  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
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. These are the homogeneous solutions (HS) for the
gravitomagnetic field, i.e. solutions with vanishing matter currents. We show
how recent results about galactic dynamics are connected to this class of
solutions.
