Another Notable Attempt To Capture Galaxy Dynamics Without DM From GR

The highly robust Tully-Fischer relation is the strongest evidence for MOND or some other gravitational explanation for dark matter phenomena. 

Multiple attempts to use gravitomagnetism as the cause of this from conventional GR have failed, because this GR effect is too small. But this is not the only possible GR effect that is ignored in the Newtonian approximation so often used in the weak-field, slow-motion regime of astronomy and cosmology. This paper looks at a different neglected GR effect and finds that it is significant and can explain the Tully-Fischer relation without dark matter.

We study the low-energy limit of General Relativity in the presence of stationarity and axial symmetry, coupled to dust. Specifically, we demonstrate that differences between the dynamics of General Relativity and those of Newtonian gravity persist even in the weak-field and slow-motion regime. Notably, these differences are driven by dragging terms that are not necessarily small, as is typically the case in the well-known gravitomagnetic limit. To highlight this distinction, we introduce the concept of strong gravitomagnetism. We provide a pedagogical discussion of how these discrepancies arise and outline a systematic procedure to solve the equations of motion for such systems. Furthermore, we present analytical results for specific cases and also give the general solution for the vacuum case. A particularly notable result is our demonstration of how General Relativity can naturally account for a Tully-Fisher-like relation.

Davide Astesiano, Matteo Luca Ruggiero, "On the low-energy limit of stationary and axisymmetric solutions in General Relativity" arXiv:2412.08598 (December 11, 2024).