  A special form of the isotropic metric in cylindrical coordinates is used to
construct what may be interpreted as the General Relativistic versions of some
wellknown potential-density pairs used in Newtonian gravity to model
three-dimensional distributions of matter in galaxies. The components of the
energy-momentum tensor are calculated for the first two Miyamoto-Nagai
potentials and a particular potential due to Satoh. The three potentials yield
distributions of matter in which all tensions are pressures and all energy
conditions are satisfied for certain ranges of the free parameters. A few
non-planar geodesic orbits are computed for one of the potentials and compared
with the Newtonian case. Rotation is also incorporated to the models and the
effects of the source rotation on the rotation profile are calculated as first
order corrections by using an approximate form of the Kerr metric in isotropic
coordinates.
