Towards a full general relativistic approach to galaxies

Abstract We analyse the dynamics of a single disk galaxy from general relativistic viewpoint. investigate dark matter (DM) effects in terms known family stationary axially-symmetric solutions Einstein equations coupled to rotating dust. These are generated by non-Newtonian features such and ascribed essential role frame dragging. Indeed, models, off-diagonal elements metric are, general, same order magnitude diagonal ones. generalize results Balasin Grumiller (BG) physical case differentially In particular, we find that for differential rotation amount energy density required account flat curves galaxies is reduced with respect BG rigid case. This stresses discrepancy between Newtonian gravity relativity (GR), even at low velocities densities.