating galactic disk.
In this case, the amount of dark matter does not depend on the chosen cosmological model. However, the fact remains that the Newtonian potential does not consider frame-dragging. The results obtained through gravitomagnetic models, though based on simplified assumptions, suggest that non-perturbative and fully relativistic solutions should be explored before definitively confirming the necessity of dark matter in explaining galactic rotation curves.
