Galactic Dynamics in General Relativity: the Role of Gravitomagnetism
  It is a well known fact that, in the absence of Dark Matter, the observation
of the rotation curves of galaxies cannot be explained in terms of Newtonian
gravity. Rotation curves become flat in the outer regions, in contrast to what
is expected according to Keplerian motion. The gravitational field far from the
galactic center is weak enough to use Newtonian gravity, however even in the
weak-field approximation, there are general relativistic effects without a
Newtonian counterpart, such as the gravitomagnetic effects originating from
mass currents. Using the gravitoelectromagnetic approach to the solution of
Einstein equations in the weak-field and slow-motion approximation, we discuss
some simple arguments that suggest the surprising result that gravitomagnetic
effects may have an important role in understanding galactic dynamics. In
addition, treating matter as a fluid of dust, we study the impact of
post-Newtonian effects on the fluid vorticity.
