We use the gravitoelectromagnetic approach to the solutions of Einstein’s equations in the weak-field and slow-motion approximation to investigate the impact of general relativity on galactic dynamics. In particular, we focus on a particular class of the solutions for the gravitomagnetic field, and show that, contrary to what is expected, they may introduce non-negligible corrections to the Newtonian velocity profile. The origin and the interpretation of these corrections are discussed and explicit applications to some galactic models are provided. These are the homogeneous solutions for the gravitomagnetic field, i.e., solutions with vanishing matter currents.

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• General relativity