Towards a full general relativistic approach to galaxies
  We analyze the dynamics of a single spiral galaxy from a general relativistic
viewpoint. We employ the known family of stationary axially-symmetric solutions
to Einstein gravity coupled with dust in order to model the halo external to
the bulge. In particular, we generalize the known results of Balasin and
Grumiller, relaxing the condition of co-rotation, thus including non
co-rotating dust. This further highlights the discrepancy between Newtonian
theory of gravity and general relativity at low velocities and energy
densities. We investigate the role of dragging in simulating dark matter
effects. In particular, we show that non co-rotance further reduce the amount
of energy density required to explain the rotation curves for spiral galaxies.
